Zibin Nan

Mei Mei

Ryma Laifa

Vincent Ngu

Fan Chen

Bolin Shen

Zhou Shen

Ao Li

Nao Wu

Tianyi Zhang

Xiaoqian Li

Zhenhang Wu

Ye Tao

Keywords: Dynamic filtration, Bibliography analysis, Hydrodynamics, Local and instantaneous pressure, Core velocity coefficient, Periodic and random pressure fluctuation, Resonance frequency, Signal reconstruction, CFD. IV Filtration dynamique, analyse bibliographique, hydrodynamique, pression locale et instantané e, coefficient de vitesse du noyau, fluctuation pé riodique Acknowledgement, I Abstract, II Ré sumé, IV

This PhD work was carried out in TBI where I have spent three and half years, and it provided me a new insight into the world. Before that, I was not an ambitious person and I didn't even dare to imagine studying abroad. From 2018, a new chapter of my life began at INSA. I can feel that I have become more different, not only from an academic point of view, but also my daily life, which makes me stronger. At this special occasion, I would like to thank those who have been with me during this memorable time.

I would like to thank the financial support from China

Laminar regime

•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.1 Validation of numerical simulation ••••••••••••••••••••••••••••••••••••••••••••• 3.1.2 Local velocity •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.3 Local pressure ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.3.1 Mixing rate ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.3.2 Viscosity ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.3.3 Blades surface area•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.3.4 Number of blades ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.3.5 Impeller/membrane gap ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.4 Local shear stress •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.4.1 Mixing rate ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.4.2 Viscosity ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.4.3 Blades surface area•••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.4.4 Number of blades ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.1.4.5 Impeller/membrane gap ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.2 Turbulent regime •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.2.1 Validation of numerical simulation ••••••••••••••••••••••••••••••••••••••••••••• 3.2.2 Local velocity •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.2.3 Local pressure ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 3.2.4 Local shear stress •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• Chapter V: Conclusions and Perspectives •••••••••••••••••••••••••••••••••••••••••••••••••••• 1 Scientific context ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 2 Answer to our initial scientific questions ••••••••••••••••••••••••••••••••••••••••• 3 Our highlights and perspectives •••••••••••••••••••••••••••••••••••••••••••••••••••• References •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• Annexes ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• XIII

List of figures

List of tables

Chapter I: Introduction 1 Background

Membrane bioreactors (MBR) are now largely applied in biotechnology (e.g., food biotechnology, environmental, industry, health, etc.) [START_REF] Smith | Germination of Macrophomina phaseoli sclerotia as effected by Pinus lambertiana root exudate[END_REF][START_REF] Aimar | Sé parations par membrane dans l'industrie alimentaire, F3250[END_REF][START_REF] Daufin | Recent and Emerging Applications of Membrane Processes in the Food and Dairy Industry[END_REF]. Then, dynamic filtration (DF) stands as a highly relevant alternative to classical filtration techniques such as dead-end and crossflow filtrations. Indeed it can be considered a more efficient filtration technology [START_REF] Jaffrin | Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems[END_REF]. In particular, the so-called Rotating and Vibrating Filtration (RVF) module is a promising dynamic filtration module. It has been investigated intensively in our laboratory for bioprocess engineering applications for several years. Their performances are strongly influenced by the complex interactions between gas and liquid hydrodynamics as well as the microorganism activities. The specificity of microbial bio-reactions in relation to irreducible couplings between heat and mass transfers and fluid mechanics, led to complex and dynamic systems [START_REF] Smith | Germination of Macrophomina phaseoli sclerotia as effected by Pinus lambertiana root exudate[END_REF].

The hydrodynamics in the DF module is related to the dimensionless Reynolds number, and their correlation with the Darcy number and power number can be used to estimate energy consumption [START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF]. Semi-local approaches include the additional pressure and local shear rate. In rotating systems, the mixing pressure caused by the rotating disk or impeller is related to the core velocity coefficient, but this theory has not been reported in vibrating systems. The empirical correlations to estimate local shear rate was proposed according to the operating conditions and specific cell geometries [START_REF] Bentzen | Analytical and numerical modelling of Newtonian and non-Newtonian liquid in a rotational cross-flow MBR[END_REF]. For local approaches, the experimental measurement allows the visualization of velocity, pressure and shear fields, then compared to computational fluid dynamics (CFD) technology [START_REF] Bentzen | Analytical and numerical modelling of Newtonian and non-Newtonian liquid in a rotational cross-flow MBR[END_REF][START_REF] Xie | Local hydrodynamic investigation by PIV and CFD within a Dynamic filtration unit under laminar flow[END_REF][START_REF] Chaudhuri | Permeate flux decrease due to concentration polarization in a closed roto-dynamic reverse osmosis filtration system[END_REF].

Some researchers have found the empirical relations between steady-state permeate flux and local shear rate [START_REF] Akoum | An hydrodynamic investigation of microfiltration and ultrafiltration in a vibrating membrane module[END_REF][START_REF] Jaffrin | A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems[END_REF][START_REF] Zsirai | The impact of mechanical shear on membrane flux and energy demand[END_REF]. The average shear rate is commonly used as a primary indicator for evaluating filtration systems. In spite of the fact that an increase in shear implies a higher permeate flux, it is also essential to account for the unit energy consumption, irreversible fouling and fluid sensitivity. The theory of critical and threshold flux was promoted in order to limit the increase of foulant, with the relevant TMP usually being a time-mean value [START_REF] Beier | Critical flux determination by flux-stepping[END_REF][START_REF] Luo | Threshold flux for shear-enhanced nanofiltration: Experimental observation in dairy wastewater treatment[END_REF]. In a rotating disk module, the disk with vans yields higher permeate flux than smooth discs at the same shear rate [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF], which is explained by both shear and pressure magnitudes and their fluctuations. In microfiltration, transmembrane pressure (TMP) can be maintained at very low values (~100 mbar), and then high-pressure fluctuation (same order of magnitude as TMP) could contribute to surface cake layer and internal reversible fouling destabilization.

This PhD thesis focuses on the investigation of local hydrodynamics in a defined DF module in relation to its applications in bioprocess. A dynamic filtration device, called RVF is specifically scrutinized. This DF device consists of several filtration chambers in series. Each filtration chamber includes two crown membranes and a specially designed impeller with three flat blades, rotating continuously (up to 50 Hz) to generate high stress (shear and pressure) as well as a hydrodynamic perturbation in the narrow membrane-blade gap. This module enables increased permeability by reducing the volume of the filtration loop, uncoupling the feeding flow rate and the local shear rate at the membrane surface, and operating at low transmembrane pressure (TMP). This PhD work is devoted to exploring RVF technology in order to get insight into its complex hydrodynamics at global and local scales, to understand and explain its performances in membrane bio-reactor (MBR), and to define the "best" operating conditions and device configurations for bioprocess intensification under realistic energetic constraints.

From scientific progress to scientific questions

In conventional membrane filtration, TMP is the primary driving force, determined by the fluid type and membrane pore size. An increase in TMP allows higher permeate flux, while it also accelerates the accumulation of matter at the membrane surface and then the formation of the cake layer (hydraulic resistance). Cross-flow filtration (CFF) aims to take benefit of the shear forces generated by tangential flow to reduce cake build-up. The retention-permeation lock remains a knowledge bottleneck in many applications. In CFF, considering the coupling between TMP, high local shear stress and feeding velocity, the threshold and critical fluxes have been defined in order to model the cake layer formation.

In dynamic filtration, the mechanical movement of one element (ex., impeller for RVF module) has been introduced to increase the shear forces in order to intensify filtration.

Confined filtration device, generation of complex hydrodynamics into filtration chamber and the uncoupling between local shear and feeding flowrate are factors of complexity for process engineers. Then, it is still crucial to deeply investigate the local hydrodynamics (flow regime, velocity, pressure and shear stress fields) inside the filtration cell and to better understand the mechanisms that take place close to the membrane during the filtration operation. The flow variables should be associated with the operating conditions and the rheological behavior of fluids.

Since 2000, RVF module has been scrutinized in order to identify qualitative and quantitative performance (brewing and wine making) or critical operating conditions (cell lysis). Characterizing and understanding its complex hydrodynamics is challenging and can be explored through global, semi-local and local approaches, as well as CFD simulation. Fig.

I.2 illustrates the existing results and the targeted objectives within this PhD work. Several scientific questions are addressed: (1) Global investigations

The empirical correlations are introduced to estimate power consumption (mixing, pumping and thermal power) in laminar and turbulent regimes. Based on the net power input, the power consumption curve was established. The friction curve derived from effective pumping power (pressure drop) was presented as a function of mixing and feeding Reynolds number. In addition, the increase in temperature (two filtration cells) due to the thermal dissipation can be expressed by the mixing rates.

(2) Local pressure

The local pressure at the membrane surface was measured with the specially designed and instrumented porous substrate, including mixing and fluctuating components. The core velocity coefficient is defined to quantify mixing pressure versus feeding flowrate, mixing rate, viscosity and impeller shape. The pressure fluctuations are analysed and modelled to reveal their magnitude and frequency at different positions along the membrane surface.

(3) CFD simulation For laminar regime, the simulations are performed on a geometry that consists of 1/3 of the filtration cell (Imp 1), taking benefit of the asymmetry of the system. Different operating conditions and cell geometries are explored. The velocity profile depicts the variation of fluid flow due to the rotation of the impeller. This contributes to explaining the time variations of pressure at the membrane surface.

For turbulent regime, the validation of numerical simulation was performed based on the velocity distribution of the rotating full disk system. To investigate the local pressure and shear stress at the membrane surface, the Shear Stress Transport (SST) k- model was selected to solve the flow close to the wall.

Finally, the overall conclusions of this manuscript are presented in chapter Ⅴ, which highlights that the pressure and shear stress fluctuations are the potential parameters to enhance filtration. Particularly, the identification of resonance phenomena, their theoretical meaning and applications need further research.

Chapter II: Bibliography

This chapter provides an extensive review about industrial and laboratory dynamic filtration modules: scientific production, configurations and performances. types according to movement and shape (filtration cell, membrane, impeller, disk…). But it appears that it remains a great challenge to complete the knowledge on the flow of fluid inside DF modules because of their complex geometries. Global, semi-local and local investigations of hydrodynamics have been detailed. They not only make it possible to estimate performances but also help to calculate energy consumption according to operating conditions. In this review, the main characteristics of DF devices and existing applications are presented. These empirical results are already very useful for the selection of DF devices for a dedicated application. However, a better understanding of local temporal variations in pressure and shear stress is still necessary to refine the choice of a device and the operating conditions. The overarching aims propose to report the main criteria that will help engineers to select DF modules or to identify the scientific and/ or technological bottlenecks about hydrodynamics or applications.

Highlights:

(1) Bibliography overview of dynamic filtration (application, research items, trends and stakeholders);

(2) Classification and specification of laboratory and industrial Dynamic Filtration Modules;

(3) Characterization of fluid flow within dynamic filtration modules;

(4) Main criteria to select dynamic filtration modules (critical conditions, performances, power).

Introduction

Membrane separation technology has become widely used in the bioprocess and food processing industry (dairy, juice, wine, water) [START_REF] Daufin | Recent and Emerging Applications of Membrane Processes in the Food and Dairy Industry[END_REF][START_REF] Cheryan | Ultrafiltration and Microfiltration Handbook[END_REF]. Among three-phase reactors, membrane bioreactors (MBR) appeared in the 70s and were primarily applied in the biotechnology field: white biotechnology, pharmaceutical and food industries [START_REF] Smith | Germination of Macrophomina phaseoli sclerotia as effected by Pinus lambertiana root exudate[END_REF][START_REF] Aimar | Sé parations par membrane dans l'industrie alimentaire, F3250[END_REF][START_REF] Daufin | Recent and Emerging Applications of Membrane Processes in the Food and Dairy Industry[END_REF]. However, membrane processes are yet to identify as an industrial alternative by users. The choice of membrane process is a multi-criteria and fundamental approach including diversities of (i) mass transfer processes (from electro-dialysis up to microfiltration), (ii) the geometry of module (plane, filter-press, tubular, spiral wound, hollow fiber), (iii) the nature of membrane (mean pore diameter and associated distribution/chemical nature: organic, mineral, metal, composite) and (iv) the operating mode (dead-end, cross-flow or dynamic filtration) and technology dedicated to fouling limitation (co-current, back-filtration, back-shock, backflush,…). The overarching aim is to improve qualitative and quantitative performances of separation processes, in other terms, their intensification and efficiency in biological, chemical, and food processes. Retention could be described as mechanical and/or physicochemical retention, but the mechanisms of retention result from a complex balance between the local hydrodynamic conditions, the product, the nature and the membrane cut-off.

Conventional dead-end filtration and cross-flow filtration

In conventional dead-end filtration (DEF) (Fig. II.1), the feeding flux is perpendicular to the permeation, and the fouling will accumulate at the membrane surface. Transmembrane pressure (TMP) increases with the formation of the cake layer, resulting in lower filtration efficiency. Cross-flow filtration (CFF), also known as tangential flow filtration, was typically designed to reduce the impact of fouling by applying a tangential feeding flow passing over the membrane and removing some of the deposits from the surface. Increasing feeding flowrate is one of the conventional ways to enhance performances in CFF. However, energy consumption rapidly increases with pumping power, proportional to the cube of flowrate in a turbulent flow regime [START_REF] Bachus | 4 -The affinity laws[END_REF].

A large number of hydrodynamic techniques have been proposed to limit or manage fouling by modifying dead-end and cross-flow filtration modules to improve performance.

The main technologies are introduced below:

• The periodic shutdown of transmembrane pressure [START_REF] Daufin | Equipment Fouling in the Dairy Application: Problem and Pretreatment[END_REF][START_REF] Wakeman | Experiments using electricity to prevent fouling in membrane filtration[END_REF];

• Co-current operation (homogeneity of TMP along with the diaphragm) [START_REF] Fillaudeau | A Practical Method to Predict Steady-State Flux and Fouling in the Crossflow Microfiltration of Rough Beer with 1.40 μm Tubular Ceramic Membranes[END_REF];

• Reversal of the permeation flow (backflush) [START_REF] Rodgers | Effect of transmembrane pressure pulsing on concentration polarization[END_REF];

• The back-shock process (periodic inversion of the permeate flow, effective backflush time of less than 0.1 s) [START_REF] Wenten | Mechanisms and control of fouling in crossflow microfiltration[END_REF];

• Cleaning by generating non-stationarity in the tangential flow: generation of Dean or

Taylor vortices [START_REF] Mallubhotla | Flux enhancement during Dean vortex microfiltration. 8. Further diagnostics[END_REF][START_REF] Mallubhotla | Flux enhancement during dean vortex tubular membrane nanofiltration. 10. Design, construction, and system characterization[END_REF][START_REF] Mallubhotla | Flux enhancement during Dean vortex tubular membrane nanofiltration: 13. Effects of concentration and solute type[END_REF], installation of static turbulence promoters such as baffled channel or stamped membrane [START_REF] Horie | Intensification of hollow fiber membrane cross-flow filtration by the combination of helical baffle and oscillatory flow[END_REF][START_REF] Akagi | Improvement of separation performance by fluid motion in the membrane module with a helical baffle[END_REF], pulsed flow [START_REF] Gupta | Permeate flux enhancement by pressure and flow pulsations in microfiltration with mineral membranes[END_REF], generation of two-phase flow (gas-liquid, liquid-solid) [START_REF] Mercier | Influence of the flow regime on the efficiency of a gas-liquid two-phase medium filtration[END_REF], ultrasound [START_REF] Borea | Wastewater treatment by membrane ultrafiltration enhanced with ultrasound: Effect of membrane flux and ultrasonic frequency[END_REF].

Although the impressive results to control fouling with these methods, the performance limitation of previous configurations and operating modes led engineers and researchers to propose an alternative named Dynamic filtration (DF). approximately up to 3×10 5 s -1 without large feeding flow rates [START_REF] Jaffrin | A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems[END_REF]. Taking advantage of this technology, DF performs its outstanding behaviors in permeability and productivity, which leads to an effective and economical process, and those major expected advantages are [START_REF] Jaffrin | Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems[END_REF][START_REF] Ding | Dynamic Filtration with Rotating Disks, and Rotating or Vibrating Membranes[END_REF]:

• Enhanced local shear rates (magnitude and time fluctuation) at the membrane surface;

• Application of low TMP;

• Reduction of fouling magnitude, which generates higher permeate flux and requires lower filtration area;

• Reduction of loop dead volume;

• Significant energy-saving (Power/ Permeate flux or Energy/ Permeate volume).

Many studies [START_REF] Chai | Application of rotational vibration in a submerged hollow fibre membrane system for bioseparation of high concentration yeast suspensions[END_REF][START_REF] Villafana-Lopez | Shear-enhanced membrane filtration of model and real microalgae extracts for lipids recovery in biorefinery context[END_REF][START_REF] Hapońska | Application of ABS membranes in dynamic filtration for Chlorella sorokiniana dewatering[END_REF] have shown an improvement in efficiency and fouling control with DF. However, additional motion modules will also generate a series of defects. The drawbacks of DF modules are mainly attributed to their mechanical and hydrodynamics complexities:

• Technical limitations:

o The complex mechanical configuration of devices may generate higher capital and operational investment, especially when scaling up;

o The increase in the filtration area for scaling-up can be difficult.

• Hydrodynamic limitations:

o Characterization of internal flow patterns is difficult (global performances and space-time resolution of velocity and pressure fields);

o Local high shear stress may generate energy dissipation and subsequent local thermal increase.

For process engineers, the balance between advantages and drawbacks should be established for industrial applications through rational criteria, generally derived from labscale investigations. These strategies include estimating local and global parameters, theoretical models and computational fluid dynamics (CFD) simulation, practical filtration performances and energy consumption. More and more new devices and investigations are emerging to deal with these issues.

In 1994, Mikulasek [START_REF] Mikulasek | Methods to reduce concentration polarization and fouling in membrane filtration[END_REF] reviewed the typical methods to reduce concentration polarization and membrane fouling thanks to chemical, physical and hydrodynamic methods.

The dynamic effects of rotating and oscillating to promote instabilities of flow were detailed.

The anti-fouling mechanisms in rotating filtration were summarized by [START_REF] Lee | Rotating Membrane Filtration and Rotating Reverse Osmosis[END_REF] [START_REF] Lee | Rotating Membrane Filtration and Rotating Reverse Osmosis[END_REF], and they also described the recent efforts to apply rotating filtration to reverse osmosis (RO). [START_REF] Jaffrin | Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems[END_REF]Jaffrin ( , 2012) ) [START_REF] Jaffrin | Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems[END_REF][START_REF] Jaffrin | Hydrodynamic Techniques to Enhance Membrane Filtration[END_REF][START_REF] Jaffrin | Dynamic filtration with rotating disks, and rotating and vibrating membranes: an update[END_REF] and [START_REF] Ding | Benefits of High Shear Rate Dynamic Nanofiltration and Reverse Osmosis: A Review[END_REF][START_REF] Ding | Dynamic Filtration with Rotating Disks, and Rotating or Vibrating Membranes[END_REF] [START_REF] Ding | Dynamic Filtration with Rotating Disks, and Rotating or Vibrating Membranes[END_REF][START_REF] Ding | Benefits of High Shear Rate Dynamic Nanofiltration and Reverse Osmosis: A Review[END_REF] summarized the industrial dynamic filtration modules with rotating and oscillating. The hydrodynamics inside the filtration cell was specialized concerning the shear rate and radial pressure. The empirical equation 𝐽 = 𝑎𝛾 𝑏 linked the permeate flux (J) and mean shear rate (γ) with two constants, a and b. Outputs from a review of available data from studies of rotating and vibrating membrane filters, as well as vibrating hollow fiber membranes, provide a direct correlation between performances (flux) and local hydrodynamics (shear rate) [START_REF] Zsirai | The impact of mechanical shear on membrane flux and energy demand[END_REF]. However, confusion remains between the mean and maximum shear rates. Meanwhile, there is still no clear classification of dynamic filtration devices.

In this review, the bibliometric analysis was conducted to confirm the research trends about DF modules over the years and summarized its application field and filtration type.

Due to the diversity of DF devices, the industrial or lab-scale modules were classified into 15 types according to the mechanical movement form and shape. The use of the available information related to internal hydrodynamics of DF allows the prediction of local performance and power consumption. They were combined with practical application requirements to guide the selection of appropriate industrial equipment.

Scientific production related to dynamic filtration

The database interrogation was carried out to review scientific publications and to gain insight into research hotspots. The scientific database Web of Science (WoS) Core Collection (Thomson-Reuter) was used to identify relevant articles concerning "dynamic filtration" and with the following methodology.

• Database: Web of Science Core Collection

• Profiles: (dynamic filtration) AND (membrane) AND (high shear OR shear enhanced OR rota* OR vibra* OR oscilla*)

• Field: Topic (Title, Abstract, Keywords)

• Period: 1975 to 2020 (Updated: February 30, 2020).

Citespace [START_REF] Chen | CiteSpace II: Detecting and visualizing emerging trends and transient patterns in scientific literature[END_REF] is one of the most commonly used tools in the visual exploration of scientific literature. It was adopted as a research tool for quantitative analysis, while qualitative analysis was associated with its application fields and filtration types to identify the investigated scientific problematics. The working database was established by filtering the related publications about dynamic filtration from WoS.

Quantitative analysis

Out

Identification of research items

Generally, the keywords are associated with the core content of the publications; the higher frequency of occurrence in specific fields reflects the research hotspots. • Applications include yeast cells, dairy effluent, microalgae, alpha-lactalbumin, etc.;

• Hydrodynamics and performances associated with flux behavior, turbulent flow, shear stress, concentration polarization and mass transfer;

• Simulations (dynamic simulation).

Table II In all processes (MF, UF, NF and RO), most membrane materials were organics (94 out of 119). In contrast, inorganic membranes (34) such as ceramic membranes and metal oxide membranes, were mainly used in MF processes.

Water treatment

In water treatment (60 articles), researchers investigated DF to treat industrial and municipal wastewater and rarely drinking water. Experimental fluids were mostly synthetic model fluids and suspensions, whereas others used wastewater from the treatment plants (paper mill [START_REF] Bhattacharjee | Ultrafiltration of black liquor using rotating disk membrane module[END_REF][START_REF] Bhattacharjee | Performance study during ultrafiltration of Kraft black liquor using rotating disk membrane module[END_REF], detergent [START_REF] Luo | Flux decline control in nanofiltration of detergent wastewater by a shear-enhanced filtration system[END_REF] and food industries [START_REF] Wisniewski | Dynamic vibratory membrane processing for use in water recovery from soluble coffee product manufacturing wastewater[END_REF][START_REF] Kerté Sz | Investigation of module vibration in ultrafiltration[END_REF], sludge from anaerobic membrane reactor [START_REF] Mertens | Membrane development for improved performance of a magnetically induced vibration system for anaerobic sludge filtration[END_REF][START_REF] Ruigómez | A novel rotating HF membrane to control fouling on anaerobic membrane bioreactors treating wastewater[END_REF]. Due to the complex composition of industrial wastewater, simple solutions, emulsions and solid-liquid suspensions were preferred as test fluids. Simple solutions were used to mitigate toxic pollutants (halogenated organic compounds [START_REF] Gao | A photo-catalysis and rotating nano-CaCO3 dynamic membrane system with Fe-ZnIn2S4 efficiently removes halogenated compounds in water[END_REF][START_REF] Gao | Photocatalysis and rotating dynamic membrane hybrid system with Fe-ZnIn2S4 efficiently removes 2,4,6-Tribromophenol in water: effect of dynamic membrane[END_REF], 2-MIB and geosmin [START_REF] Choi | Removal of taste and odor model compounds (2-MIB and geosmin) with the NF membrane[END_REF], polyvinyl alcohol [START_REF] Sarkar | Recovery of Polyvinyl Alcohol from Desizing Wastewater Using a Novel High-Shear Ultrafiltration Module[END_REF], heavy metal ions [START_REF] Zakrzewska-Trznadel | Reducing fouling and boundary-layer by application of helical flow in ultrafiltration module employed for radioactive wastes processing[END_REF][START_REF] Cojocaru | Removal of cobalt ions from aqueous solutions by polymer assisted ultrafiltration using experimental design approach Part 2: Optimization of hydrodynamic conditions for a crossflow ultrafiltration module with rotating part[END_REF] and sodium dodecylbenzene sulfonate [START_REF] Tu | Studies on treatment of sodium dodecyl benzene sulfonate solution by high shear ultrafiltration system[END_REF][START_REF] Moulai-Mostefa | Treatment of Aqueous Ionic Surfactant Solutions by Dynamic Ultrafiltration[END_REF]), artificial seawater (NaCl, KCl, MgCl2, CaCl2, and MgSO4) [START_REF] Su | Concentration polarization and permeate flux variation in a vibration enhanced reverse osmosis membrane module[END_REF][START_REF] Hwang | Fine particle removal from seawater by using cross-flow and rotating-disk dynamic filtration[END_REF], viscous solutions (polyethylene glycol-6000 [START_REF] Sarkar | Simulation of continuous stirred ultrafiltration process: an approach based on surface renewal theory[END_REF][START_REF] Sarkar | Design and performance characterization of a new shear enhanced module with inbuilt cleaning arrangement[END_REF][START_REF] Sarkar | Modeling and analytical simulation of rotating disk ultrafiltration module[END_REF], carboxymethyl cellulose [START_REF] Ri | Experimental Study on Revolving Crossflow Microfiltration of Highly Viscous Liquids[END_REF], ethanol [START_REF] Marke | Investigation of the velocity factor in a rotational dynamic microfiltration system[END_REF]), soluble salts (CaSO4 [START_REF] Lee | Control of scale formation in reverse osmosis by membrane rotation[END_REF], NaCl [START_REF] Su | Permeate flux increase by colloidal fouling control in a vibration enhanced reverse osmosis membrane desalination system[END_REF]), model wastewater in dairy process [START_REF] Frappart | Effect of vibration frequency and membrane shear rate on nanofiltration of diluted milk, using a vibratory dynamic filtration system[END_REF][START_REF] Zhang | Investigation of membrane fouling mechanisms using blocking models in the case of shear-enhanced ultrafiltration[END_REF][START_REF] Frappart | Treatment of dairy process waters modelled by diluted milk using dynamic nanofiltration with a rotating disk module[END_REF][START_REF] Akoum | Treatment of dairy process waters using a vibrating filtration system and NF and RO membranes[END_REF][START_REF] Frappart | Reverse osmosis of diluted skim milk: Comparison of results obtained from vibratory and rotating disk modules[END_REF][START_REF] Ladeg | CFD Simulation of the Distribution of Pressure and Shear Rate on the Surface of Rotating Membrane Equipped with Vanes for the Ultrafiltration of Dairy Effluent[END_REF][START_REF] Zhang | Membrane cleaning assisted by high shear stress for restoring ultrafiltration membranes fouled by dairy wastewater[END_REF] and space mission [START_REF] Lee | Experimental verification of a model for rotating reverse osmosis[END_REF]. For emulsion, oil/water mixtures with surfactants were considered [START_REF] Ebrahimi | Dynamic crossflow filtration of oilfield produced water by rotating ceramic filter discs[END_REF][START_REF] Li | Recovery of linseed oil dispersed within an oil-in-water emulsion using hydrophilic membrane by rotating disk filtration system[END_REF][START_REF] Moulai-Mostefa | Comparison between rotating disk and vibratory membranes in the ultrafiltration of oil-in-water emulsions[END_REF][START_REF] Moulai-Mostefa | Separation of water from metal working emulsions by ultrafiltration using vibratory membranes[END_REF][START_REF] Murase | Dynamic microfiltration of dilute O/W emulsion in rotating cylindrical membrane filter[END_REF][START_REF] Murase | Microfiltration-Rate Increase of O/W Emulsion by Use of Rotating Membrane Filter with Additional Suspended Solids[END_REF][START_REF] Ullah | Membrane oscillation and slot (pore) blocking in oil-water separation[END_REF]. Solid-liquid suspensions with dispersed particles as model effluent included bentonite [START_REF] Li | Fouling control of submerged hollow fibre membranes by vibrations[END_REF], polymethyl methacrylate (PMMA) [START_REF] Murase | Dynamic microfiltration of dilute slurries with a rotating ceramic membrane[END_REF][START_REF] Hwang | Analysis on the nonuniformity of cake formation in rotating-disk dynamic microfiltration[END_REF][START_REF] Murase | Microfiltration Characteristics of High-Viscosity Slurries in Rotating Dynamic Filter[END_REF], styrene butadiene rubber (SBR) latex [START_REF] Takata | Structure of shear-enhanced flow on membrane surface with horizontal vibration and its effect on filtration performance[END_REF], polystyrene latex [START_REF] Aim | Influence of particle size and size distribution in granular bed filtration and dynamic microfiltration[END_REF], CaCO3 [START_REF] Ding | Investigation of performances of a multishaft disk (MSD) system with overlapping ceramic membranes in microfiltration of mineral suspensions[END_REF][START_REF] Tu | Microfiltration of mineral suspensions using a MSD module with rotating ceramic and polymeric membranes[END_REF][START_REF] Bouzerar | Local permeate flux-shear-pressure relationships in a rotating disk microfiltration module: implications for global performance[END_REF][START_REF] He | Experimental study of a dynamic filtration system with overlapping ceramic membranes and non-permeating disks rotating at independent speeds[END_REF][START_REF] Loginov | Dead-End Dynamic Filtration of Highly Concentrated CaCO3 Suspensions in the Presence of a Dispersant[END_REF], SiO2 [START_REF] Hadzismajlovic | Flux enhancement in laminar crossflow microfiltration using a collapsible-tube pulsation generator[END_REF][START_REF] Park | A study on dynamic separation of silica slurry using a rotating membrane filter 1. Experiments and filtrate fluxes[END_REF][START_REF] Wu | Structural design of a rotating disk dynamic microfilter in improving filtration performance for fine particle removal[END_REF][START_REF] Choi | A study on dynamic separation of silica slurry using a rotating membrane filter: 2. Modelling of cake formation[END_REF],

Al2O3 [START_REF] Ben Aim | Recent Development of Membrane Processes for Water and Waste Water Treatment[END_REF], ZnO, Fe(OH)3 [START_REF] Bouzerar | Concentration of ferric hydroxide suspensions in saline medium by dynamic cross-flow filtration[END_REF][START_REF] Bouzerar | Concentration of mineral suspensions and industrial effluents using a rotating disk dynamic filtration module[END_REF] and hollow glass microspheres [START_REF] Ji | Dynamic crossflow filtration with a rotating tubular membrane: Using centripetal force to decrease fouling by buoyant particles[END_REF].

The within the filtration cell and membrane surface. Only one article used PIV (particle image velocimetry) [START_REF] Li | Fouling control of submerged hollow fibre membranes by vibrations[END_REF] to examine the local hydrodynamics and compared it with the filtration performances.

Food processing

In food processing (19 articles), DF was applied in liquid food production (dairy, brewing and extract juice). 12 articles (63%) were related to the concentrations of milk protein from casein micelle [START_REF] Jaffrin | A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems[END_REF][START_REF] Ding | Milk protein concentration by ultrafiltration with rotating disk modules[END_REF][START_REF] Al-Akoum | Casein micelles separation from skimmed milk using a VSEP dynamic filtration module[END_REF][START_REF] Akoum | Concentration of total milk proteins by high shear ultrafiltration in a vibrating membrane module[END_REF][START_REF] Espina | Separation of casein micelles from whey proteins by high shear microfiltration of skim milk using rotating ceramic membranes and organic membranes in a rotating disk module[END_REF][START_REF] Espina | Separation of casein from whey proteins by dynamic filtration[END_REF][START_REF] Meyer | High concentration of skim milk proteins by ultrafiltration: Characterisation of a dynamic membrane system with a rotating membrane in comparison with a spiral wound membrane[END_REF][START_REF] Schä Fer | Concentration of skim milk by means of dynamic filtration using overlapping rotating ceramic membrane disks[END_REF] and the separation of α-lactalbumin and βlactoglobulin [START_REF] Espina | Comparison of rotating ceramic membranes and polymeric membranes in fractionation of milk proteins by microfiltration[END_REF][START_REF] Espina | Extraction and Separation of α-lactalbumin and β-Lactoglobulin from Skim Milk by Microfiltration and Ultrafiltration at High Shear Rates: A Feasibility Study[END_REF][START_REF] Espina | Fractionation of pasteurized skim milk proteins by dynamic filtration[END_REF][START_REF] Espina | Comparison of permeate flux and whey protein transmission during successive microfiltration and ultrafiltration of UHT and pasteurized milks[END_REF]. The fluids commonly came from commercial UHT skim milk and low heat powder milk. Defatted soy milk was also used to recover trypsin inhibitor and soy milk protein [START_REF] Akoum | Recovery of trypsin inhibitor and soy milk protein concentration by dynamic filtration[END_REF]. Microfiltration in brewing (rough and clarified beer) [START_REF] Fillaudeau | Investigation of rotating and vibrating filtration for clarification of rough beer[END_REF] and winemaking (crude simulated and filtered wine) [START_REF] Rayess | Wine clarification with Rotating and Vibrating Filtration (RVF): Investigation of the impact of membrane material, wine composition and operating conditions[END_REF] were investigated with DF.

Retention/permeation performances were reported in terms of product quality and costeffectiveness. Juices of sugar beets [START_REF] Zhu | Dead-End Dynamic Ultrafiltration of Juice Expressed from Electroporated Sugar Beets[END_REF], Alfalfa [START_REF] Zhang | Leaf protein concentration of alfalfa juice by membrane technology[END_REF][START_REF] Zhang | Application of UF-RDM (Ultafiltration Rotating Disk Membrane) module for separation and concentration of leaf protein from alfalfa juice: Optimization of operation conditions[END_REF] and Jerusalem Artichoke [START_REF] Zhu | Clarification of Jerusalem Artichoke Extract Using Ultra-filtration: Effect of Membrane Pore Size and Operation Conditions[END_REF] contain a large number of nutritional compounds, such as sugar, leaf protein and inulin, which have been separated, purified and/or concentrated by ultrafiltration with DF.

All works are associated with technical locks about product concentration and quality.

Performances versus volume reduction ratio and modeling of hydraulic resistance stand as major scientific questions. To increase filtration efficiency, optimizations of operating conditions and modifications of DF geometrical configurations are handsome strategies. The filtration performances do not only focus on the permeate flux but also on permeate quality (purification and separation rate). These analyses mainly rely on the permeate/retentate turbidity, coloration or conductivity, and the concentration or °Brix of target products. It should be mentioned that membrane selectivity (membrane materials, structure and cut-off) is a critical issue for some particular compositions.

Bioprocess engineering

For bioprocess engineering, 42 papers were carried out associated with DF modules due to their wider coverage (cell productions: prokaryote, eukaryote, microalgae, animal cells; biomolecule productions: recombinant proteins, antibody, exopolysaccharides, etc.). Most of tested fluids are biological suspensions (fermentation broth) containing microalgae [START_REF] Hapońska | Application of ABS membranes in dynamic filtration for Chlorella sorokiniana dewatering[END_REF][START_REF] Frappart | Influence of hydrodynamics in tangential and dynamic ultrafiltration systems for microalgae separation[END_REF][START_REF] Rí Os | Antifouling microfiltration strategies to harvest microalgae for biofuel[END_REF][START_REF] Rios | Dynamic Microfiltration in Microalgae Harvesting for Biodiesel Production[END_REF][START_REF] Nurra | Vibrating membrane filtration as improved technology for microalgae dewatering[END_REF][START_REF] Hwang | Filtration flux-shear stress-cake mass relationships in microalgae rotating-disk dynamic microfiltration[END_REF][START_REF] Nurra | Biorefinery concept in a microalgae pilot plant. Culturing, dynamic filtration and steam explosion fractionation[END_REF][START_REF] Kim | Dynamic microfiltration with a perforated disk for effective harvesting of microalgae[END_REF][START_REF] Hwang | Disk structure on the performance of a rotating-disk dynamic filter: A case study on microalgae microfiltration[END_REF][START_REF] Slater | Shear-enhanced microfiltration of microalgae in a vibrating membrane module[END_REF][START_REF] Kim | Harvesting of Scenedesmus obliquus using dynamic filtration with a perforated disk[END_REF][START_REF] Lorente | Microalgae fractionation using steam explosion, dynamic and tangential cross-flow membrane filtration[END_REF][START_REF] Jung | Dynamic filtration with a perforated disk for dewatering of Tetraselmis suecica[END_REF][START_REF] Ye | Microalgal dewatering using a polyamide thin film composite forward osmosis membrane and fouling mitigation[END_REF][START_REF] Lorente | Steam Explosion and Vibrating Membrane Filtration to Improve the Processing Cost of Microalgae Cell Disruption and Fractionation[END_REF][START_REF] Hapońska | Pilot scale dewatering of Chlorella sorokiniana and Dunaliella tertiolecta by sedimentation followed by dynamic filtration[END_REF][START_REF] Zhang | Algal fouling control in a hollow fiber module during ultrafiltration by angular vibrations[END_REF], yeast [START_REF] Akoum | An hydrodynamic investigation of microfiltration and ultrafiltration in a vibrating membrane module[END_REF][START_REF] Jaffrin | A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems[END_REF][START_REF] Beier | Critical flux determination by flux-stepping[END_REF][START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF][START_REF] Mateus | Steroid recovery by a rotary membrane system[END_REF][START_REF] Lee | Microfiltration of recombinant yeast cells using a rotating disk dynamic filtration system[END_REF][START_REF] Adach | Mechanism of microfiltration on the rotating track membrane[END_REF][START_REF] Beier | Dynamic microfiltration with a vibrating hollow fiber membrane module: Filtration of yeast suspensions[END_REF][START_REF] Gomaa | Intensification of membrane microfiltration using oscillatory motion[END_REF][START_REF] Kola | Application of low frequency transverse vibration on fouling limitation in submerged hollow fibre membranes[END_REF][START_REF] Gomaa | Energetic consideration and flux characteristics of roughed-surface membrane in presence of reversing shear[END_REF][START_REF] Giorges | Flow Dynamic Effect in Cake Shape and Resistance in Membrane Filtration[END_REF], bacteria [START_REF] Brou | Microfiltration and ultrafiltration of polysaccharides produced by fermentation using a rotating disk dynamic filtration system[END_REF][START_REF] Harscoat | Influence of fermentation conditions and microfiltration processes on membrane fouling during recovery of glucuronane polysaccharides from fermentation broths[END_REF][START_REF] Mellal | Separation of oligoglucuronans of low degrees of polymerization by using a high shear rotating disk filtration module[END_REF] and animal cell [START_REF] Vogel | Controlled shear filtration: A novel technique for animal cell separation[END_REF][START_REF] Cole | Dynamic membrane filtration in cell and protein production[END_REF][START_REF] Castilho | CFD-aided design of a dynamic filter for mammalian cell separation[END_REF].

Other dispersions were produced by commercial or fermented biological products, including bovine serum albumin (BSA) [START_REF] Sarkar | Simulation of continuous stirred rotating disk-membrane module: An approach based on surface renewal theory[END_REF][START_REF] Sarkar | Performance characterization and CFD analysis of a novel shear enhanced membrane module in ultrafiltration of Bovine Serum Albumin (BSA)[END_REF][START_REF] Naskar | Design, performance characterization and hydrodynamic modeling of intermeshed spinning basket membrane (ISBM) module[END_REF], polygalacturonic acid 140, α-lactose monohydrate [START_REF] Gursch | Continuous Processing of Active Pharmaceutical Ingredients Suspensions via Dynamic Cross-Flow Filtration[END_REF], ibuprofen [START_REF] Gursch | Continuous Processing of Active Pharmaceutical Ingredients Suspensions via Dynamic Cross-Flow Filtration[END_REF], recombinant human growth hormone [START_REF] Maa | Investigation on fouling mechanisms for recombinant human growth hormone sterile filtration[END_REF] and monoclonal antibody [START_REF] Fernandez-Cerezo | An ultra scale-down method to investigate monoclonal antibody processing during tangential flow filtration using ultrafiltration membranes[END_REF]. Within the research, 17 publications (40%) focused on the concentration and separation (biomass) of microalgae and constituted a new hotspot over the last decade.

Saccharomyces cerevisiae (baker's yeast) was commonly used in DF for its widespread applications in the biotechnological industry. Model suspensions were formed by the mixture of yeast with ultrapure osmosed water [START_REF] Jaffrin | A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems[END_REF][START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF] and buffer [START_REF] Beier | Critical flux determination by flux-stepping[END_REF][START_REF] Beier | Dynamic microfiltration with a vibrating hollow fiber membrane module: Filtration of yeast suspensions[END_REF] or directly extracted from fermentation broth [START_REF] Mateus | Steroid recovery by a rotary membrane system[END_REF][START_REF] Lee | Microfiltration of recombinant yeast cells using a rotating disk dynamic filtration system[END_REF].

In bioprocess engineering, flux decline induced by the fouling layer was discussed.

Methods to improve critical flux are generally consistent with water treatment and food processing, but cell viability needs to be considered under high shear stress [START_REF] Espina | Comparison of rotating ceramic membranes and polymeric membranes in fractionation of milk proteins by microfiltration[END_REF][START_REF] Frenander | Cell harvesting by cross-flow microfiltration using a shear-enhanced module[END_REF].

Several publications are dedicated to the formation of cell cake layers, which exhibit high specific filtration resistance due to their high compressibility. The empirical correlations between cake mass and operating conditions (TMP and wall shear stress) were reported and interpreted [START_REF] Hwang | Filtration flux-shear stress-cake mass relationships in microalgae rotating-disk dynamic microfiltration[END_REF]. CFD has been combined with experimental data to investigate local operating conditions with biological fouling within DF devices [START_REF] Hwang | Filtration flux-shear stress-cake mass relationships in microalgae rotating-disk dynamic microfiltration[END_REF][START_REF] Kim | Dynamic microfiltration with a perforated disk for effective harvesting of microalgae[END_REF][START_REF] Hwang | Disk structure on the performance of a rotating-disk dynamic filter: A case study on microalgae microfiltration[END_REF][START_REF] Castilho | CFD-aided design of a dynamic filter for mammalian cell separation[END_REF][START_REF] Sarkar | Performance characterization and CFD analysis of a novel shear enhanced membrane module in ultrafiltration of Bovine Serum Albumin (BSA)[END_REF][START_REF] Naskar | Design, performance characterization and hydrodynamic modeling of intermeshed spinning basket membrane (ISBM) module[END_REF][START_REF] Gursch | Continuous Processing of Active Pharmaceutical Ingredients Suspensions via Dynamic Cross-Flow Filtration[END_REF].

3 Specifications of Laboratory and Industrial Dynamic Filtration Modules

Classification of dynamic filtration modules

In recent decades, many efforts and a great number of studies have been achieved to develop novel DF modules at the lab or pilot-plant scales. From scientific and technical literature, 55 modules with 85 configurations were designed and produced by 29 industries and 21 laboratories. Reviewing the existing DF modules, they can be classified by the type of movement, including rotation, oscillation and vibration. These movements can occur to the membrane, the mechanical device (disk, impeller and cylinder) or the whole filtration module.

Oscillating and Vibrating movements are easily confused, and there is no clear definition to distinguish them. In this paper, oscillation and vibration are defined as mechanical movement, which can be perpendicular and parallel to the direction of permeate flux, respectively. Based on the shapes of the moving part and the membrane, the 55 identified modules could be classified into 15 types considering the movement form and part (Table II.5). Table II

Rotating systems

Rotating systems can be split into three categories: rotating membrane modules (21 modules), rotating mechanical devices (14 modules) and the association of rotating membrane and mechanical devices (2 modules).

Rotating membrane modules

Rotating disk membrane

The disk membranes are one of the most commonly used in rotating membrane filters.

From the literature, 10 modules (corresponding to 16 configurations, Table II.6) were designed and produced by local companies. These modules consist of membranes mounted onto the porous support driven by one or more central shafts. Such supports can be one or more rotary disks, allow a flexible configuration, and lead to easy scale-up with larger filtration area capacity. Cell design, geometrical configurations and operating conditions are the most critical parameters to optimize module efficiency.

In high shear rotary membrane system (HSR-MS) [START_REF] Bendick | Effect of Backpulsing and Continuous Surface Cleaning on High-Shear Rotary Membrane System Permeate Flux Performance for Naval Shipboard Wastewaters[END_REF][START_REF] Reed | Treatment of Oily Wastes Using High-Shear Rotary Ultrafiltration[END_REF][START_REF] Viadero | Study of series resistances in high-shear rotary ultrafiltration[END_REF][START_REF] Jr | Rotation and Concentration Effects in High-Shear Ultrafiltration[END_REF][START_REF] Viadero | Two-phase limiting flux in high-shear rotary ultrafiltration of oil-in-water emulsions[END_REF], flat round membrane disk packs are attached to the highly porous nylon meshes. A solid disk pack is placed between two meshes and sets on a hollow rotating shaft for permeation channels. By the central shaft rotation, the maximum liquid velocities close to the membrane can reach up to 18 m/s, compared to 4.5 m/s for conventional cross-flow UF systems [START_REF] Viadero | Two-phase limiting flux in high-shear rotary ultrafiltration of oil-in-water emulsions[END_REF]. Henrik et al. [START_REF] Marke | Investigation of the velocity factor in a rotational dynamic microfiltration system[END_REF] tried to add a metal insert in the rotary membrane chamber. It generates disturbances in the bulk flow, which increase the filtration pressure.

Industrial applications of DF modules require technical improvements in order to increase the filtration area. A compact rotating disc filter (CRD) is a lab-scale module with 3 disk membranes compressed on the same hollow rotating shaft. In wastewater treatment, it has an available effective filtration area of 0.1 m 2 [START_REF] Ebrahimi | Dynamic crossflow filtration of oilfield produced water by rotating ceramic filter discs[END_REF]. Signal shaft disk filter (SSDF-312) can equip with 75-100 filter disks mounted on a single shaft with a 10-15 m 2 filter area [START_REF] Liebermann | Dynamic cross flow filtration with Novoflow's single shaft disk filters[END_REF].

With the same concept, modular span disk filtration (MSDF) is manufactured by Novoflow GmbH (Germany), with a lot of disk membranes mounted on a single shaft, and the filtration area ranging from 1 m 2 up to 100 m 2 [START_REF]Modular Spin Disk Filter MSDF[END_REF]. Vacuum rotation membrane (VRM, HUBER, Berching, Germany) filtration unit also designed with an available large-scale membrane area (diameter approx. 2.3 and 3.2 m, and membrane surface approx. 900 m 2 and 3840 m 2 ) and coupled with a powerful aerator to clean the contaminated membrane [START_REF] Alnaizy | Performance assessment of a pilot-size vacuum rotation membrane bioreactor treating urban wastewater[END_REF]167,[START_REF] Komesli | Investigation of sludge viscosity and its effects on the performance of a vacuum rotation membrane bioreactor[END_REF]. Rocket M7 was designed for the purification of grape juice in winemaking; 35 disk membranes (total filtration area of 7 m 2 ) were installed in the rotating shaft and driven by a 3 kW power motor [165].

Besides, some systems equipped with multi-shaft (rotate in the same direction), overlapping membranes were developed and well-studied. A two-shaft system, Dynamic cross-flow filter (DCF) commercialized and made by KMPT, was tested with microalgae for biofuel production [START_REF] Rí Os | Antifouling microfiltration strategies to harvest microalgae for biofuel[END_REF][START_REF] Rios | Dynamic Microfiltration in Microalgae Harvesting for Biodiesel Production[END_REF]. In the optimized condition, pilot experiments achieved a concentration factor up to 200 and permeability up to 600 L/h/m 2 /bar (with pre-concentration) [START_REF] Rí Os | Antifouling microfiltration strategies to harvest microalgae for biofuel[END_REF]. Another two shafts filter, a lab-scale Multi-shaft disk (MSD, Westfalia Separator, Aalen, Germany) module, was studied by Ding et al. [START_REF] Ding | Investigation of performances of a multishaft disk (MSD) system with overlapping ceramic membranes in microfiltration of mineral suspensions[END_REF][START_REF] He | Experimental study of a dynamic filtration system with overlapping ceramic membranes and non-permeating disks rotating at independent speeds[END_REF][START_REF] Jaffrin | Effect of membrane overlapping on performance of multishaft rotating ceramic disk membranes[END_REF]. They found that the permeate with two shafts module is about twice higher than the static membrane module with the same azimuthal rim velocity. The overlapping of disks generates the maximum shear rate [START_REF] Ding | Investigation of performances of a multishaft disk (MSD) system with overlapping ceramic membranes in microfiltration of mineral suspensions[END_REF].

With this knowledge, a larger MSD system was commercialized by Westfalia Separator. It is equipped with 8 shafts and fixed a pile of membrane-disks; all shafts and membrane-disks rotate at the same speed [START_REF] Jaffrin | Dynamic filtration with rotating disks, and rotating and vibrating membranes: an update[END_REF].

Bendick et al. [START_REF] Bendick | Using a high shear rotary membrane system to treat shipboard wastewaters: Experimental disc diameter, rotation and flux relationships[END_REF][START_REF] Bendick | Effect of Backpulsing and Continuous Surface Cleaning on High-Shear Rotary Membrane System Permeate Flux Performance for Naval Shipboard Wastewaters[END_REF] compared to 760 L/(h• m 2 ) for the ceramic membrane. In the fractionation of milk protein, Espina et al. [START_REF] Espina | Comparison of rotating ceramic membranes and polymeric membranes in fractionation of milk proteins by microfiltration[END_REF] found that the PVDF membrane performed better than the ceramic one regarding permeate flux and casein rejection. In another paper [START_REF] Espina | Fractionation of pasteurized skim milk proteins by dynamic filtration[END_REF], the concentrated fluid from the MF for ceramic membrane achieved the transmissions of α-lactalbumin and βlactoglobulin between 0.8 and 0.98, for further filtration with UF was applied to separate them.

In UF, the West Virginia University team compared the performances of polymeric (100 kDa) and ceramic (0.11 μm) membranes for treating oily wastes from metal-working. The latter was superior to the polymeric membrane in terms of permeate flux and quality, as well as for cleaning and durability [START_REF] Reed | Treatment of Oily Wastes Using High-Shear Rotary Ultrafiltration[END_REF]. With CRD, oily wastewater with different concentrations was treated in MF and UF (ceramic membrane). High oil (>99%) and TOC (>98%) rejection rates were achieved with both membranes; their performances were independent of the rotational speed and the feed concentration [START_REF] Ebrahimi | Dynamic crossflow filtration of oilfield produced water by rotating ceramic filter discs[END_REF]. With VRM, the wastewater treatment was performed at a very low rotational speed (1.8 rpm), and UF polyether sulfone flat membranes (NADIR P-150F) were compacted with a total filtration area equal to108 m 2 . The COD in the final permeate flux was reduced to 3 mg/L without suspended solids for an initial retentate concentration equal to 601 mg/L. Moreover, the membrane immersed in wastewater could be used longer due to the air sourcing [START_REF] Alnaizy | Performance assessment of a pilot-size vacuum rotation membrane bioreactor treating urban wastewater[END_REF].

Rotating rectangular membrane

Only two modules (lab scale) were identified with rotating rectangular membranes, but their designs are entirely different.

Gurpreet Engineering Works in India [START_REF] Sarkar | Recovery of Polyvinyl Alcohol from Desizing Wastewater Using a Novel High-Shear Ultrafiltration Module[END_REF][START_REF] Sarkar | Design and performance characterization of a new shear enhanced module with inbuilt cleaning arrangement[END_REF][START_REF] Sarkar | Performance characterization and CFD analysis of a novel shear enhanced membrane module in ultrafiltration of Bovine Serum Albumin (BSA)[END_REF][START_REF] Sarkar | Performance characterization and design evaluation of spinning basket membrane (SBM) module using computational fluid dynamics (CFD)[END_REF] developed the first module named Spinning basket membrane (SBM). Four flat rectangular membranes (each of dimension 65×145 mm 2 with an effective area of 55×130 mm 2 ) are fitted on alternate sides of adjacent radial arms, and the other side remains impermeable. These arms are driven by a hollow shaft and allow the permeate to pass. In continuous running, the membrane filtration cycle rotated as a normal run, followed by a short time cleaning cycle rotated in the reverse direction. With the same theory, the intermeshed spinning basket membrane (ISBM) consists of two identical spinning baskets, which are intermeshed with a phase difference of 45° and able to operate at the same speed but in a reverse direction [START_REF] Naskar | Design, performance characterization and hydrodynamic modeling of intermeshed spinning basket membrane (ISBM) module[END_REF]. Sarkar et al.

[59]investigated the separation of PEG 6000 with the SBM module and PES (5kDa) UF membrane. It indicated superior performance in terms of shear enhancement and flux recovery compared with other shear enhanced systems, namely the single stirred (SS) and the rotating disk-membrane (RD-M) modules. The steady flux of the SBM module was 45-95% higher than its RD-M counterpart; in comparison with SS, it was 300-450% enhanced when rotating at 62.5 rad/s. With its inbuilt cleaning facility, the module restricts the flux decline within 15% of its start-up value, even after 21 h of continuous running. In the UF of Bovine Serum Albumin, the average permeates flux of ISBM was observed to be approximately 1.8 times higher than that of the SBM module due to comparatively higher membrane shear stress. Maximum permeate flux was evaluated to be as high as 2.4×10 -4 m 3 /(m 2 s) at moderate transmembrane pressure and rotational speed (588 kPa and 52.36 rad/s). It also showed better performance in treating extremely fouling feed solutions than other standard membrane units [START_REF] Sarkar | Performance characterization and CFD analysis of a novel shear enhanced membrane module in ultrafiltration of Bovine Serum Albumin (BSA)[END_REF][START_REF] Naskar | Design, performance characterization and hydrodynamic modeling of intermeshed spinning basket membrane (ISBM) module[END_REF].

The second module is named helical lab-scale filter [START_REF] Gao | A photo-catalysis and rotating nano-CaCO3 dynamic membrane system with Fe-ZnIn2S4 efficiently removes halogenated compounds in water[END_REF][START_REF] Gao | Photocatalysis and rotating dynamic membrane hybrid system with Fe-ZnIn2S4 efficiently removes 2,4,6-Tribromophenol in water: effect of dynamic membrane[END_REF][START_REF] Liu | Rotating a helical membrane for turbulence enhancement and fouling reduction[END_REF]. Two pieces of the flat membranes are supported on an aluminum spacer to maintain the helical angles (0°, 180°, 270°, 360° and 450°). A tubing outlet is assembled in the central of the aluminum spacer, for one side is sealed out and allowed for the collection of permeate water. The filter sheet is immersed in the tube container and driven by a DC motor, which is able to rotate at the speed of 75 and 160 rpm. Different particle suspensions (yeast, kaolin and CaCO3) were tested in MF with dynamic membranes (PES, 0.22 μm) with a total filtration area of 0.018 m 2 . 360° stood as an optimal helical angle considering the permeate flux, and the energy consumption for this condition was smaller (0.069 kWh/m 3 ) than the rotating flat membrane (0.081 kWh/m 3 ). The order of membrane fouling was yeast> kaolin> nano-CaCO3 at the same concentration of 5.0 g/L, even the mean diameter of yeast is smaller than others [START_REF] Liu | Rotating a helical membrane for turbulence enhancement and fouling reduction[END_REF]. To remove halogenated compounds (Cl -, Br -) in water, pre-coated nano-CaCO3 dynamic membranes with an effective area of 0.0092 m 2 were applied in the batch and the continuous photocatalytic experiments. This coated (fouling) layer enhanced the filtration performances and the retention of photocatalysts [START_REF] Gao | A photo-catalysis and rotating nano-CaCO3 dynamic membrane system with Fe-ZnIn2S4 efficiently removes halogenated compounds in water[END_REF][START_REF] Gao | Photocatalysis and rotating dynamic membrane hybrid system with Fe-ZnIn2S4 efficiently removes 2,4,6-Tribromophenol in water: effect of dynamic membrane[END_REF].

Rotating cylinder membrane

In 1967, Sherwood et al. [START_REF] Sherwood | Desalination by Reverse Osmosis[END_REF] suggested a rotating cylinder filter in reverse osmosis for salt and water transport, including an inner cylinder membrane rotating in a cylindrical stationary housing. 8 other modules with similar configurations have been reported in the literature. The reduction of membrane polarization is improved by taking advantage of Taylor vortices in the annular gap of the filter apparatus [START_REF] Kroner | Dynamic filtration of microbial suspensions using an axially rotating filter[END_REF].

Early-commercialized filters, Biodruck-filter (BDF-01, Sulzer AG, Winterthur, Switzerland) was dedicated to cell harvesting and cell debris removal [START_REF] Kroner | Dynamic filtration of microbial suspensions using an axially rotating filter[END_REF], with 66 mm diameter and 200 mm length inner cylinder membrane (0.04 m 2 filtration area) at rotation speed up to 3000 rpm. With the Teflon membrane (0.2 μm), 3.3 and 10 concentration ratios were tested. Flux increments have been observed during the increase of rotation speed and TMP. In E. coli broth concentration, the Biodruck-filter showed a significantly higher flux (about three-fold) than cross-flow filtration techniques over a broad concentration range.

Murase et al. [START_REF] Murase | Dynamic microfiltration of dilute slurries with a rotating ceramic membrane[END_REF] described the same dynamic microfiltration system with a rotating ceramic membrane (0.2 μm alumina ceramic membrane). Polymethyl methacrylate as slurry material was circulated in the annual gap of 3.3 mm. The same fluid was treated with the increase in outer cylinder diameter to achieve a larger gap (12.5 mm) in the filtration cell.

PMMA solutions were diluted with glycerin at concentrations of 72, 53 and 0% to obtain different viscosities. Results showed that high-speed rotating dynamic filtration was considered to be more useful when the slurry has a higher viscosity [START_REF] Murase | Microfiltration Characteristics of High-Viscosity Slurries in Rotating Dynamic Filter[END_REF]. In the separation of oil in water emulsion, high rotation speed helped limit the oil layer at the membrane surface.

With additional suspended particles in the emulsion, a further increase in steady-state flux was observed from 5.41×10 -4 to 1.14×10 -3 cm/s in 49 kPa, from 5.1×10 -4 to 4.65×10 -3 cm/s in 147 kPa [START_REF] Murase | Microfiltration-Rate Increase of O/W Emulsion by Use of Rotating Membrane Filter with Additional Suspended Solids[END_REF]. This value would decrease for higher concentration fluids, but normalized filtrate flux seemed to be constant. In the range of tests, normalized filtrate flux increased by reducing the gap radio or working at a higher rotation speed; a linear relationship was observed with

Taylor number (Ta) when ω>34.1 rad/s [START_REF] Park | A study on dynamic separation of silica slurry using a rotating membrane filter 1. Experiments and filtrate fluxes[END_REF].

A company 'Mebrex' [START_REF] Mateus | Steroid recovery by a rotary membrane system[END_REF], developed a Benchmark Biopurification System for the steroid recovery from yeast suspensions. It equips with a 100000 molecular weight cut-off hydrophilized polyacrylonitrile membrane (0.02 m 2 surface area). Steroid recovery in the permeate showed a significant increase with the Taylor number and obtained the best recovery conditions at Ta=2346 (2000 r/min).

Lee and Lueptow [START_REF] Lee | Control of scale formation in reverse osmosis by membrane rotation[END_REF][START_REF] Lee | Experimental verification of a model for rotating reverse osmosis[END_REF] took advantage of Taylor-Couette flow instabilities to reduce the flux decline related to concentration polarization and membrane fouling in reverse osmosis. Commercial polymeric RO membranes with an outer radius of 2.41 cm and length of 12.7 cm (corresponded to the total area of 0.0192 m 2 ) were applied in the filtration of space mission wastewater (wash water, condensate, and urine). Rotational speed and TMP showed to enhance the flux and rejection in rotating RO [START_REF] Lee | Experimental verification of a model for rotating reverse osmosis[END_REF]. In the concentration test of CaSO4, the permeate flux for rotating RO at ω=180 rpm remained constant up to a volume concentration factor (VCF) of 4.2. Further treatment would lead to a sharp decrease in permeate flux due to the scale formation of soluble salts [START_REF] Lee | Control of scale formation in reverse osmosis by membrane rotation[END_REF].

With the same concept, a plasmapheresis filter was commercialized for plasma collection. An inner cylinder (capacity, 7 ml) was assembled in the filter, driven by a magnet, and rotated inside the cell. Blood was separated for the centrifugal force and reached into the collection system, which permits the collection of 500 mL of plasma within 30 min [START_REF] Rock | Plasma collection using an automated membrane device[END_REF].

The last one was described by Amgar [START_REF] Salama | Investigation of the problem of filtration of oily-water systems using rotating membranes: A multicontinuum study[END_REF] in oily-water systems. Three parameters (membrane rotation speed, membrane radius and azimuthal velocity profile) were investigated, the rejection capacity of the membrane and fouling problem were reported. With the rotation of the membrane, due to the centrifugal force, the oil droplets will gather in the middle and reduce the membrane fouling. The rejection rate of the oil phase increase with the rotation speed and diameter of the membranes.

Rotating hollow fibre

One module equipped with hollow fiber (HF) membranes has been investigated in a rotating system, named rotating hollow fiber membrane (R-HFM) [START_REF] Ruigómez | A novel rotating HF membrane to control fouling on anaerobic membrane bioreactors treating wastewater[END_REF]. In a 3 L tank (inner diameter of 0.15 m), 97 fibers package were assembled vertically, and each fiber shows a length of 0.08 m with an outer diameter of 1.9 mm. The membrane modules have an average pore size of 0.04 μm and a nominal membrane surface area of 0.047 m 2 . Compared with the conventional strategy, HF membranes were immersed in the filtrate, but one top header of membranes rotated to restrict the cake layer formation. In the UF of anaerobic suspensions, the fouling rate increased with permeate flux. The turbulence promoters were introduced to evaluate the effectiveness of fouling limitations. With the increase of permeate flux from 8 to 14 L/(m 2 • h), this value decreased from 44.4% to 40.7% within the conventional gas-sparging membrane module, while sharply improving to 96% and 93% at the rotation speed of 260 rpm [START_REF] Ruigómez | A novel rotating HF membrane to control fouling on anaerobic membrane bioreactors treating wastewater[END_REF].

Rotating mechanical device module

Rotating disk

Unlike the rotating membrane system, the filter cake layer formation was limited by the rotation of external mechanical devices (such as disks, impellers or cylinders). 9 rotating disk modules (14 configurations) have been well documented in the literature. They solved the problem of flux decline by the design of inlet/outlet, disk structure, and the distance between rotating disk and membrane, mixing rate and TMP.

Dynamic Membrane Filter (DMF, Pall Corp., Cortland, NY) appeared as the first commercial system [START_REF] Lee | Microfiltration of recombinant yeast cells using a rotating disk dynamic filtration system[END_REF][START_REF] Frenander | Cell harvesting by cross-flow microfiltration using a shear-enhanced module[END_REF][START_REF] Meyer | Analysis and simulation of complex interactions during dynamic microfiltration of Escherichia coli suspensions[END_REF]. This filtration unit houses a 6-in.-diameter stainless-steel solid disk with a maximum rotating speed of 3450 rpm rotating in the clockwise direction only. The gap between the membrane (7.5 cm radius and a total area of 0.0137 m 2 ) and the rotating disk is 4 mm. The feed entered the system from the center at the bottom side of the rotating disk, flowing into the gap between the stationary membrane and disk toward the center where the concentrate or retentate was collected. Lee et al. [START_REF] Lee | Microfiltration of recombinant yeast cells using a rotating disk dynamic filtration system[END_REF] and 12000 s -1 , which were 5 and 7.5-fold higher than cross-flow systems, respectively.

Rotating Disk Module (RDM) has been largely reported concerning the filtration performances [START_REF] Jaffrin | A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems[END_REF][START_REF] Luo | Threshold flux for shear-enhanced nanofiltration: Experimental observation in dairy wastewater treatment[END_REF][START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF][START_REF] Villafana-Lopez | Shear-enhanced membrane filtration of model and real microalgae extracts for lipids recovery in biorefinery context[END_REF][START_REF] Luo | Flux decline control in nanofiltration of detergent wastewater by a shear-enhanced filtration system[END_REF][START_REF] Zhang | Investigation of membrane fouling mechanisms using blocking models in the case of shear-enhanced ultrafiltration[END_REF][START_REF] Frappart | Treatment of dairy process waters modelled by diluted milk using dynamic nanofiltration with a rotating disk module[END_REF][START_REF] Ladeg | CFD Simulation of the Distribution of Pressure and Shear Rate on the Surface of Rotating Membrane Equipped with Vanes for the Ultrafiltration of Dairy Effluent[END_REF][START_REF] Zhang | Membrane cleaning assisted by high shear stress for restoring ultrafiltration membranes fouled by dairy wastewater[END_REF][START_REF] Li | Recovery of linseed oil dispersed within an oil-in-water emulsion using hydrophilic membrane by rotating disk filtration system[END_REF][START_REF] Moulai-Mostefa | Comparison between rotating disk and vibratory membranes in the ultrafiltration of oil-in-water emulsions[END_REF][START_REF] Tu | Microfiltration of mineral suspensions using a MSD module with rotating ceramic and polymeric membranes[END_REF][START_REF] Bouzerar | Local permeate flux-shear-pressure relationships in a rotating disk microfiltration module: implications for global performance[END_REF][START_REF] Ding | Milk protein concentration by ultrafiltration with rotating disk modules[END_REF][START_REF] Espina | Comparison of rotating ceramic membranes and polymeric membranes in fractionation of milk proteins by microfiltration[END_REF][START_REF] Espina | Fractionation of pasteurized skim milk proteins by dynamic filtration[END_REF][START_REF] Akoum | Recovery of trypsin inhibitor and soy milk protein concentration by dynamic filtration[END_REF][START_REF] Zhang | Leaf protein concentration of alfalfa juice by membrane technology[END_REF][START_REF] Zhang | Application of UF-RDM (Ultafiltration Rotating Disk Membrane) module for separation and concentration of leaf protein from alfalfa juice: Optimization of operation conditions[END_REF][START_REF] Brou | Microfiltration and ultrafiltration of polysaccharides produced by fermentation using a rotating disk dynamic filtration system[END_REF][START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF][START_REF] Ding | Concentration of Milk Proteins for Producing Cheese Using a Shear-Enhanced Ultrafiltration Technique[END_REF][START_REF] Luo | Application of NF-RDM (nanofiltration rotating disk membrane) module under extreme hydraulic conditions for the treatment of dairy wastewater[END_REF][START_REF] Luo | Treatment of dairy effluent by shear-enhanced membrane filtration: The role of foulants[END_REF][START_REF] Luo | Fouling behavior of dairy wastewater treatment by nanofiltration under shear-enhanced extreme hydraulic conditions[END_REF][START_REF] Zhu | Chicory juice clarification by membrane filtration using rotating disk module[END_REF][START_REF] Luo | Influence of pH on treatment of dairy wastewater by nanofiltration using shear-enhanced filtration system[END_REF][START_REF] Zhu | Study of rotating disk assisted dead-end filtration of chicory juice and its performance optimization[END_REF][START_REF] Zhu | Rotating Disk-Assisted Cross-Flow Ultrafiltration of Sugar Beet Juice[END_REF][START_REF] Ding | High shear skim milk ultrafiltration using rotating disk filtration systems[END_REF][START_REF] Luo | Flux behavior in clarification of chicory juice by high-shear membrane filtration: Evidence for threshold flux[END_REF]. 2 modules were built similar to DMF, but with different sizes, both include a disk that rotates inside a cylindrical housing around a hollow shaft, through which the retentate is evacuated. But the larger module (RDM-2) receives a 460 cm 2 annular membrane area, compared with a 190 cm 2 flat disk membrane in a smaller one (RDM-1). The module performances for 5 inlet/outlet configurations (lateral housing wall, back plate or axial) were compared at a 3 mm disk-membrane gap. The highest permeate flux was obtained at high speeds with the inlet at the backplate and axial retentate outlet. With the increase of the diskmembrane gap from 4 to 18 mm, almost no effect on the permeate flux was observed. In the gap of 10 mm, by equipping the disk with nylon mesh in module 1, or eight pairs of 2-mm aluminum rods in module 2, permeate flux increased due to the increment of core velocity coefficient [START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF]. The gap ratio (disk-membrane gap divided by disk radius) seems relevant to this coefficient [START_REF] Jaffrin | A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems[END_REF][START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF][START_REF] Ding | High shear skim milk ultrafiltration using rotating disk filtration systems[END_REF]. Bouzerar et al. [START_REF] Bouzerar | Local permeate flux-shear-pressure relationships in a rotating disk microfiltration module: implications for global performance[END_REF] applied RDM in MF of CaCO3 suspension. First, the disk speed was decreased in steps from 1500 rpm to rest in order to evaluate steady-state flux. Then speed was raised again to 1500 rpm to investigate the irreversibility of fouling. Initial peripheral pressure was fixed at 15 kPa, and experiments were performed with 0.1 μm PVDF membranes. Final permeate flux almost kept the same value but represented only 64% of the initial one when conducted at 50 kPa. When the rotation speeds up to 1100 rpm, permeate flux increases with radius, and fouling almost disappears at r>4 cm. But in the central part, relatively lower local velocity was not able to eliminate the cake layer. In dairy wastewater treatment [START_REF] Zhang | Investigation of membrane fouling mechanisms using blocking models in the case of shear-enhanced ultrafiltration[END_REF], the RDM configuration was a disk equipped with 4 pairs of 6 mm-high vanes (disk membrane-gap not specified), which can rotate up to 2500 rpm. Performances were scrutinized versus shear rate (0.169×10 5 to 2.05×10 5 s -1 ), TMP (3 to7 bar), temperature (35 to 55℃) and membrane cut-off (30 to 10 kDa). Flux decline was observed due to membrane blocking by lactose and milk protein.

Shear rate and TMP showed a great effect on membrane fouling control and contributed to the cleaning process. Evaluating the membrane permeability recovery rate, concluded that a high shear rate combined with a cleaning agent is more conducive to fouling elimination.

Low TMP presented that the concentration polarization of casein micelles and the cake layer was reduced on the membrane surface [START_REF] Zhang | Membrane cleaning assisted by high shear stress for restoring ultrafiltration membranes fouled by dairy wastewater[END_REF]. In the concentration tests of leaf protein (MF, UF), Zhang et al. [START_REF] Zhang | Leaf protein concentration of alfalfa juice by membrane technology[END_REF] seemed to enhance electrostatic repulsion and led to the increase of permeate flux, but conductivity rejection showed the opposite trend [START_REF] Luo | Flux decline control in nanofiltration of detergent wastewater by a shear-enhanced filtration system[END_REF]. In this rotating system, the net power consumed by the rotating disk was proportional to the square of rotation speed. Disk with vans presented much higher net power than smooth disk in the same condition. However, it was opposite with specific energy consumption [START_REF] Li | Recovery of linseed oil dispersed within an oil-in-water emulsion using hydrophilic membrane by rotating disk filtration system[END_REF][START_REF] Brou | Microfiltration and ultrafiltration of polysaccharides produced by fermentation using a rotating disk dynamic filtration system[END_REF]. There were other studies focused on various test fluids [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF][START_REF] Luo | Flux decline control in nanofiltration of detergent wastewater by a shear-enhanced filtration system[END_REF][START_REF] Tu | Studies on treatment of sodium dodecyl benzene sulfonate solution by high shear ultrafiltration system[END_REF][START_REF] Moulai-Mostefa | Treatment of Aqueous Ionic Surfactant Solutions by Dynamic Ultrafiltration[END_REF][START_REF] Frappart | Treatment of dairy process waters modelled by diluted milk using dynamic nanofiltration with a rotating disk module[END_REF][START_REF] Bouzerar | Concentration of ferric hydroxide suspensions in saline medium by dynamic cross-flow filtration[END_REF][START_REF] Ding | Milk protein concentration by ultrafiltration with rotating disk modules[END_REF][START_REF] Akoum | Recovery of trypsin inhibitor and soy milk protein concentration by dynamic filtration[END_REF][START_REF] Frappart | Influence of hydrodynamics in tangential and dynamic ultrafiltration systems for microalgae separation[END_REF][START_REF] Harscoat | Influence of fermentation conditions and microfiltration processes on membrane fouling during recovery of glucuronane polysaccharides from fermentation broths[END_REF][START_REF] Mellal | Separation of oligoglucuronans of low degrees of polymerization by using a high shear rotating disk filtration module[END_REF][START_REF] Francis | Optimizing the rotor design for controlled-shear affinity filtration using computational fluid dynamics[END_REF][START_REF] Torras | Numerical simulation of the flow in a rotating disk filtration module[END_REF] was installed at the bottom of the module, while the feed inlet and concentrate outlet were connected to the upper surface. With this module, a CFD simulation was performed by Kim et al. [START_REF] Kim | Dynamic microfiltration with a perforated disk for effective harvesting of microalgae[END_REF]. Fluid velocity and average shear stress of a perforated disk on the membrane surface were found to be 2 and 7-fold higher than an unperforated disk, respectively. As the average shear stress increased from 0.23 (0 rpm) to 28.99 Pa (800 rpm), the microalgal fouling resistance reduced by 87%, and the plateau permeate flux was increased 6.7-fold to 381 L/(h• m 2 ). Effect of rotation speed, TMP, membrane cut-off or biomass concentration on filtration performances had been illustrated to be associated with permeate flux and fouling resistance [START_REF] Kim | Harvesting of Scenedesmus obliquus using dynamic filtration with a perforated disk[END_REF][START_REF] Jung | Dynamic filtration with a perforated disk for dewatering of Tetraselmis suecica[END_REF].

Another rotating disk module derived from Central South University (China) was assembled to separate heavy metal from wastewaters [START_REF] Chen | Removal of Cd (II) from dilute aqueous solutions by complexation-ultrafiltration using rotating disk membrane and the shear stability of PAA-Cd complex[END_REF][START_REF] Tang | Removal of Zn (II) by complexation-ultrafiltration using rotating disk membrane and the shear stability of PAA-Zn complex[END_REF][START_REF] Tang | Computation fluid dynamic simulation and experimental validation of shear induce dissociation coupling ultrafiltration technology for the treatment of lead contained wastewater[END_REF]. It shared the same configuration of the inlet and outlet with the RDM module. A disk with a radius of 83 mm was driven by a rotating shaft in an 88 mm inner radius circular housing, enable to speed up to 3000 rpm. The model waste of lead nitrate was fully complexed with poly acrylic acid sodium (PAAS) or copolymer of maleic acid and acrylic acid (PMA), then removed by UF.

These metal complexes were sensitive to the high shear rate. The results indicated that the critical shear rate of the PMA-Pb complex was less than that of the PAA-Pb complex. But the former case was preferred for the treatment of lead contained wastewater due to its higher load capacity of Pb (II) and easier regeneration [START_REF] Tang | Computation fluid dynamic simulation and experimental validation of shear induce dissociation coupling ultrafiltration technology for the treatment of lead contained wastewater[END_REF]. For the separation of Zn (II) from aqueous solutions, the critical shear rate for PAA-Zn complexes was 1.58×10 5 s -1 at pH 7.0 [START_REF] Tang | Removal of Zn (II) by complexation-ultrafiltration using rotating disk membrane and the shear stability of PAA-Zn complex[END_REF]. Another publication investigated the critical speed of two disks (smooth disk and disk with 6 vans) to remove the PAA-Cd complex. The critical shear rate for both disks was calculated to be 1.31×10 5 s -1 at pH 6.0, and the rejection of Cd reached 99.7% [START_REF] Chen | Removal of Cd (II) from dilute aqueous solutions by complexation-ultrafiltration using rotating disk membrane and the shear stability of PAA-Cd complex[END_REF].

A rotating-disk dynamic filter was designed by Tamkang University (China) [START_REF] Hwang | Fine particle removal from seawater by using cross-flow and rotating-disk dynamic filtration[END_REF][START_REF] Hwang | Analysis on the nonuniformity of cake formation in rotating-disk dynamic microfiltration[END_REF][START_REF] Wu | Structural design of a rotating disk dynamic microfilter in improving filtration performance for fine particle removal[END_REF][START_REF] Hwang | Filtration flux-shear stress-cake mass relationships in microalgae rotating-disk dynamic microfiltration[END_REF]. The diameter and height of the chamber are both 38 mm. Two vanes (10 mm×10 mm×1 mm) are placed beneath a rotating disk with a diameter of 30 mm. A low circular inlet and a high circular outlet are connected to the chamber for feed inflow and concentrate outflow. A circular membrane is installed on the porous bottom plate with a filtration area of 1.12×10 -3 m 2 [START_REF] Hwang | Filtration flux-shear stress-cake mass relationships in microalgae rotating-disk dynamic microfiltration[END_REF]. In MF, SiO2 was separated from artificial seawater. The pseudo-steady filtration flux was only 1.65 m 3 /(m 2 • s) for a static disk, but it increased by 170% as ω increased to 500 rpm at a distance of 1.5 mm between vans and membrane. This increase in the flux was more considerable for a smaller gap of 0.8 mm, and the filtration flux increased 2.4-fold as ω rose from 0 to 500 rpm [START_REF] Hwang | Fine particle removal from seawater by using cross-flow and rotating-disk dynamic filtration[END_REF]. From another article, 2 vans disk (Type 1), 4 vans disk (Type 2) or 2 vans disk with circular orifices (Type 3) was able to rotate 15 mm above the membrane. It indicated that increasing the disk rotation speed or the number of vanes improves the mean filtration flux, and the holes in the disk have no effect on flux enhancement. The specific filtration flux (flux divided by energy) could be ordered as Type 3>Type 1>Type 2, and it also decreased with the increase of rotation speed [START_REF] Wu | Structural design of a rotating disk dynamic microfilter in improving filtration performance for fine particle removal[END_REF]. For the same purpose, a larger module with a filtration area of 0.0377 m 2 was established by Hwang et al. [START_REF] Hwang | Disk structure on the performance of a rotating-disk dynamic filter: A case study on microalgae microfiltration[END_REF]. By modifying the disk, 6 types of disks were constructed with different concepts (distance between disk and membrane, number of vans and vans' structure). Considering the filtration flux and power consumption, disk and disk with 2 vans (has an uneven rectangular cross-section) showed to be the optimal designs, and even 4 uniform vans could generate the highest shear stress and result in the highest permeate flux.

A particular configuration of the rotor could be observed in the controlled shear filtration (CSF) module [START_REF] Vogel | Controlled shear filtration: A novel technique for animal cell separation[END_REF]. It has a conical rotor (inclination angle of 4°) of 70 mm diameter rotating at 0.2 mm above a PVDF membrane (51.5 cm 2 effective filtration area) for MF of recombinant BHK cell suspension. The threshold level of shear stability was determined during the sharp decrease of cell viability for the step improvement of rotating speed. An optimal growing cell showed better resistance with shear stress up to 17.2 N/m 2 instead of 7.12 N/m 2 for a lower growing cell. Compared with traditional cross-flow filtration, constant flux 30 L/(h• m 2 ) and cell viability percentage 83% greatly improved to 97%-91%, 290 L/(h• m 2 ) with CSF, respectively. Almost with the same configuration, the controlled shear affinity filtration (CSAF) module was investigated with CFD simulation. A new rotor (0.2 mm gap to the membrane) was designed with a variable inclination angle, which permitted the constant shear stress at all radial positions except the center-point. Meanwhile, the threshold shear stress of 0.17 Pa was achieved across virtually the entire membrane surface at a rotor speed of 250 rpm. It was 60% less than the rotor speed required in the original CSAF device [START_REF] Francis | Optimizing the rotor design for controlled-shear affinity filtration using computational fluid dynamics[END_REF].

In rotating cross-flow (RCF) MBR [START_REF] Bentzen | Analytical and numerical modelling of Newtonian and non-Newtonian liquid in a rotational cross-flow MBR[END_REF], a 156 mm radius of the membrane is placed in the support. With a gap of 5 mm, a disk of 140 mm radius can rotate between 50 and 350 rpm.

In a single-use medical product LIFE 18-Disk Separator, which was designed to separate plasma from whole blood, two membranes are configured with a spinning disk rotating between them within a plastic housing and only reaches 50 ml for the volume [189].

Rotating impeller

Similar to the rotating disk module, the shape of the impeller also draws much attention.

3 modules were developed into 10 configurations by compacting even up to hundreds of membranes in the filtration cell and increasing the diameter of membranes for large-scale applications.

Cross Rotational Filters (CR-filters) were designed by Metso-Paper corp., equipped with two-blade impellers between two membranes. The company proposed several scales for users;

the diameter could range from 200 to 1010 mm, e.g., the Opti Filter CR-1010/100, with 100 cassettes of 1010 mm diameter, achieves filtration area up to 140 m 2 [START_REF] Nuortila-Jokinen | Tailoring an economical membrane process for internal purification in the paper industry[END_REF][START_REF] Huuhilo | Influence of shear on flux in membrane filtration of integrated pulp and paper mill circulation water[END_REF][START_REF] Mä Nttä Ri | Evaluation of nanofiltration membranes for filtration of paper mill total effluent[END_REF][START_REF] Mä Nttä Ri | Influence of filtration conditions on the performance of NF membranes in the filtration of paper mill total effluent[END_REF]. The DYNO (Bokela GmbH, Karlsruhe, Germany) filter was installed with a blade-like rotor for each filtration cell and reached 12 m 2 of total membrane area [START_REF] Bott | Dynamic cross flow filtration[END_REF]. The same concept also has been applied to the Rotating and Vibrating Filtration (RVF) module. A lab-scale RVF module has two identical filtration cells. Each consisted of a three-blade impeller with 135 mm diameter and 8 mm thickness, rotating in a 14 mm gap between two porous substrates, which can operate up to 50 Hz [START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF][START_REF] Fillaudeau | Investigation of rotating and vibrating filtration for clarification of rough beer[END_REF].

Gursch et al. [START_REF] Gursch | Continuous Processing of Active Pharmaceutical Ingredients Suspensions via Dynamic Cross-Flow Filtration[END_REF] reported the continuous manufacturing of active pharmaceutical ingredients with a lab-scale Dynotest system, aluminum oxide disk membranes (0.5 μm) were equipped with a total filtration area of 0.013 m 2 . A material-dependent linear relationship of the permeate flow as a function of cumulated feed flow was found with different fluids; slope k made it possible to establish a constant concentration factor to predict filtration performance for any given product.

In the paper industry, Jutta et al. [START_REF] Nuortila-Jokinen | Comparison of membrane separation processes in the internal purification of paper mill water[END_REF] described the UF process with a CR module; polymeric and ceramic membranes ranging from 8 to 200 kDa were tested. It was shown that the relatively low cut-off (30 kDa) hydrophilic C30G membrane made from regenerated cellulose had higher fluxes both at neutral and acidic pH. It could last six days of filtration with good permeation. The same reports also have been investigated in NF and RO [START_REF] Mä Nttä Ri | Evaluation of nanofiltration membranes for filtration of paper mill total effluent[END_REF][START_REF] Mä Nttä Ri | Influence of filtration conditions on the performance of NF membranes in the filtration of paper mill total effluent[END_REF].

Rayess et al. [START_REF] Rayess | Wine clarification with Rotating and Vibrating Filtration (RVF): Investigation of the impact of membrane material, wine composition and operating conditions[END_REF] employed MF (PES and PTFE, 0.2 μm) with the RVF module in wine clarification. In the filtration of crude simulated wine, the permeability of PTFE membranes was slightly higher than PES membrane with N=0 Hz, but it is the opposite during filter wine filtration respectively, for 1676 L/(h• m 2 • bar) (PES) and 170 L/(h• m 2 • bar) (PTFE). When N was increasing, PES seemed to be sensitive to the mixing effect, while PTFE showed to be unaffected by the frequency increase. Fillaudeau et al. [START_REF] Fillaudeau | Investigation of rotating and vibrating filtration for clarification of rough beer[END_REF] also tested two ceramic membranes (0.6 to 4 μm) with rough beer. In this research, the driving force at the membrane surface and the core velocity coefficient associated with fluid dynamics were determined with water. Afterward, the performance of RVF was evaluated for two different rough beers and model beers, which resulted in the ceramic membrane achieving a more satisfying quality and flux value than traditional filtrations.

Rotating cylinder

As discussed in the rotating cylinder membrane, studies on fixed membrane cylinders have also been reported. 2 modules have been designed in the lab-scale application.

The application of helical Couette-Taylor flow (CTF) [START_REF] Zakrzewska-Trznadel | Reducing fouling and boundary-layer by application of helical flow in ultrafiltration module employed for radioactive wastes processing[END_REF] could help to reduce fouling in the process of filtration. A tubular membrane module is configured with a tubular metallic membrane (diameter of 30/34 mm, filtration area of 0.04 m 2 ) as a housing and a coaxial inner cylinder as a rotor (diameter of 20 mm). In order to be applied to radioactive wastes, cobalt ions solution was fed in UF with the metallic membrane. After 720 min circulation, the permeate flux decreased to 8 L/(m 2 s) without mixing. Due to the instability of the flow, it was almost 3-fold when the inner cylinder was rotating up to 1500 rpm. Further improvement in the rotation speed seemed to have little effect on the permeation [START_REF] Zakrzewska-Trznadel | Reducing fouling and boundary-layer by application of helical flow in ultrafiltration module employed for radioactive wastes processing[END_REF]. The optimal hydrodynamic conditions were established by response surface methodology. The maximal permeate flux and the minimal flux decline were observed at TMP of 70kPa, retentate flowrate 108 L/h and rotating speed of 2800 rpm [START_REF] Cojocaru | Removal of cobalt ions from aqueous solutions by polymer assisted ultrafiltration using experimental design approach Part 2: Optimization of hydrodynamic conditions for a crossflow ultrafiltration module with rotating part[END_REF]. DYNAMIC HPHT Filtration system [START_REF] Balavi | Dynamic filtration of drilling fluids and fluid loss under axially rotating crossflow filtration[END_REF] equipped with a rotating cylinder, which could simulate the build-up of filter cake on the formation. A 6.

Rotating disk and membrane module

The request for DF of large shear stress led to the introduction of a rotating disk and membrane system (2 modules). Disk and membrane are mounted on different shafts and could rotate in the reverse direction.

A shear-enhanced system, namely rotating disk-membrane (RD-M) module, was investigated on microfiltration of black liquor [START_REF] Bhattacharjee | Ultrafiltration of black liquor using rotating disk membrane module[END_REF][START_REF] Bhattacharjee | Performance study during ultrafiltration of Kraft black liquor using rotating disk membrane module[END_REF], Ultrafiltration of PEG 6000 and Bovine serum albumin [START_REF] Sarkar | Simulation of continuous stirred ultrafiltration process: an approach based on surface renewal theory[END_REF][START_REF] Sarkar | Modeling and analytical simulation of rotating disk ultrafiltration module[END_REF][START_REF] Sarkar | Simulation of continuous stirred rotating disk-membrane module: An approach based on surface renewal theory[END_REF]. The membrane was placed on disk-shaped porous support with an effective filtration area of 24.6 cm 2 . A stirrer is provided inside the cell, having the same diameter as that of the membrane. They rotate in the opposite direction and give a maximum shear rate of 2×10 5 s -1 at the membrane surface. In the UF of BSA, the increment of membrane rotation speed, stirring speed, and TMP are likely to improve the permeate flux. It has been demonstrated that 79.7% of steady-state permeate flux decreased on increasing bulk concentration from 1 g/L to 30 g/L, resulting in the mean residence time increasing from 0.17 s to 0.28 s. However, TMP did not affect residence time by increasing 294 kPa to 882 kPa [START_REF] Sarkar | Simulation of continuous stirred rotating disk-membrane module: An approach based on surface renewal theory[END_REF]. The influence of membrane disc rotation was found to increase the flux substantially, more than so obtained by stirrer rotation. Nevertheless, the pre-treatment steps proved to be highly efficient in minimizing flux decline [START_REF] Bhattacharjee | Ultrafiltration of black liquor using rotating disk membrane module[END_REF][START_REF] Bhattacharjee | Performance study during ultrafiltration of Kraft black liquor using rotating disk membrane module[END_REF].

By modifying dynamic cross-flow filtration (DCF), Johannes et al. [START_REF] Schä Fer | Concentration of skim milk by means of dynamic filtration using overlapping rotating ceramic membrane disks[END_REF] described a new module. Two rotating shafts equipped with two ceramic membrane disks and one smooth metal blind disk individually, resulting in a membrane filtration area of 0.14 m 2 . The disks from each shaft overlapped each other by 26.4% of their surfaces. As a result, MF (0.06 μm pore size) of pasteurized skim milk (3.4%, w/w, protein) could preferably be applied in smallscale manufacture of milk retentate for protein contents of ≥14.8% (w/w).

Oscillating system

Considering the movement part, oscillating could happen in the whole filtration cell (3 modules with 12 configurations) or just occur in the membrane (9 modules with 9 configurations). These motions could be azimuthal, horizontal or axial oscillation. In addition, the spacer oscillation (1 module) also promoter turbulence in the flow. The VSEP L101 was a relatively small pilot-scale module. An annular membrane with an area of 503 cm 2 in a circular housing (with a gap of 3.5 mm) is placed at the top of a vertical shaft, and driven by a torsion spring. This shaft amplified the vibrations to reach the amplitude from 6.35 to 31.75 mm, corresponding to the frequency between 55 and 60.75 Hz.

The feed and retentate channels are distributed on both sides of the rotating shaft at the bottom plate. The permeation through the membrane was collected through the holes in the membrane plate support [START_REF] Zouboulis | Treatment of Tannery Wastewater with Vibratory Shear-Enhanced Processing Membrane Filtration[END_REF]. Akoum et al. [START_REF] Akoum | An hydrodynamic investigation of microfiltration and ultrafiltration in a vibrating membrane module[END_REF] investigated the MF of yeast suspensions and the UF of BSA solutions with this module. In the case of yeast MF, the permeate flux was found to be proportional to γ 0.19 at a frequency below 59.7 Hz and to γ 0.50 at a higher frequency. In the UF of BSA, the permeate flux was proportional to γ 0.426 at all frequencies.

As for the treatment of dairy process water, the membrane oscillated at 60. to other suspensions, such as tannery wastewater [START_REF] Zouboulis | Treatment of Tannery Wastewater with Vibratory Shear-Enhanced Processing Membrane Filtration[END_REF], latex solution [START_REF] Takata | Structure of shear-enhanced flow on membrane surface with horizontal vibration and its effect on filtration performance[END_REF], metal working emulsions [START_REF] Moulai-Mostefa | Separation of water from metal working emulsions by ultrafiltration using vibratory membranes[END_REF] and microalgae [START_REF] Hapońska | Application of ABS membranes in dynamic filtration for Chlorella sorokiniana dewatering[END_REF][START_REF] Slater | Shear-enhanced microfiltration of microalgae in a vibrating membrane module[END_REF][START_REF] Lorente | Microalgae fractionation using steam explosion, dynamic and tangential cross-flow membrane filtration[END_REF].

PallSep PS10 VMF unit consists of two membrane discs, both covered with a hydrophobic PTFE membrane on both sides, giving a total membrane surface area of 0.2 m 2 .

The feed is delivered to the first membrane disc through a feed channel at the bottom endplate of the VMF membrane assembly. Each membrane disk has 18 circular holes (8.5 mm diameter), whose 12 holes are located at 270 mm on the outer edge and 6 holes at 26 mm in the inner diameter of the disc. The fluid then flows outward in the retentate channel and inwards tangential to the membrane surface towards 6 equally spaced, which is collected in a series of grooves and exits the VMF system through the top end plate permeate port. In the recycle mode of 200 g/L yeast suspension, a decline in permeate flux was observed until a steady-state was achieved after about 20 min with the vibration at 19.5 mm amplitude.

Without any vibration, permeate flux fell to zero in 10 min at the same cross-flow rate of 1 L/min. In the concentration tests of yeast suspension, increased the gap width from 1.4 to 4.2 mm, the maximum solids loading capacity was improved from 561 to 633 g/L. It also indicated that the volume concentration factor would increase with a larger gap width [START_REF] Postlethwaite | Flux and transmission characteristics of a vibrating microfiltration system operated at high biomass loading[END_REF].

Oscillating rectangular cell

Another lab-scale oscillating filtration cell is vibration enhanced reverse osmosis (VERO) [START_REF] Su | Concentration polarization and permeate flux variation in a vibration enhanced reverse osmosis membrane module[END_REF][START_REF] Su | Permeate flux increase by colloidal fouling control in a vibration enhanced reverse osmosis membrane desalination system[END_REF][START_REF] Li | Reverse osmosis membrane, seawater desalination with vibration assisted reduced inorganic fouling[END_REF], derived from Texas A&M University (USA). CFD simulation also showed excellent agreement with the results over different Reynolds numbers.

Oscillating membrane module

Oscillating rectangular membrane

Compared with the oscillation filtration cell modules, another kind of device is realized by immersing the oscillating membrane in the filtered liquid. The principle of shear enhancement by the oscillating membrane is generally applied in a rectangular membrane.

Different technics aimed to create the horizontal motion of membranes, and 4 modules are reported in recent publications.

The oscillatory flat surface membrane (OFSM) module was proposed by Gomaa et al. [START_REF] Gomaa | Intensification of membrane microfiltration using oscillatory motion[END_REF][START_REF] Gomaa | Energetic consideration and flux characteristics of roughed-surface membrane in presence of reversing shear[END_REF][START_REF] Gomaa | Analysis of flux enhancement at oscillating flat surface membranes[END_REF][START_REF] Gomaa | Dynamic analysis of mass transfer at vertically oscillating surfaces[END_REF][START_REF] Gomaa | Flux characteristics at oscillating membrane equipped with turbulent promoters[END_REF][START_REF] Gomaa | Flux enhancement using oscillatory motion and turbulence promoters[END_REF]. A flat membrane (filtration area of 0.06 m 2 ) is mounted on a membrane frame, fixed with a metal mesh, and immersed in a yeast solution. A vacuum pump is used to collect permeate and control transmembrane pressure. Hydrophilic nylon membranes (0.22 μm) were used in the re-hydrated baker's yeast under the condition of 0-25 Hz (frequency), 3-30 mm (amplitude) and 0.2-0.6 bar (TMP). Increasing oscillation frequency or amplitude resulted in higher permeate flux; the effect of oscillation frequency was found to be stronger than the amplitude [START_REF] Gomaa | Intensification of membrane microfiltration using oscillatory motion[END_REF]. Using higher oscillation frequency and lower amplitude were found to be more effective for flux enhancement and energy utilization [START_REF] Gomaa | Energetic consideration and flux characteristics of roughed-surface membrane in presence of reversing shear[END_REF]. Furthermore, membrane surface equipped with both flat turbulence promoters and grooved turbulence promoters has been proved to improve microfiltration flux further. The combined effect of oscillatory motion and turbulence promoters can result in substantial flux augmentation. Such an effect increased with increasing the oscillation frequency but decreased with its amplitude [START_REF] Gomaa | Energetic consideration and flux characteristics of roughed-surface membrane in presence of reversing shear[END_REF][START_REF] Gomaa | Flux characteristics at oscillating membrane equipped with turbulent promoters[END_REF][START_REF] Gomaa | Flux enhancement using oscillatory motion and turbulence promoters[END_REF].

With the same concept, a magnetically induced membrane vibration (MMV) system [START_REF] Mertens | Membrane development for improved performance of a magnetically induced vibration system for anaerobic sludge filtration[END_REF][START_REF] Mertens | Magnetically induced membrane vibration (MMV) system for wastewater treatment[END_REF][START_REF] Bilad | Novel magnetically induced membrane vibration (MMV) for fouling control in membrane bioreactors[END_REF][START_REF] Zhao | A highly efficient and energy-saving magnetically induced membrane vibration system for harvesting microalgae[END_REF][START_REF] Li | Application of a magnetically induced membrane vibration (MMV) system for lignocelluloses hydrolysate filtration[END_REF][START_REF] Bilad | Harvesting microalgal biomass using a magnetically induced membrane vibration (MMV) system: filtration performance and energy consumption[END_REF] consists of one or more flat sheet membranes and is mounted on a metal frame. The oscillation is created by the magnetic attraction/repulsion forces to alternate membrane modules that move up and down with a specific frequency and amplitude. For UF of bioethanol from the hydrolysate, 4 membranes were placed in series with a gap of 1 cm with a filtration area of 0.04 m 2 . With undiluted feeds (extremely viscous), permeate and TMP showed the same trends with oscillation (frequency:10 Hz, amplitude: 6 mm) and without oscillation. However, these differences were enlarged with diluted feeds (dilution rate: 4 or 6 times). It also indicated that fouling control could be improved by suitable membranes (nature) and higher oscillating amplitude [START_REF] Li | Application of a magnetically induced membrane vibration (MMV) system for lignocelluloses hydrolysate filtration[END_REF]. In other fields such as wastewater treatment, [START_REF] Mertens | Membrane development for improved performance of a magnetically induced vibration system for anaerobic sludge filtration[END_REF][START_REF] Mertens | Magnetically induced membrane vibration (MMV) system for wastewater treatment[END_REF][START_REF] Bilad | Novel magnetically induced membrane vibration (MMV) for fouling control in membrane bioreactors[END_REF] microalgae harvesting [START_REF] Zhao | A highly efficient and energy-saving magnetically induced membrane vibration system for harvesting microalgae[END_REF][START_REF] Bilad | Harvesting microalgal biomass using a magnetically induced membrane vibration (MMV) system: filtration performance and energy consumption[END_REF] has also been investigated.

Tongji University (China) has designed a constant-shear vibration device named the uniform shearing vibration membrane (USVM) [START_REF] Zhao | A uniform shearing vibration membrane system reducing membrane fouling in algae harvesting[END_REF] system. By the rotating shaft, the flat rectangular membrane (effective membrane area of 0.02 m 2 ) installed on a cassette can be operated with a uniform circular motion (not rotating), which induces a constant shear rate at the membrane surface. On the membrane frame, there is an outlet connecting a tube, and the permeate can be taken away through the tube using a peristaltic pump. Another axial vibration membrane (AVM) [START_REF] Wu | Structural design of a rotating disk dynamic microfilter in improving filtration performance for fine particle removal[END_REF][START_REF] Zhao | Using axial vibration membrane process to mitigate membrane fouling and reject extracellular organic matter in microalgae harvesting[END_REF][START_REF] Zhao | Microalgae harvesting by an axial vibration membrane: The mechanism of mitigating membrane fouling[END_REF] device that reduces membrane fouling by vibrating the shaft along the vertical axis was developed by the same lab. By controlling the servo motor and changing the structure of the rotating shaft, different vibration frequencies and amplitudes for both devices can be achieved. On a cassette, 1 to 100 flat membranes can be installed in the square frame (11 cm) with the distance between membranes from 1 to 50 mm. Zhao et al. [START_REF] Zhao | Using axial vibration membrane process to mitigate membrane fouling and reject extracellular organic matter in microalgae harvesting[END_REF] investigated AVM in microalgae harvesting; a 0.1 μm PVDF membrane was used to work at any frequency up to 15 Hz and amplitude from 5 to 40 mm.

The critical flux is proportional to γmax 0.2284 ; the motion not only prevents the deposition of algae cells on the membrane but also reduces the adsorption of extracellular organic matter on the membrane. The horizontal system (USVM) worked at a lower frequency (5 Hz) and amplitude of 20 mm; the same membrane was used. The TMP visibly reduced when the frequency increased from 1 to 5 Hz. Even at a relatively low frequency of 5 Hz, reversible and irreversible membrane fouling could also be limited [START_REF] Zhao | A uniform shearing vibration membrane system reducing membrane fouling in algae harvesting[END_REF].

Oscillating cylinder membrane

With the same concept, azimuthal or axial oscillation can be achieved with the cylinder membrane. 2 lab-scale modules were described, and the effect of oscillating frequency, amplitude or angle was investigated.

A cylinder membrane (14 mm outside diameter, 64 mm membrane working length) was immersed in calcite suspension, and two modes of oscillations were performed [START_REF] Holdich | A comparison of azimuthal and axial oscillation microfiltration using surface and matrix types of microfilters with a cake-slurry shear plane exhibiting non-Newtonian behaviour[END_REF]. The axial oscillations can be operated with an adjustable displacement and frequency up to 100

Hz. The azimuthal movement oscillates at 3 degrees with 20 to 100 Hz, and the highest shear stress of 240 Pa is reached. The vibration mode did not influence the filtration performance, while it corresponded to the shear stress peak delivered by the oscillating system [START_REF] Holdich | A comparison of azimuthal and axial oscillation microfiltration using surface and matrix types of microfilters with a cake-slurry shear plane exhibiting non-Newtonian behaviour[END_REF].

With a vibrating head, an axial oscillation of the slotted-pore nickel membrane is controlled up to 100 Hz (frequency) and 10 mm (amplitude) [START_REF] Ullah | Membrane oscillation and slot (pore) blocking in oil-water separation[END_REF]. The fouling of the membrane pore area is reduced in the presence of the shear. Compared with crude oil, Tween 20-stabilized oil with decreasing interfacial tension and smaller droplet size, and led to a lower blocking area. The blocking constant at 1000 L/(m 2 • h) (permeate flux) was approximately five times smaller than 200 L/(m 2 • h), caused by the increased permeation of the deformable oil droplets [START_REF] Ullah | Membrane oscillation and slot (pore) blocking in oil-water separation[END_REF].

Oscillating hollow fibre membrane

The principle of shear enhancement by oscillation has also been applied to hollow fiber membranes by attaching them to a sliding rod connected to a rotating head. 3 modules have investigated the oscillation of the HF membrane in the axial direction.

A Vibrating hollow fiber microfiltration (VHM) system [START_REF] Genkin | The effect of vibration and coagulant addition on the filtration performance of submerged hollow fibre membranes[END_REF] has 7 MF hollow fiber membranes (40 cm in length) with a surface area of 0.0057 m 2 . They were potted in a cassette using Araldite glue and then submerged in a yeast suspension tank. This cassette vibrated using a 250 W electric motor at any frequency up to 10 Hz with an amplitude of 4 cm. A relatively monotonic increase in critical flux was observed during the frequency increase from 0 to 10 Hz. A two-step correlation between critical permeate flux and rotating frequency was established and separated in the frequency of 5 Hz [START_REF] Genkin | The effect of vibration and coagulant addition on the filtration performance of submerged hollow fibre membranes[END_REF]. A similar observation has been investigated by Jaffrin et al. [START_REF] Jaffrin | A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems[END_REF] with RDM and VSEP. Specific critical flux was defined as the ratio between critical flux and specific power consumption. The peak value was observed at a low oscillating frequency below 2 Hz and followed by a subsequent drop to a low value as the specific power consumption increased [START_REF] Genkin | The effect of vibration and coagulant addition on the filtration performance of submerged hollow fibre membranes[END_REF].

The second module was described by the Technical University of Denmark [START_REF] Beier | Critical flux determination by flux-stepping[END_REF][START_REF] Beier | Dynamic microfiltration with a vibrating hollow fiber membrane module: Filtration of yeast suspensions[END_REF][START_REF] Beier | Separation of enzymes and yeast cells with a vibrating hollow fiber membrane module[END_REF]. The vibrating membrane bioreactor (VMBR) system consists of a module with hollow fibers fixed in parallel between a steel plate at the bottom of the module and a permeate gap at the top. Despite different versions of modules equipped with diverse membranes (filtration area range between 84 and 488 cm 2 ) and liquid levels, these systems were almost identical. A total membrane area of 488 cm 2 is composed of 54 hollow fibers with a length of 12.5 cm; it oscillates with the displacement of 1.175 mm (the peak-to-peak amplitude is twice as big)

and frequency up to 30 Hz. In yeast suspension, the PES membrane with a nominal pore size of 0.45 μm was tested, and the critical flux was improved up to the maximum oscillating degree. The correlation between shear rate and critical flux was similar to the oscillating rectangular membrane module [START_REF] Zhao | Using axial vibration membrane process to mitigate membrane fouling and reject extracellular organic matter in microalgae harvesting[END_REF][START_REF] Beier | Separation of enzymes and yeast cells with a vibrating hollow fiber membrane module[END_REF].

The last module was described by Li et al. [START_REF] Li | Fouling control of submerged hollow fibre membranes by vibrations[END_REF]. Membrane modules (13 HFs with a length of 40 cm, inner/outer diameters of 1/1.7 mm and 1/2 mm) were aligned vertically in parallel, with the distance between two adjacent fibers of 15 mm, and driven by a rotating head. The vibration amplitude varied from 0 to 12 mm accurately, while the vibration frequency from 0 to 15 Hz. In a 4 g/L bentonite solution, experiments were conducted at both constants permeate flux and constant suction pressure conditions. In the constant permeate flux of 30 L/(m 2 • h), the fouling rate of 1.7 mm HFs was almost twice as in 2 mm HFs without oscillation. The fouling rate typically decreased when vibration was applied. There was an 85% reduction in the fouling rate when the 2 mm HFs vibrated with 5 mm amplitude and 5 Hz frequency, compared to no vibration. At constant suction pressure of -24 kPa, cake resistance implied that the larger fiber size could perform better in an oscillating system. As for the power consumption, 95% fouling reduction was observed with 8 mm amplitude and 10 Hz frequency, and consumed 16.6 W power. With the same setup, 21 W power was needed to achieve a 10% fouling reduction by 5 L/min bubbling rate [START_REF] Li | Fouling control of submerged hollow fibre membranes by vibrations[END_REF].

Oscillating spacers module

Rotating or oscillating membrane/filtration cell involves the movement of membrane cassette and permeates inside of the membrane module. It requires a relatively high mechanical energy and a complicated membrane module. The alternative of a lightweight spacer in turbulence promoter permits to minimize the energy consumption regarding oscillation.

A submerged flat sheet membrane filtration system with vibrating spacers was introduced by Nanyang Technological University (Singapore) [START_REF] Wu | Spacer vibration for fouling control of submerged flat sheet membranes[END_REF]. Two pieces of flat sheet membranes (8 cm×12 cm) with a total area of 70 cm 2 were mounted into a membrane module and then submerged into a tank. With a distance of 0.1 or 1 mm, both spacers were placed at each side of the membrane module and enabled to oscillate at 1-2.5 Hz (frequency) and 0.8-2 cm (amplitude). At a distance of 0.1 mm between the spacers and membrane, the hill-like spacers more efficiently alleviated membrane fouling than smooth and grooved spacers. The increase in vibration frequency and amplitude led to the reduction of fouling, but the threshold operation presented to be 2 Hz and 1.2 cm with a hill-like spacer. As expected, spacer vibration consumed significantly less power (<0.008 W/m 2 ) than gas sparging (5.7

W/m 2 ) under the comparable fouling control effectiveness [START_REF] Wu | Spacer vibration for fouling control of submerged flat sheet membranes[END_REF].

Oscillating and vibrating system

A vibrating system is not helpful for the permeate flux due to the compacting/cleaning effect during the back-and-forth movement of the membrane, and a pure vibrating system does not exist yet. By the oscillation or vibration of HF membranes, transverse or axial movements may lead to a variety of flux directions, which correspond to the combination of oscillating and vibrating modes. Five devices at a lab-scale were investigated.

The transverse vibrating hollow fiber membrane system was reported and compared with the case of oscillating liquid [START_REF] Kola | Application of low frequency transverse vibration on fouling limitation in submerged hollow fibre membranes[END_REF]. The former one was driven by the rotor to vibrate the hollow fiber membrane, with the displacement varying from 0.5 to 5 mm. Another one performed the circular movement of a container (liquid) with an eccentric axis (fixed radius:

2.5 mm) and a frequency of up to 2200 oscillations per minute (36.6 Hz). MF of 100mg/L alginate solution with 0.2 μm HF membrane resulted in the permeate flux of 70 L/(m 2 • h), increased to 105 L/(m 2 • h) with the aid of a liquid oscillation frequency of 6.7 Hz. However, this method was limited to small-scale applications. Oscillating transverse motion via vibrating membranes was expected to be more practical for large-scale applications. The critical flux of 4 g/L yeast solution with the transverse membrane vibrations (10.3 Hz, displacement 2.5 mm) was found to be 40 L/(m 2 h), while it was 35 L/(m 2 h) under the oscillating liquid (at 10 Hz, displacement 2.5 mm) [START_REF] Kola | Application of low frequency transverse vibration on fouling limitation in submerged hollow fibre membranes[END_REF]. In the separation and concentration of milk proteins with 0.04 μm PVDF HF membrane, Chai et al. [START_REF] Chai | Separation and concentration of milk proteins with a submerged membrane vibrational system[END_REF] summarized that the frequency of 10.3 Hz applied could fully reject the casein micelle and maintain very high transmission rates of whey proteins (α-LA and β-LG) and lactose.

Derived from the same institution (University of New South Wales, Australia), the axial vibration module was introduced [START_REF] Chai | Application of rotational vibration in a submerged hollow fibre membrane system for bioseparation of high concentration yeast suspensions[END_REF]. 32 hollow fiber membranes (total membrane area: 0.0131 m 2 ) were arranged in a tube-like shaft, immersed in a 6 L filtration column and held in place through a rod connected to an oscillation converter. This configuration allows the angular displacement to vary from 18.3° to 55°. Different yeast concentrations of 10, 100 and 200 g/L in MF had little effect on the permeate flux with the aid of oscillating or vibrating at 10.3 Hz. The critical flux was not sensitive to the packing density of HFs in the module but highly dependent on frequency [START_REF] Chai | Application of rotational vibration in a submerged hollow fibre membrane system for bioseparation of high concentration yeast suspensions[END_REF].

The same idea was also applied in another module. Two ends of the hollow fiber membrane were potted together to access the permeable channel, 7 fibers with a length of 10 cm, resulting in a total membrane area of approximately 45 cm 2 . Angular vibrations generated by the motor convertor worked with fixed angular displacement of 180°, and frequency controlled between 0 and 2 Hz. The results indicated the effects of angular vibrations on the fouling rate at the frequency of 2 Hz in the following order: algal cells (~97.4%) > debris (~93.6%) > intracellular organic matter (~81.8%) > extracellular organic matter (~52.3%). A poor effect was found on pore blocking due to a large portion of extracellular organic matter fouling [START_REF] Zhang | Algal fouling control in a hollow fiber module during ultrafiltration by angular vibrations[END_REF].

Zhejiang University (China) introduced a vibrated submerged HF membrane module that achieved two motion modes by adjusting the vibrating shaft. The membrane was moved from forth and back in axial (mode-1) or left to right (mode-2) displacement through a sine wave pattern. Membrane oscillation could be vertical or parallel to the module, respectively.

In the standard module (without oscillation), the steady-state membrane permeability was 3.27 L/(m 2 • h• bar), whereas mode-1 and mode-2 (optimal) were stabilized over 21 L/(m 2 • h• bar) at 20 rpm. Increasing the vibrating speed also helped reduce the permeability decline [START_REF] Qin | A submerged membrane bioreactor with pendulum type oscillation (PTO) for oily wastewater treatment: membrane permeability and fouling control[END_REF].

The San Bortolo Hospital (Italy) introduced the concept of mechanical vibration to the hollow fiber dialysis membrane system [START_REF] Kim | Computational modeling of effects of mechanical shaking on hemodynamics in hollow fibers[END_REF][START_REF] Kim | Enhancement of Solute Removal in a Hollow-Fiber Hemodialyzer by Mechanical Vibration[END_REF]. Four types of shaking models were established to increase the shear rate at the membrane surface: i) longitudinal shaking produced the reverse flow in the central and peripheral region of a single hollow fiber; ii) transverse shaking developed a symmetric swirling to shaking direction and spiral flow path lines; iii) rotational shaking to longitudinal axis also developed symmetric swirling flow regimes inside the HF, but the local shear rate presented non-uniform distribution in the radial position of HF bundle; and iv) rotational shaking to the centroid resulted in lengthwise nonuniform hemodynamic enhancement and reached the maximum at the inlet and outlet [START_REF] Kim | Computational modeling of effects of mechanical shaking on hemodynamics in hollow fibers[END_REF].

Characterization of fluid flow in dynamic filtration

It is well known that the principle of dynamic filtration consists of creating relative motion between the membrane and its housing to generate a high shear rate at the membrane surface and/or oscillating flows. Among the advantages of DF devices, the ability to generate a high shear rate independently of the feed flow, the preservation of a high membrane permeability associated with the filtration at low TMP, and the reduction of the filtration loop volume can be highlighted. Combining all these factors limits the fouling propensity and compressibility at the membrane surface [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF][START_REF] Zhang | Investigation of membrane fouling mechanisms using blocking models in the case of shear-enhanced ultrafiltration[END_REF][START_REF] Bouzerar | Local permeate flux-shear-pressure relationships in a rotating disk microfiltration module: implications for global performance[END_REF][START_REF] Bouzerar | Concentration of mineral suspensions and industrial effluents using a rotating disk dynamic filtration module[END_REF][START_REF] Espina | Comparison of rotating ceramic membranes and polymeric membranes in fractionation of milk proteins by microfiltration[END_REF][START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF]], which appears as major advantages for UF and MF, especially for the filtration of biological matrices. Film theory stands as the most common theoretical approach to describe permeation flux independently of pressure for mass transfer limited system. As can be seen, the hydraulic diameter dh is equal to the outer diameter of the tube minus inner diameter (do: outer diameter; di: inner diameter) for an annulus tube in Eq. (II.3).

According to the different operating conditions, the velocity scale can be defined using flowrate Q, see Eqs. (II.1) and (II.2). However, when this annulus coaxial cylinder was fed by axial flow, it can be defined as the axial velocity [START_REF] Park | A study on dynamic separation of silica slurry using a rotating membrane filter 1. Experiments and filtrate fluxes[END_REF][START_REF] Chandrasekhar | The stability of spiral flow between rotating cylinders[END_REF].

In the rotating system, the Reynolds number is calculated from the angular velocity ω as 𝑅𝑒 = (𝜌𝜔𝑟 2 )/𝜇 or by mixing rate N as shown in Eq. (II.5). But in practical applications, angular velocity should be replaced by kω considering the transmission of impeller velocity to the fluid. Reynolds number induced by rotating disk/impeller is described by Eq. (II. 6). An axial Reynolds number of a rotating conical rotor system was given as Eq. (II.7), where the rotor height h and the inclination angle α were taken into account [START_REF] Vogel | Controlled shear filtration: A novel technique for animal cell separation[END_REF][START_REF] Francis | Optimizing the rotor design for controlled-shear affinity filtration using computational fluid dynamics[END_REF]. And Reynolds number can be expressed as a reverse of the Ekman number Ek as Eq. (II.8) shows. Ekman number characterizes the ratio of viscous drag forces in a fluid to the Coriolis forces [START_REF] Cé Bron | Tidal instability in a rotating and differentially heated ellipsoidal shell[END_REF].

Four different flow patterns of rotating disk in a housing system were proposed by researchers [START_REF] Bentzen | Analytical and numerical modelling of Newtonian and non-Newtonian liquid in a rotational cross-flow MBR[END_REF][START_REF] Lee | Microfiltration of recombinant yeast cells using a rotating disk dynamic filtration system[END_REF]: Rer is radial Reynolds number, z/Rm refers to the gap ratio (z is the distance between rotor and membrane, Rm is the radius of the rotor). With a flowrate equal to zero, four flow regimes (Table II.8) may appear in the filtration cell, and they have been described by [START_REF] Murkes | Crossflow filtration: Theory and practice[END_REF] [237]: Laminar regime I correspond to a small gap with Couette flow and pressure gradient.

When it comes to laminar regime II, the gap is more critical, and limiting layers are developing at stator and rotor surfaces. Close to the rotor, centrifugal forces eject the fluid outwardly compared to the shaft, whereas, at the membrane surface (stator), radial velocity induced centripetal forces concerning the continuity equation. The thickness of the limiting layer on the stator surface is theoretically four times higher than on the stator for an infinite disk. With this theory, limiting layers are separated in turbulent regime IV.

In the oscillating system, the flow is governed by various parameters (oscillation frequency, amplitude, gap). This system was early studied by Rosenblat [START_REF] Rosenblat | Flow between torsionally oscillating disks[END_REF], who used two parallel infinite plane disks, oscillate torsional driven by a common axis for a Newtonian fluid. The Reynolds number is defined as a function of oscillation frequency F and the distance between disks, shown as Eq. (II.9). It has been applied to a commercial VSEP system, and a Reynolds number could reach 3×10 5 [START_REF] Akoum | An hydrodynamic investigation of microfiltration and ultrafiltration in a vibrating membrane module[END_REF][START_REF] Slater | Shear-enhanced microfiltration of microalgae in a vibrating membrane module[END_REF].

Taylor number

The flow between two concentric cylinders with the inner one is rotating, and an axial flow in the annulus cylinder. Due to the shear generated by the rotation, inertial forces tend to

𝑣

. Ta <42, the flow is in laminar regime. Further increase the rotation speed, Taylor vortices start to form, and these vortices increase until 400 (as described in the transition zone) [START_REF] Mori | Rheological measurements of sewage sludge for various solids concentrations and geometry[END_REF]. When the Taylor number is above 400, these vortices degenerate into fully developed turbulent flow. with 𝛾 = 8𝑢/𝑑 ℎ .

In turbulent regime (Dittus-Boelter's equation): 𝑆ℎ = 0.023𝑅𝑒 0.80 𝑆𝑐 1/3 with Re>10000.

In an agitated cylindrical vessel, Colton [START_REF] Colton | Permeability and transport studies in batch and flow dialyzers with applications to hemodialysis[END_REF] has proposed the following correlation: In laminar boundary layer, 8000 < In a continuous process, the friction curve represents Darcy's number, Da (Eq. (II.12)) against Reynolds number, ReQ (Eq. (II.11)). This curve predicts the frictional energy loss in a pipe or equivalent pipe based on the geometrical properties, fluid characteristics and operating conditions. The friction curve can be described using a unique expression (Eq. (II.13)) based on Churchill's model [START_REF] Manon | On-line rheology of cell cultures in a bioreactor[END_REF]. This general expression can be used for laminar, transitory or turbulent flow regimes.

𝑅𝑒 𝑄 = 𝜌𝑢𝑑 ℎ 𝜇 = 2𝜌𝑄 𝜇𝜋𝑑 ℎ (II.11) 𝐷𝑎 = 8𝜏 𝑝 𝜌𝑢 2 = Δ𝑝𝑑 ℎ 4𝐿𝜌𝑢 2 (II.

Radial pressure

The impact of additional pressure due to mixing was studied previously [START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF][START_REF] Fillaudeau | Investigation of rotating and vibrating filtration for clarification of rough beer[END_REF][START_REF] Rayess | Wine clarification with Rotating and Vibrating Filtration (RVF): Investigation of the impact of membrane material, wine composition and operating conditions[END_REF]. Bouzerar et al. [START_REF] Jaffrin | A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems[END_REF][START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF][START_REF] Hoek | Influence of Crossflow Membrane Filter Geometry and Shear Rate on Colloidal Fouling in Reverse Osmosis and Nanofiltration Separations[END_REF] indicated that in the core fluid layer, fluid velocity could be calculated by•2 kN, where k is the core velocity coefficient inferior to 1. The core velocity coefficient highly depends on system geometry, such as the configuration of the mixer, the distance from the mixer to the membrane. Therefore, the radial pressure gradient in the core layer can be expressed by: 𝜕𝑝 𝜕𝑟 = 𝜌𝑟(2𝜋𝑘𝑁) 2 (II.15)

𝑝(𝑟) = 𝑝 0 + 𝜌𝑔𝑧(𝑟) + 2𝜌(𝑘𝜋𝑁) 2 𝑟 2 (II. 16
)
where p is the pressure and R is the radius.

The pressure field is then obtained by the integration of Eq. (II.15), and achieved the mean additional pressure by Eq. (II.16) over the membrane area from R0 to Rmax. Due to the specification of impeller design [START_REF] Fillaudeau | Investigation of rotating and vibrating filtration for clarification of rough beer[END_REF], the hydrodynamic perturbation generated by this three-

µ 𝑝 𝑅 ℎ (II.18)
where Rh is the hydraulic resistance of the clean membrane. Transmembrane pressure can be expressed by 𝛥𝑃 = 𝑝(𝑟) -𝛥𝑃 𝑎𝑔 (𝑁, 𝑟).

TMP is related to the permeate flowrate in dynamic filtration. Fig. II.9 showed the linear relationship between the additional pressure induced by the rotating impeller with R 2 . The rotating disk equipped with 8 vans increases peripheral pressure in the filtration cell [START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF].

Fillaudeau et al. [START_REF] Fillaudeau | Investigation of rotating and vibrating filtration for clarification of rough beer[END_REF] have investigated the local pressure by replacing the membrane with radial permeable crowns in a rotating system. A 5 mm gap permits measurement of the radial pressure at the membrane surface. The final results agree with the empirical equation (Eq.

(II.15)) and almost share the same core velocity coefficient with the same configuration [START_REF] Fillaudeau | Investigation of rotating and vibrating filtration for clarification of rough beer[END_REF][START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF], indicating that the k value could help to estimate the local pressure. It means that local pressure is highly dependent on the configurations of devices and operating conditions.

Furthermore, many efforts (special-designed rotors [START_REF] Wu | Structural design of a rotating disk dynamic microfilter in improving filtration performance for fine particle removal[END_REF][START_REF] Hwang | Disk structure on the performance of a rotating-disk dynamic filter: A case study on microalgae microfiltration[END_REF][START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF], inserts [START_REF] Marke | Investigation of the velocity factor in a rotational dynamic microfiltration system[END_REF][START_REF] Meyer | High concentration of skim milk proteins by ultrafiltration: Characterisation of a dynamic membrane system with a rotating membrane in comparison with a spiral wound membrane[END_REF],

turbulence promoters [START_REF] Gomaa | Energetic consideration and flux characteristics of roughed-surface membrane in presence of reversing shear[END_REF][START_REF] Wu | Spacer vibration for fouling control of submerged flat sheet membranes[END_REF], and aeration [START_REF] Bilad | Harvesting microalgal biomass using a magnetically induced membrane vibration (MMV) system: filtration performance and energy consumption[END_REF]) focused on the improvement of shear stress by generating the disturbance of flow, which resulted in the variation of local pressure over time. The fluctuation of local pressure should be further investigated to reveal the benefits of non-stationary effects on the improvement of filtration.

Core velocity coefficient

Core velocity coefficient, k, the ratio of mean fluid velocity to impeller velocity, is one of the critical factors that present the mechanical efficiency of the rotating system as an indicator to quantify the mechanical efficiency. The k for different configurations of DF modules were displayed in Table II.9.

The flow between a stationary and a rotating disk system was early studied by Wilson et al. [START_REF] Wilson | Flow between a stationary and a rotating disk with suction[END_REF]. They proved that the flow pattern between these two disks was different. Radial flow close to the rotor was centrifugally outwards, and it was directly inwards close to the stator. Two cases had different boundary layers, and the suction effect reduced the thickness.

Then a concept of rotation rate was presented and equal to 0.3131 at Re=10 4 ; it characterized the fluid rotating at an angular velocity of 0.3131×2πN with the rotor rotating at 2πN.

Most people are likely to be interested in improving k by increasing surface roughness or modifying device configurations. The flow field between a stationary membrane and a rotating disk was studied by Bouzerar et al. [START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF]. The velocity coefficient was influenced by system geometry and configuration, to be 0.34 for a smooth flat disk, and rise to 0.62 for a flat disk equipped with vanes. Furthermore, this influence was further investigated by Brou et al. [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF] by modifying the distance of the disk to the membrane, and they found that the coefficient rises from 0.45 with the smooth disk in 17 mm gap to 0.65 in 15 mm gap for disk equipped with eight pairs of 2 mm thickness vanes. In addition, a disk equipped with more vans or vans with larger height but with the same gap between disk and membrane has been confirmed to be useful in increasing the core velocity coefficient. The disk has reached a larger k value (0.84) with eight pairs of 6 mm thickness vanes [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF][START_REF] Ding | High shear skim milk ultrafiltration using rotating disk filtration systems[END_REF]. As for another rotor, a three-blade impeller in a 3 mm rotor-to-membrane gap has been performed in the RVF module with k equal to 0.71 [START_REF] Fillaudeau | Investigation of rotating and vibrating filtration for clarification of rough beer[END_REF]. [START_REF] Xie | Local hydrodynamic investigation by PIV and CFD within a Dynamic filtration unit under laminar flow[END_REF].

Among the different rotating systems, the ratio z/Rm was used to characterize the geometry of the DF module, where z is the minimal distance between the impeller or the disk (considering geometrical modification) and the membrane, Rm is the radius of the rotor. The lowest values in Zone 1 (k=0.3-0.5) and the enhanced mechanical efficiency in Zone 2 (k>0.5) were described by Xie et al. [START_REF] Xie | Local hydrodynamic investigation by PIV and CFD within a Dynamic filtration unit under laminar flow[END_REF].

Little researches are focused on the investigation of the core velocity coefficient in the laminar regime. Bentzen et al. [START_REF] Bentzen | Analytical and numerical modelling of Newtonian and non-Newtonian liquid in a rotational cross-flow MBR[END_REF] have conducted CFD simulations in laminar and turbulent regimes. They report k=0.8 (turbulent) and 0.9 (laminar) for a rotating cross-flow MBR installed with a plastic disk rotor (z/Rm=0.0357). These values are very close, which is unexpected for the laminar regime. In the RVF module (with a three blades impeller), the local flow was identified by PIV measurements and CFD simulation in the laminar regime, which provides a similar value of 0.3 and 0.35, respectively [START_REF] Xie | Local hydrodynamic investigation by PIV and CFD within a Dynamic filtration unit under laminar flow[END_REF].

Shear rate and shear stress

In dynamic filtration, separation efficiency and productivity are highly dependent on the selection of membrane types and materials. However, as mentioned previously, the shear rate is one of the crucial factors which can control membrane fouling and enhance permeate flux.

Some theoretical and semi-empirical mathematical models for calculating the shear rate in different systems are presented in this section.

In general, the shear rate between two disks can be estimated according to viscosity law, with the flow velocity, u and the gap, y:

γ = 𝑑𝑢 𝑑𝑦 (II.19)
Or by the shear stress, τ and the fluid viscosity, μ:

γ = 𝜏 𝜇 (II.20) 4

Oscillating systems

Azimuthal and axial oscillation are two strategies to reduce fouling by generating torsion or oscillating on the membrane. VSEP is a general module that has been largely reported.

Rosenblatt et al. early studied the flow between oscillating disks [START_REF] Rosenblat | Flow between torsionally oscillating disks[END_REF]. And Akoum et al.

[10] calculated the local shear rate on the membrane in a lab-scale VSEP system by Eq.

(II.34): where dr was the membrane displacement at radius r, R2 was the outer radius of the membrane, h was the gap between the disks, t was the operating times, F was oscillation frequency. The maximum shear rate occurred at the periphery (r=R2), which generated the maximum displacement d, and could be calculated by Eq. (II.36):

𝛾 𝑤 (𝑟, 𝑡) = 𝜕𝑉 𝜕𝑍 | 𝑧=0 = 𝜕𝑉 𝜕𝑍 | 𝑧=ℎ = 𝑟Ω ℎ √ 𝑅𝑒 2 𝐺(𝑡) (II.
𝛾 𝑤 𝑚𝑎𝑥 = 2 0.5 𝑑(𝜋𝐹) 1.5 𝑣 -0.5 (II.36)

Moreover, the mean value of the shear rate can be defined by computing the absolute value over a specific area. For example, the annular limited by inner radius R1 and outer radius R2, in this case, shown as Eq. (II.37).

𝛾̅ 𝑤 = 2 3/2 (𝑅 2 3 -𝑅 1 3 ) 3π𝑅 2 (𝑅 2 2 -𝑅 1 2 ) 𝛾 𝑤 𝑚𝑎𝑥 (II.37)
For the VSEP system [START_REF] Akoum | An hydrodynamic investigation of microfiltration and ultrafiltration in a vibrating membrane module[END_REF], the result showed that the maximum and mean shear rates at the membrane were 112000 and 37000 s -1 , respectively, with water at 20°C. These expressions were also used to estimate the maximum shear rates with Eq. (II.36) [START_REF] Akoum | Concentration of total milk proteins by high shear ultrafiltration in a vibrating membrane module[END_REF] and calculate the mean shear rate with Eq. (II.37) [START_REF] Akoum | Treatment of dairy process waters using a vibrating filtration system and NF and RO membranes[END_REF][START_REF] Al-Akoum | Casein micelles separation from skimmed milk using a VSEP dynamic filtration module[END_REF] in 45°C milk solution.

𝛾 𝑚𝑎𝑥 = 𝐴𝑤 1.5 2𝑣 0.5 (II.39)
As described in the oscillating rectangular membrane, AVM [START_REF] Zhao | Using axial vibration membrane process to mitigate membrane fouling and reject extracellular organic matter in microalgae harvesting[END_REF] stands as a typical system; the membrane moves horizontally in a direction parallel to them. The local shear rate is evenly distributed on the membrane surface, which could be expressed by Eq. (II.40):

𝛾 𝑤 (𝑡) = 𝑑(𝜋𝐹) 1.5 𝑣 -0.5 (cos(2𝜋𝐹𝑡) -sin(2𝜋𝐹𝑡)) (II.40)

Zhao et al. [START_REF] Zhao | Using axial vibration membrane process to mitigate membrane fouling and reject extracellular organic matter in microalgae harvesting[END_REF] found the shear decreased with the increment of distance to the membrane. At 10 Hz frequency and 1 cm amplitude, the shear rate induced by the oscillation membrane could be ignored and decreased from 4000 to 0 s -1 at a distance of about 1 mm.

Another similar device described by Su et al. [START_REF] Su | Concentration polarization and permeate flux variation in a vibration enhanced reverse osmosis membrane module[END_REF] achieved the oscillation frequency up to 50 Hz but with a lower amplitude (1.2 mm) in the desalination of simulated seawater. The membrane boundary shear rate was more than 6000 s -1 in this condition (Re=344).

Hollow fiber membranes are often applied in the oscillating system. The shear rate in this membrane module was calculated by Beier et al. [START_REF] Beier | Dynamic microfiltration with a vibrating hollow fiber membrane module: Filtration of yeast suspensions[END_REF]. They showed that the shear rates (Eq. (II.41)) at the membrane surface should be:

𝛾 𝑠 = 𝑣 0 √ 𝜔 2𝑣 [𝑠𝑖𝑛(𝜔𝑡) -𝑐𝑜𝑠(𝜔𝑡)] (II.41)
where ω was angular velocity (ω=2πf), v0 was the amplitude of velocity (v0=Aω, A was the peak-to-peak amplitude), t was time.

Based on this expression, a time mean average of shear rate was computed as Eq. (II.42).

At the frequency of 30 The maximum shear rate of these kinds of systems was compared as follows in Eq.

(II.43). The shear rate for VSEP (frequency 60 Hz, amplitude 30 mm) is 28-fold higher than the hollow membrane system (30 Hz, 3 mm) [START_REF] Jaffrin | Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems[END_REF]. It is 33-fold higher than the VERO system (50 Hz, 1.2 mm). But what we also need to take into consideration is the distribution of shear rate at the membrane surface. The shear rate in VSEP increases with a higher radius of the disk membrane, while the other two modules are uniformly distributed at the membrane surface.

Oscillating and vibrating systems

Except for oscillating parallel to the HF membrane, other forms of movement applied with the HF membrane would be classified into Oscillating and vibrating, where the motion is perpendicular to the fiber axis [START_REF] Kola | Application of low frequency transverse vibration on fouling limitation in submerged hollow fibre membranes[END_REF] or with a defined angle [START_REF] Qin | A submerged membrane bioreactor with pendulum type oscillation (PTO) for oily wastewater treatment: membrane permeability and fouling control[END_REF]. The shear force is cylindrically asymmetric around the fiber, and using a simple equation to describe it is not available.

Local approaches

Local velocity and shear stress

In the DF system, the complexity of the flow field is of course expected to improve filtration performances. It is promoted by different phenomena related to the specific geometrical configuration and the associated moving walls. Indeed, the flow pattern is not only time-dependent but also highly influenced by the different length scales that exist in the system. Moreover, the rheological behaviors of the fluid that can be non-Newtonian in some applications may also affect the flow field. Global and semi-local approaches to getting quantitative information on velocity, pressure and shear stress show their limitation in revealing what really happens in the system.

From an experimental point of view, recent optical measurement/visualization techniques are becoming more and more popular for accurate and reliable local measurements, resulting in the velocity field, concentration field, temperature field, etc.

Particle Image Velocimetry (PIV)/ Particle Tracking Velocimetry (PTV)

PIV allows the estimation of the velocity field by the average displacement of multiple small tracer particles in a given interval Δt. In comparison, PTV is developed in the case of low seeding densities to calculate the particle velocity by measuring the optical track length of the particle under a specific exposure time [START_REF] Adrian | Bibliography of Particle Image Velocimetry Using Imaging Methods: 1917-1995[END_REF][START_REF] Yoshizawa | Handbook of optical metrology: Principles and Applications[END_REF]. Typically, the tested device needs to have a good light transmission to ensure a better acquisition of particle images by laser light scattering. Trace particles seeded in the flow are assumed to move with the fluid without any velocity lag, fluorescent, polystyrene, silver-coated particle, or other reflective particles are used [START_REF] Yoshizawa | Handbook of optical metrology: Principles and Applications[END_REF]. Li et al. [START_REF] Li | Fouling control of submerged hollow fibre membranes by vibrations[END_REF] seeded 0.1 g/L particles with a diameter of 20 μm in the oscillating system to establish a velocity vector map; the data acquisition system was performed at 6Hz. In a rotating system, Xie et al. [START_REF] Xie | Local hydrodynamic investigation by PIV and CFD within a Dynamic filtration unit under laminar flow[END_REF][START_REF] Xie | Local hydrodynamics investigation within a dynamic filtration unit under laminar flow[END_REF] investigated the velocity fields in radial and vertical profiles with BREOX solution. They found that velocity is highly organized and stable within the filtration cell and is mainly governed by the impeller shape.

Molecular Tagging Velocimetry (MTV)

MTV determines the velocity field in fluid flow by tagging specific molecular instead of macroscopic particles as in PIV, and tracking its displacement by imaging twice. There are three optical ways to visualize these tagged molecules: fluorescence, phosphorescence and laser-induced fluorescence [START_REF] Gendrich | Molecular tagging velocimetry and other novel applications of a new phosphorescent supramolecule[END_REF]. This technology is achieved on a molecular basis to avoid the non-uniformed seeding and the impact of the suspended particle on the fluid itself.

Simultaneously, the capital cost would increase sharply for the complex experimental system [START_REF] Johnson | Handbook of fluid dynamics[END_REF].

Laser Doppler Velocimetry (LDV)

LDV, also known as Laser Doppler Anemometry (LDA), is one of the techniques of using the Doppler shift in a laser beam to measure the velocity in transparent or semitransparent fluid, or the linear or vibratory motion of opaque, reflecting, surfaces. The measurement with LDA is absolute, linear with speed, and requires no pre-calibration [START_REF] Cenedese | LDA and PIV velocity measurements in free jets[END_REF][START_REF] Drain | The laser Doppler technique[END_REF][START_REF] Kilander | Energy dissipation and macro instabilities in a stirred square tank investigated using an LE PIV approach and LDA measurements[END_REF]. But the drawbacks are the high precise optical arrangement and bothersome signal processing [START_REF] Yoshizawa | Handbook of optical metrology: Principles and Applications[END_REF]. Bentzen et al. [START_REF] Bentzen | Analytical and numerical modelling of Newtonian and non-Newtonian liquid in a rotational cross-flow MBR[END_REF] measured tangential velocity with the LDA system at the rotating speed between 50 and 350 rpm. Wall shear stress in 15 locations was achieved and indicated a good agreement with CFD simulation.

Electrochemical method

Electrochemical method is based on the redox reaction of the electrolyte combination.

The magnitude of the current was measured and derived from calculating the shear stress from the theoretical relationship. For most of these solutions, ferried and ferrocyanide is used as oxidizing and reducing ions, respectively [START_REF] Böhm | Application of the Electrodiffusion Method to Measure Wall Shear Stress: Integrating Theory and Practice[END_REF]. A reaction is conducted at high enough voltages to reduce the concentration of the reacting species to zero at the surface of the working electrode. Therefore, the reaction rate is controlled by the speed of mass transfer, which is directly related to the local shear stress. What should be concerned are the nonuniform flow across the probe and the response of the instrument to fluctuations in the velocity field [START_REF] Mitchell | A study of turbulence at a wall using an electrochemical wall shear-stress meter[END_REF][START_REF] Toyama | Development of Wearable Sheet-Type Shear Force Sensor and Measurement System that is Insusceptible to Temperature and Pressure[END_REF].

Computational Fluid Dynamics (CFD)

As an alternative to the experimental studies, Computational fluid dynamics can be used to solve mass and momentum balances governing equations for fluid flow, the so-called Navier-Stokes equations, to determine the velocity and pressure fields in the geometrical domain. It is of great use to replenish our knowledge about increasing the filtration performances without further experimental verification. Although attractive, this theoretical approach is often complicated to implement in particular to take into account the mobile walls of the domain and the turbulent flow regime, especially in the complex-geometries modules. Moreover, a proper calculation mesh should adapt to the geometry and the numerical method according to the specific problem [START_REF] Günther | Modeling the effect of packing density on filtration performances in hollow fiber microfiltration module: A spatial study of cake growth[END_REF][START_REF] Oxarango | Laminar flow in channels with wall suction or injection: a new model to study multi-channel filtration systems[END_REF][START_REF] Linkè | Numerical investigation of subgrid mixing effects on the calculation of biological reaction rates[END_REF]. In laminar flow, with a relatively lower mixing rate of 2 Hz in the RVF module, CFD simulation was in good agreement with PIV regarding velocity fields and profile [START_REF] Xie | Local hydrodynamic investigation by PIV and CFD within a Dynamic filtration unit under laminar flow[END_REF]. The simulated shear stress distributions indicated that the rotating speed and disk structure are the main factors affecting shear stress on the membrane surface [START_REF] Wu | Structural design of a rotating disk dynamic microfilter in improving filtration performance for fine particle removal[END_REF][START_REF] Hwang | Disk structure on the performance of a rotating-disk dynamic filter: A case study on microalgae microfiltration[END_REF]. For the requirement of uniform surface shear stress, CFD simulation was used to optimize the design of the rotor in a rotating system, which permits the same mean shear stress with relatively low rotation speed [START_REF] Francis | Optimizing the rotor design for controlled-shear affinity filtration using computational fluid dynamics[END_REF].

Discussion

Dynamic filtration permits to reduce fouling and concentration polarization thanks to high local shear stress generated by rotating, oscillating or vibrating movements. Various systems have been described and investigated, but no instruction or procedure helps engineers select a suitable DF module.

As for conventional filtration, engineers should previously define the specifications of the application, including objectives (separation, concentration), expected performances and operating limitations. Capital expenditure (CAPEX) and operational expenditure (OPEX) associated with DF modules should be evaluated in the business plan. For CAPEX (equipment, land, construction, etc.), production capacity and scaling should be known. For OPEX, the main cost will be associated with DF energy demand. In this last situation, several approaches can be proposed to estimate total power consumption.

Energy demand associated with DF module

Compared with cross-flow filtration, dynamic filtration shows great performance in fouling control with higher critical flux, which leads to longer filtration run between cleaning steps. However, the power consumption is much more delicate to estimate in DF modules than in the conventional ones (DEF, CFF).

The total power PT in the basic filtration unit includes mechanical power PM and pumping power PP (Eq. (II.44)). Energy consumption for the mixing, oscillating or vibrating movements is usually much higher than pumping energy. The driving force for filtration (TMP) is highly dependent on the filtration type: MF (0. Therefore, three strategies are described: i) the global approach (power consumption curves, friction curves), ii) semi-local empirical correlation estimating the mean shear stress and iii) local measurements (or simulation) of the velocity field.

For global approach, power consumption curves and friction curves (friction factor or Euler) can be determined for each module, as reported by Fillaudeau et al. [START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF] for RVF labscale module. With mixing Reynolds numbers ranging from 10 to 10 6 , semi-empirical dimensionless correlations were established. The power number was calculated with the global electrical power of the motor, and the mechanical power was estimated by subtracting consumed power without charge. They demonstrated that the power consumption curve was independent of the flowrate. On the opposite, the friction curve was strongly affected by mixing conditions and a semi-empirical correlation was established to take it into account.

For semi-local approach, the mechanical power could be estimated by the local shear stress, which has been presented in § 4.2. In the RDM module (rotating system, type 5), the mechanical power PM developed by friction force was given in Eq. (II.45) [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF]. τd and τdb are the shear stress on two sides of the disk (b: smooth backside); kd and kdb are the core velocity coefficients. Mechanical power was found to vary linearly with electric power (efficiency close to 0.39 for disks with vanes and 0.63 for smooth disks). Using Murkes and Carlson's equation (Table II.10, Eq. (II.27)), the turbulent shear stress was estimated. It implied that electrical power varied as ω 14/5 [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF], which was verified by Brou et al. [START_REF] Brou | Microfiltration and ultrafiltration of polysaccharides produced by fermentation using a rotating disk dynamic filtration system[END_REF]. In the SBM module [START_REF] Sarkar | Design and performance characterization of a new shear enhanced module with inbuilt cleaning arrangement[END_REF] (rotating system, type 2), with a different configuration, it was reported that electrical power was proportional to ω. In laboratory oscillating (type For local approach, Xie [START_REF] Xie | Investigation of local and global hydrodynamics of a dynamic filtration module (RVF technology) for intensification of industrial bioprocess[END_REF] has investigated the local shear stress with PIV measurements at the static walls in the RVF module (rotating system, type 6). Considering the angular momentum balance, the torque along the rotor is equal to the torque on the surrounded housing. The corresponding mechanical power was lower than those estimated with the power consumption curve, due to the non-uniform distribution of torque on the lateral/external walls. The contribution of periodic motions and turbulence needs to be considered.

Pumping power

In industrial applications, the pumping power is represented by the electric consumption (Eq. (II.47)) by knowing current (U) and tension (I). Mechanical power can also be estimated from the pressure difference between the inlet and outlet and the flow rate. In both filtration modes (Fig. II.11), the contribution of pumping will significantly differ.

𝑃 𝑃 = 𝑈𝐼 (II.47)

For single-pass continuous filtration, the power is calculated from feeding flowrate (Qf) and pressure difference with Eq. (II.48). It is equivalent to the pressure differences associated with permeate and retentate flowrate. Pin, Pout and P0 represent the inlet/outlet pressure of the DF module and the atmospheric pressure; Qr and Qp are the retentate and permeate flowrate.

By neglecting the pressure drop in the DF module, it could be assumed that (𝑃 𝑜𝑢𝑡 -𝑃 0 ) ≈ ∆𝑃. In NF and RO where TMP is maintained at high pressure (>10 bar), pumping power cannot be neglected. But these powers are still greatly reduced for the relatively lower feeding flowrate applied compared with conventional CF, which needs a high shear rate produced by a high feeding flowrate. In DF modules, the uncoupling of flowrate and local shear rate is ensured by mechanical power. Feeding flowrate should satisfy permeate and retentate concentration and volume reduction ratio. Consequently, pumping power can be drastically reduced up to a negligible contribution.

𝑃 𝑃 = 𝑄 𝑓 (𝑃 𝑖𝑛 -𝑃 0 ) ≈ 𝑄 𝑟 (𝑃 𝑜𝑢𝑡 -𝑃 0 ) + 𝑄 𝑝 ∆𝑃 (II.48)

For Feed & Bleed mode, the pumping power is equal to the sum of feed and circulation powers associated with Qf and Qc, given in Eq. (II.49). In conventional filtration, this configuration enables uncouples of the feeding and circulation flowrate. Consequently, the pumping power can be significantly reduced for the high-pressure filtration process (NF, RO).

With the DF module, this configuration will be simplified by eliminating the circulation pump. Feed & Bleed mode will have a negligible interest except if a pre-concentration of the fluid is used. The knowledge of the friction curves is required to estimate the pressure loss within the DF module [START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF]. However, the pumping power (feed) is expected to be lower than in a single-pass configuration.

𝑃 𝑃 = 𝑄 𝑓 (𝑃 𝑜𝑢𝑡 -𝑃 0 ) + 𝑄 𝑐 (𝑃 𝑖𝑛 -𝑃 𝑜𝑢𝑡 ) (II.49)

Luo et al. [START_REF] Luo | Application of NF-RDM (nanofiltration rotating disk membrane) module under extreme hydraulic conditions for the treatment of dairy wastewater[END_REF] proposed a linear relationship between pumping power and TMP, within the range of 0 to 40 bar, Pin-P0 would approximate the transmembrane pressure in the openloop when neglecting the pressure drop of DF. In the UF of PEG 6000 with SBM, the retentate flowrate was fixed at 10 -4 m 3 /s, but the maximum permeate flowrate was 8×10 -7 m 3 /s, which is negligible in comparison with the retentate flow [START_REF] Sarkar | Design and performance characterization of a new shear enhanced module with inbuilt cleaning arrangement[END_REF]. These limited permeate flux would reduce the output of the feeding pump, especially in configuration (b) in Fig. II.11.

Specific energy demand

Specific energy demand, E (Eq. (II.50)) is defined as the total energetic consumption per m 3 of permeate, equal to the ratio between total power and permeate flowrate. The total power is supposed to be the sum of pumping and mechanical power previously discussed.

But in most publications, the pumping power is negligible or a very low concern in MF and UF. It could be ignored compared with mechanical power, as demonstrated in the RDM module for mixing rates up to 2000 rpm [START_REF] Luo | Application of NF-RDM (nanofiltration rotating disk membrane) module under extreme hydraulic conditions for the treatment of dairy wastewater[END_REF]. For several rotating and oscillating DF modules (MSD, RDM, VSEP, VHFM), membrane type (NF, MF, UF with polymeric and ceramic membranes) and experimental fluids, Zsirai et al. [START_REF] Zsirai | The impact of mechanical shear on membrane flux and energy demand[END_REF] demonstrated that permeate steady-state flux increased as a power law of shear rate, 𝐽 = 𝑘𝛾 𝑛 with 0.186<n<1.560 and 0.00003<k<6.7. The empirical correlation of 𝑛 = (1.98 -𝑙𝑜𝑔𝑘)/5.04 was fitting well except for the high viscosity liquid and nonuniform shear rate distributed in MSD. However, confusion remains between the mean and maximal shear rates being applied.

𝐸 = 𝑃

In rotating RDM modules, since the maximum shear rate was proportional to ω 9/5 (Eqs.

(II.27) and (II.28)), and permeate flux increased as a power law of maximum shear rate, γmax with an exponent of 0.5-1 [START_REF] Jaffrin | Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems[END_REF][START_REF] Jaffrin | A hydrodynamic comparison between rotating disk and vibratory dynamic filtration systems[END_REF][START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF][START_REF] Ding | Milk protein concentration by ultrafiltration with rotating disk modules[END_REF][START_REF] Akoum | Recovery of trypsin inhibitor and soy milk protein concentration by dynamic filtration[END_REF][START_REF] Ding | High shear skim milk ultrafiltration using rotating disk filtration systems[END_REF][START_REF] Akoum | Recovery of trypsin inhibitor by soy milk ultrafiltration using a rotating disk system[END_REF]. Then the specific energy demand can be easily estimated knowing the mechanical power and the steady-state flux, indicating that E is proportional to ω 1-1.9 . In the concentration of skim milk with NF membrane, operating conditions at 2000 rpm and extreme TMP (40 bar) resulted in the lowest mean specific energy demand, around 170 kWh/m 3 . In comparison, it increased up to 303 kWh/m 3 under 1000 rpm and 40 bar [START_REF] Luo | Application of NF-RDM (nanofiltration rotating disk membrane) module under extreme hydraulic conditions for the treatment of dairy wastewater[END_REF]. The same fluid was tested by Ding et al. [START_REF] Ding | High shear skim milk ultrafiltration using rotating disk filtration systems[END_REF] in UF, and specific energy demand increased from 30 kWh/m 3 with smooth disk up to 65 kWh/m 3 with disk equipped with vans. In MSD, a solution of 200 g/L CaCO3 was filtered at 3 bar TMP. The maximum specific energy consumption was 2.9 kWh/m 3 for the nylon membranes and 1.7 kWh/m 3 for the ceramic ones [START_REF] Tu | Microfiltration of mineral suspensions using a MSD module with rotating ceramic and polymeric membranes[END_REF].

In the oscillating VSEP (type 9) system, Frappart et al. [START_REF] Frappart | Reverse osmosis of diluted skim milk: Comparison of results obtained from vibratory and rotating disk modules[END_REF] estimated the power consumed by the oscillation of the module at 60.2 Hz (amplitude: 2.5 cm). Specific energy demand was evaluated at 1.63 kWh/m 3 by assuming a permeate flux equal to 55 L/(m 2 • h).

With defined operating conditions (Qp=8.42 m 3 /h, S=151 m 2 , TMP=1500 kPa and F=60.4

Hz), the power demand for the oscillation and pumping are 8.83 kW and 6.58 kW, respectively. The estimated specific energy demand was below 1 kWh/m 3 for oscillating [START_REF] Akoum | Concentration of total milk proteins by high shear ultrafiltration in a vibrating membrane module[END_REF]. Gomaa et al. [START_REF] Gomaa | Energetic consideration and flux characteristics of roughed-surface membrane in presence of reversing shear[END_REF] compared the specific energy consumption based on low and highefficiency power recovery of 20% and 80% with the oscillating membrane (type 11); they were 0.3 kWh/m 3 and 0.1 kWh/m 3 at the highest frequency (25 Hz), respectively. In the VERO module (type 10), equipped with a small membrane area of 0.006 m 2 for desalination, the estimated specific energy demand was in the order of 10 3 kWh/m 3 .

In oscillating and vibrating systems, Kola et al. [START_REF] Kola | Application of low frequency transverse vibration on fouling limitation in submerged hollow fibre membranes[END_REF] investigated the energy consumption in terms of productivity in a linear transverse vibration HF system (type 15)

with the vibration frequency at 3.7 Hz and displacement of 2.5 mm for 0.04 μm PVDF membrane. The specific energy consumption for oscillation and vibration was around 0.0009 kWh/m 3 at permeate flux of 30 L/(m 2 • h). It increased to 0.20 kWh/m 3 at the same permeate flux for the highest frequency of 21.8 Hz and 2.5 mm displacement.

In conclusion, specific energy demand can be estimated if information about power consumption and permeate flux are known. However, the different configurations and scales do not allow the comparison of absolute values between different modules.

Specifications and decision tree for DF application

Dynamic filtration is a reliable alternative to the dead-end and the cross-flow filtrations as reported in the present documents. Their performances are associated with complex flow patterns generating high and fluctuating local shear rates and pressure at the membrane surface.

Considering the 15 types of DF devices (corresponding to 55 known modules), the overarching aims propose to elaborate the main criteria for helping engineers to select a DF module or to identify the missing information about the DF module or fluid to be treated. The best choice for a given application will be driven by several basic questions:

➢ What is the limitation associated with the fluids?

➢ How to determine the operating conditions?

➢ What should we know about dynamic filtration equipment?

A framework (Fig. II.12) is proposed with criteria operating conditions and knowledge barriers in DF application, which would help to select a module with available information and identify the missing knowledge.

Fig. II.12 Main criteria and knowledge gap in DF application

Firstly, basic information about nature, composition, physico-chemical properties of the fluid to be treated (ex. rheological behaviors, density, temperature, pH, particle size distribution, concentration) and the objectives of the process (concentration, purification or separation), as well as the production capacity and mode (volume, time, batch, continuous…), should be known. This information will help to select the filtration type (MF, UF, NF or RO)

and the membrane (cut-off and nature). Coupled with the limitation of fluid and DF module, the operating conditions can be defined in terms of steady-state/ critical flux, TMP, frequency/ amplitude and volume reduction ratio.

In the dynamic filtration module, the behaviors of experimental fluid under stringent hydrodynamics conditions should be investigated (ex. sensitivity to shear rate magnitude, temperature increase, mechanical degradation such as cell or particles…) before process design and scaling (filtration area, power consumption, acceptable operating conditions).

Meanwhile, the knowledge of local hydrodynamics (velocity, shear or pressure field), including maximum, average and time-dependent values, may enable to estimate performances as well as critical local operating conditions.

Finally, Table II.12 summarizes the empirical applicative and hydrodynamics data available for the 15 types of DF modules as discussed in § 3 and 4. It leads to highlight the knowledge gap for future scientific research and industrial applications.

P(x,y,z,t) CFD 1 X X X X X n.a n.a X X X n.a n.a X 2 X n.a X X n

Impeller configuration

Three impellers with two shapes of blades (shape 1 has increased surface area and 8 mm

Experimental set-up

The experimental set-up is displayed in

Data acquisitions

There are two types of data acquisition systems applied in our tests (Fig

Operating conditions and fluids

Water

Tap water was used as the model fluid in the turbulent regime. The basic information on thermal-physical properties and their thermal dependency were reported in the literature. At where a and b are concentration-dependent coefficients that can be represented by the concentration of BREOX, c is the temperature coefficient. Thus, heat capacity Cp can be presented as Eq (III.1). At the constant temperature (20 ℃), the viscosity 𝜇(20℃) is the function of concentration. The thermal dependent viscosity 𝜇(𝑇) is estimated using Eq (III.2).

Global investigation: friction and power consumption curve

For dynamic filtration devices, power consumption is the critical point that needs to be considered during practical work. The first case is the pumping power for the feeding fluid, which is the key element in cross-flow filtration. However, the mechanical power (rotating, oscillating and/or vibrating) is much more important than the pumping power in the dynamic filtration module. The energy consumption can be evaluated comprehensively by means of the empirical equations.

Raw data

For global measurement, the counter pressure is kept around 300 mbar, as shown in Fig.

Friction curve

From a global standpoint, RVF modules can be assimilated to a hydraulic singularity generating a pressure drop and as a mixing device. Linear pressure drops in the RVF module (ΔPRVF) are attributed to the friction loss, which can be expressed by Euler dimensionless number, Eu, given by Eq. (III.3).

T (s) 𝐸𝑢 = ∆𝑃 𝑅𝑉𝐹 1/2𝜌𝑢 2 (III.3)
where ΔPRVF is pressure drop, ρ is the fluid density, u is the velocity at the inlet of RVF module. The Reynolds number for feeding (Refeeding) and mixing (Remixing) are defined as follows:

𝑅𝑒 𝑓𝑒𝑒𝑑𝑖𝑛𝑔 = 𝜌𝑑𝑢 𝜇 (III.4) 𝑅𝑒 𝑚𝑖𝑥𝑖𝑛𝑔 = 𝜌𝑁𝑑 𝑖 2 𝜇 (III.5)
where d is the inlet diameter (12 mm), di is the diameter of the rotating impeller (135 mm), μ is dynamic viscosity, N represents the mixing rate of the impeller.

Power consumption curve

In the rotating system, the mixing power is highly affected by the configuration of the impeller sharp. In 1963, Bates et al. [START_REF] Bates | Examination of some geometric parameters of impeller power[END_REF] reported the power consumption curve in the baffled tanks with Newtonian fluids. The great changes of the Power number from laminar to turbulent regimes. In contrast with the RVF module, the impeller rotates within a narrow gap in order to generate high shear stress at the membrane surface, which needs further investigation.

Power consumption of the rotor is given by the current I and tension U of the motor. The electrical power needed to drive the shaft was measured without fluid, considered shaft loss (U0I0). Thus, the net power ΦN consumed by the rotating impeller is equal to the difference between total power and shaft losses [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF], as displayed in Eq. (III.6). It can be described by the Power number Np in Eq. (III.7).

𝛷 𝑁 = 𝑈𝐼 -𝑈 0 𝐼 0 (III.6)

𝑁𝑝 = 𝛷 𝑁 𝜌𝑁 3 𝑑 𝑖 5 (III.7)

Energy balance

For incompressible fluids, gravity is neglected. A non-slip condition is imposed on the walls, and the inlet speed profile is the same as the outlet profile. It gives:

∆𝑃 • 𝑄 + ∬ ∑ ∑ 𝜏 𝑖𝑓 𝑛 𝑖 𝑈 𝑗

Thermal power

We assume the uniform temperature at the inlet and outlet sections, the heat capacity (CP) is independent of T. Thus, the heat dissipation can be simplified by thermal power (ФT) during the insulation of the boundary walls:

Ф 𝑇 = ∭ 𝜌𝜀 𝑉 𝑑𝑣 𝐷 = 𝜌𝐶 𝑝 (𝑇 𝑖𝑛𝑙𝑒𝑡 -𝑇 𝑜𝑢𝑡𝑙𝑒𝑡 )𝑄 𝐹 (III.9)
where Tinlet and Toutlet are the inlet and outlet temperature, respectively, QF is the feeding flowrate.

Mechanical power

In the turbulent regime (Rer>3×10 5 ), the boundary layers merge together at a narrow gap (s=3 mm), and the local shear stress τ on the rotating disk in Eq. (III.10) illustrates the linear relation with N 1.75 [START_REF] Bouzerar | Concentration of ferric hydroxide suspensions in saline medium by dynamic cross-flow filtration[END_REF][START_REF] Bouzerar | Filtration dynamique dans un module plan à disque rotatif : Application à des suspensions miné rales[END_REF]. As mentioned by Brou et al. [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF], the mechanical power ΦM generated by the friction force on the plate disk is calculated by Eq. (III.11). R0 and Ri are the inner and outer radius of the impeller, respectively. 𝜏 = 0.008𝜌 0.75 (2𝜋𝑁 • 𝑟) In the laminar flow regime (Rer<3×10 5 ), the local shear rate is equal to the angular velocity divided by the gap. Thus, the mechanical power for a full disk system is shown as:

𝛷 𝑀 = 2 ∫ 2𝜏 𝑅 𝑖 𝑅 0 (2𝜋𝑁 • 𝑟)(2𝜋𝑟)𝑑𝑟 = 248 ( 𝜇 𝑠 ) (𝑅 𝑖 4 -𝑅 0 4 )𝑁 2 , s/Ri<0.05
𝛷 𝑀 = 1125μ 0.5 𝜌 0.5 𝑘 1.5 (𝑅 𝑖 4 -𝑅 0 4 )𝑁 2.5 , s/Ri≥0.05 (III.12)

Semi-local investigation: core velocity coefficient

Since the impeller is installed with a narrow gap to the membrane, assuming the inviscid core layer rotates at the mixing rate of N, it results in the angular velocity of 2πkN. According to Bernoulli's equation in Eq. (III.13) [START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF], the mean local pressure 𝑃 ̅ (𝑁, 𝑟) at the membrane surface equals the sum of P0 and ΔPmixing. P0 is the pressure at the centre of membrane or be given by the pressure when the absence of mixing, while ΔPmixing is the additional pressure driven by the rotating impeller.

𝑃 ̅ (𝑁, 𝑟) = 𝑃 0 + ∆𝑃 𝑚𝑖𝑥𝑖𝑛𝑔 = 𝑃 0 + 1 2 𝜌(𝑘 • 2𝜋𝑁) 2 𝑟 2 (III.13)
where r is the radius at the membrane surface. In the previous study, the local pressure was measured with the radial permeable crowns, and the mean values at the large gap (5 mm)

were overestimated [START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF]. In this study, using a pressure tap of 1 mm radius to measure the local pressure can be more accurate, and the number of measurement points is increased to 8.

It is yet important for the analysis of local k value.

Statistical analysis (SA)

The standard deviation of the signal has been widely accepted to quantify fluctuating

Probability distribution function (PDF)

Another method for obtaining the intensity of fluctuating pressure can be carried out with probability analysis. By subtracting the average pressure, the deviation signal is divided

Fast Fourier transform (FFT)

The Fast Fourier Transform decomposes a signal into a series of sinusoid waves to be analyzed and given by the frequency domain signal. It has been used to extract information about fluctuation (amplitude and frequency) from the time-series signal. Continuous and discrete Fourier transform can be represented by:

𝑃(𝑓) = ∫ 𝑃 ̃(𝑁, 𝑟, 𝑡)𝑒 -𝑗2𝜋𝑓𝑡 𝑑𝑡 +∞ -∞ ≈ ∑ 𝑃 ̃(𝑁, 𝑟, 𝑡 𝑖 )𝑒 -𝑗2𝜋𝑓𝑖 𝑚 𝑚-1 𝑖=0 , 𝑓 = 0,1, … , 𝑚 -1 (III.20)
where 𝑃 ̃(𝑁, 𝑟, 𝑡 𝑖 ) is the deviation of pressure at point i, f is the frequency. This formula is associated with the complex plane, composed of real and imaginary parts, and its amplitude (A) can be expressed as follows:

𝐴 = 2 𝑚 √𝑃 (

Reconstruction of PDF with periodic and random functions

The fluctuating signal consists of two parts: periodic and random contributions (Table III.6). The periodic signal can be simplified as a single sinusoidal fluctuation with f=3N, whose intensity is determined by the amplitude A. Since only one peak is considered, the A presented here is higher than the FFT amplitudes at the same frequency. The random signal conforms to a normal distribution with a zero mean, and σ denotes the standard deviation.

The energy input in each contribution is given by their root mean square (RMS). The fluid flows along the central shaft at the bottom and leaves at the upper end. We define the xy-axis parallel to the plane of the impeller and the z-axis along the direction of rotation.

On the other hand, the cylindrical coordinate is also defined in the geometry:  and r indicate the angular and radial components, respectively, and a along the shaft direction. The simulations are carried out under the following conditions:

• The flow is assumed to be periodic in the angular direction (sections 1 and 2);

• Periodic boundary conditions are also used at the inlet and outlet faces [START_REF] Daufin | Recent and Emerging Applications of Membrane Processes in the Food and Dairy Industry[END_REF][START_REF] Jaffrin | Dynamic shear-enhanced membrane filtration: A review of rotating disks, rotating membranes and vibrating systems[END_REF]. Here an average pressure gradient in the z-direction is imposed, which magnitude is adjusted to get the expected flowrate;

• A reference pressure constraint point at the outlet face ( 4) is set as the back pressure, Pb;

• A no-slip boundary condition is imposed at both walls: the velocity is zero at membrane surfaces [START_REF] Bentzen | Analytical and numerical modelling of Newtonian and non-Newtonian liquid in a rotational cross-flow MBR[END_REF] and cell walls (8), the velocity is equal to 2Nr in the  direction at both blade and shaft walls [START_REF] Xie | Investigation of Local and Global Hydrodynamics of a Dynamic Filtration Module (RVF Technology) for Intensification of Industrial Bioprocess[END_REF][START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF] to account for the rotation of the impeller.

Mesh

The so-called "normal" mesh (Fig.

Computational domain

In turbulence simulations, the solution of the flow field requires simplifying the computational model as much as possible. Due to the comparatively complex structure of Imp 1, it is difficult to converge even with a very fine mesh. Therefore, we simulate a 60° three-blade impeller instead, which shares the same surface area and impeller thickness as Imp 1. The computational domain was defined as one-third of the cell. In addition, we also simplified the rotating full disk, and a 10° (1/36) structure was used for the simulation.

Model

In laminar flow, the flow field is predicted by solving the steady-state N-S equations. As The standard k- model was employed to determine stationary turbulence flow. Thus, the transport equations for the turbulent kinetic energy (k) and its dissipation rate (ε) were solved.

Since the variation of the pressure is determined by the main fluid velocity, this turbulence model has been applied in the simulation of pressure at the membrane surface in RD modules [START_REF] Sarkar | Performance characterization and CFD analysis of a novel shear enhanced membrane module in ultrafiltration of Bovine Serum Albumin (BSA)[END_REF][START_REF] Sarkar | Performance characterization and design evaluation of spinning basket membrane (SBM) module using computational fluid dynamics (CFD)[END_REF][START_REF] Hoseini | Impeller shapeoptimization of stirred-tank reactor: CFD and fluid structure interaction analyses[END_REF]. Another two-equation model (k-) substitutes the turbulent kinetic energy dissipation rate () by ratio dissipation (), which is also available for solving the pressure in the RD modules [START_REF] Ladeg | CFD Simulation of the Distribution of Pressure and Shear Rate on the Surface of Rotating Membrane Equipped with Vanes for the Ultrafiltration of Dairy Effluent[END_REF][START_REF] Torras | Numerical simulation of the flow in a rotating disk filtration module[END_REF]. The wall function was used to approximate the flow field close to the wall for these two models, while the flow field of the viscous sublayer cannot be solved perfectly. Yu et al. [START_REF] Yu | Numerical investigation of tip clearance effects on propulsion performance and pressure fluctuation of a pump-jet propulsor[END_REF] used the shear-stress transport (SST) k- model to solve the pressure fluctuation in pump-jet propulsor. The mesh near the wall surface is enhanced and offers a superior resolution [START_REF] Marke | Investigation of the velocity factor in a rotational dynamic microfiltration system[END_REF]. That can be applied in the simulation of wall pressure and shear stress variation [START_REF] Bentzen | Analytical and numerical modelling of Newtonian and non-Newtonian liquid in a rotational cross-flow MBR[END_REF][START_REF] Ratkovich | Experimental and CFD simulation studies of wall shear stress for different impeller configurations and MBR activated sludge[END_REF].

Boundary conditions

In turbulent flow, the configuration of impeller and disk in the cell can be seen in Fig.

III.7. The boundary conditions are similar to those under laminar flow; only the inlet and outlet conditions are redefined:

• Inlet is imposed with constant normal phase velocity;

• Uniform outlet pressure is maintained at 300 mbar.

Mesh

Global investigations

Due to the presence of additional movement, the power consumption in RVF should be quantified, including pumping and mixing power. For industrial applications, it is useful to establish effective empirical equations for estimating energy consumption based on the operating conditions. In the turbulent regime, the pressure drop increase with the mixing rate and the feeding flowrate. By increasing the fluid viscosity, the pressure drop at lower mixing rate (<20 Hz) for BREOX 0.2 (0.05 Pa.s) higher than that of BREOX 0.1 (0.01 Pa.s). The opposite result is obtained when N is superior to 20 Hz. At high viscous fluid (BREOX 0.4, 0.6 Pa.s), a decrease of ΔPRVF can be observed with the mixing rate. This phenomenon indicates that the high shear force contributes to the flow of fluid through the RVF module.

Friction curve

At the process scale, the RVF module can be identified as a hydraulic singularity (generating pressure drop) or a confined mixing device (power consumption). The evolution of Euler number versus feeding (0. For process engineering and scaling, it appears useful to establish simple semi-empirical correlations to estimate the pressure drop and power consumption in such a module. By subtracting Eu(N=0 Hz), the Euler number increment is plotted as a function of mixing and feeding conditions in

Mixing power

In order to generate sufficient shear on the membrane surface, the mixing power is dominant compared to the pumping power. The power consumption curves can be established based on the mixing condition with Remixing ranging from 10 2 to 10 6 . proportional to N 2.9 , slightly higher than the exponent (N 2.75 ) estimated from the local shear stress [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF]. By increasing the viscosity, the regression of ФN versus mixing rate is presented in Fig. IV.5 b, with the exponent count decreasing to 1.9. This value is very close to the N 2 in the laminar regime (s/R<0.05).

Power consumption curve

Just like the mixing tank, the net power of the rotor can be estimated by the power consumption curve, as shown in

F N (W) N (Hz) a F N =0.0058N 2.9 , R 2 =0.9866 b BREOX 0.2-50 L/h BREOX 0.2-100 L/h BREOX 0.2-130 L/h BREOX 0.3-25 L/h BREOX 0.3-40 L/h BREOX 0.4-12 L/h BREOX 0.2 BREOX 0.3 BREOX 0.4 F N (W) N (Hz) F N =0.055N 2.5 , R 2 =0.9998 F N =0.17N 2.3 , R 2 =0.9996 F N =1.03N 1.9 ,

Thermal balance

The mechanical power is dissipated during the mixing of the impeller. If heat loss at the surrounding wall is not considered, the energy dissipation in the filtration cell is equal to the input power, which can be identified by the inlet and outlet temperature.

Thermal power

The thermal power ФT is shown in Fig. IV.8. For Imp 1 at 50 Hz, ФT increases by 30% at 300 L/h than 50 L/h, while these values are limited below 10% for Imp 2 and 3. The same phenomenon can be seen with BREOX 0.1, which shows more than a 45% of increase at 50

Hz. With the increase of viscosity, even at a very low flowrate (12 L/h), the thermal power increase dramatically. The numerical coefficient a by the regression of thermal power is In a turbulent regime (Fig. IV.9a), the boundary layers merge together in a narrow gap (3 mm), and the local shear stress τ on the rotating disk is the linear relation with N 1.75 [START_REF] Bouzerar | Concentration of ferric hydroxide suspensions in saline medium by dynamic cross-flow filtration[END_REF][START_REF] Bouzerar | Filtration dynamique dans un module plan à disque rotatif : Application à des suspensions miné rales[END_REF]. As mentioned by Brouet al. [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF], the mechanical power ΦM generated by the friction force on the plate disk is calculated. With this model, ΦM varies linearly with the nominal power, and it is underestimated by 22.7%. If the impeller surface area is considered, this ratio reduces to 11%. It demonstrates that the local shear stress on the blades only corresponds to a minor fraction of the torque. The major contribution of driving force contributes to the pressure difference between the leading and trailing edge of blades, which needs to be further investigated. In the laminar flow regime (Fig. IV.9b), the local shear stress is calculated using the classical model as Eq. (II. [START_REF] Wakeman | Experiments using electricity to prevent fouling in membrane filtration[END_REF]). However, the mechanical power is overestimated (119%) during the integration on a full disk. Thus, approximately 60% of power can be achieved at the blade surface. The pressure driving force on the leading and trailing edge is not considered.

F T =0.867F N R 2 =0.9824 b F M =1.185F N R 2 =0.9995 F T =0.569F N R 2 =0.9914 F T F M F T (W) F N (W)

❖ Summary of Global investigation Objectives:

(1) To evaluate the pumping and mixing power in the RVF module during different mixing conditions (flowrate QF and mixing rate N);

(2) To distinguish the flow pattern (laminar and turbulent regimes);

(3) To estimate power consumption (mixing, pumping and thermal power) with established empirical equations;

Contents:

(1) Pumping power

The effective pumping power can be estimated with feeding and mixing conditions. For high viscosity fluids, the rotation of the impeller can even reduce the pumping power; and as the viscosity decreases, the increase in speed is positive to the pumping power.

(2) Mixing power In the turbulent regime, the net power for the rotor indicates a linear with N 2.9 for both water and 10% BREOX solution. In comparison, the exponent of N reduces with the increase of viscosity due to the different boundary layers in the laminar regime. The feeding flowrate shows no effect on net power.

Compared with the mixing tank system, the relation between Np and Remixing in RVF shows the same shape. It illustrates that the transition from laminar to turbulent regime occurs at the Remixing around 30000. The constant values of Np for three impellers in the turbulent regime follow the order: Imp 1> Imp 2> Imp3.

(3) Thermal balance Due to the heat dissipation, the thermal increase of fluid should be considered in the biotic application. Properly increasing the flowrate or limiting the mixing rate contributes to the control of the fluid temperature.

After the integration of local shear stress with the empirical equations based on the merged boundary layer, the mechanical power shows a linear relation with net power. It indicates 22.7% and 118.5% of mechanical efficiency in the turbulent and the laminar regimes, respectively. The merged boundary layer theory is not suitable in the RVF module due to the large gap between the two blades. On the other hand, thermal power also can be used to estimate net power. But the slope is higher in the turbulent than in the laminar regime.

Local pressure at the membrane surface

In RVF, TMP is another essential factor affecting membrane filtration in addition to local shear stress. According to Eq. (III.13), the TMP can be estimated with back pressure and mixing conditions during the rotation of the impeller. The additional pressure is the function of the mixing rate, indicating a linear with N 2 . In microfiltration, TMP can be maintained at very low values (~100 mbar), and then high-pressure fluctuation (same order of magnitude as TMP), as an additional component, could contribute to surface cake layer and internal reversible fouling destabilization. The local pressures include the mean and fluctuating components at the membrane surface were measured at different radii (26.2-64.9 mm), mixing rates (0-50 Hz), flowrates (12-300 L/h) and viscosities (0.001-0.6 Pa.s).

Mean pressure

Mixing pressure

The mixing pressures as a function of mixing rates and radius are presented in Fig.

IV.10. In the global overview, it can be seen that Imp 1 and 2 generate the same level of additional pressure and are superior to Imp 3. In Fig. IV.11, with an increase in flowrate, the mixing pressure is slightly increased, whatever the laminar and turbulent regime. For the change in viscosity, the water mixing pressure was slightly higher than that of BREOX 0.1 below 40 Hz under turbulent conditions.

However, the mixing pressures of both were close at 50 Hz, probably due to the fact that the BREOX solution was then easily bubbled under high shear conditions. In the laminar regime, the viscosity increases from 0.05 to 0.6 Pa.s, and no visible distinction at mixing pressures below 20 Hz can be found. Above 20 Hz, a small decrease in mixing pressure can be noted as

Core velocity coefficient

Impeller geometry

In rotating systems, the angular velocity in the main fluid can be written as 2𝜋𝑘𝑁. As the tangential velocity is considered as the dominant component of the velocity vector, the additional pressure due to mixing can be approximated as the proportion of N 2 r 2 , i.e., the square of the tangential velocity component. Therefore, it appears that the value of k is larger than the actual value. in the annular cavity, the k value was overestimated using the mean radius. By the regression of mixing pressure at all the conditions (rotation frequencies and radii), Fig. IV.12 indicates the k follows the order: Imp 1>Imp 2>Imp 3 (0.65>0.63>0.56). It can be concluded that more blades and a larger surface area seem to increase the k value. Similar results can be found in the rotating disk with vans [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF][START_REF] Ding | High shear skim milk ultrafiltration using rotating disk filtration systems[END_REF].

Flowrate

The ideal conditions based on a full disk system assume that mean local velocity (horizontal) results from radial and tangential velocities, Ur(r) is determined by feeding flowrate and local cross-section, and Uθ(r) by mixing rate and core velocity coefficient. The horizontal velocity is shown as:

𝑈 𝑟𝜃 2 (𝑟) = (𝑘 𝑡ℎ𝑒𝑜 2𝜋𝑁𝑟) 2 + ( 𝑄 𝐹 2𝜋𝑟𝑠 ) 2 = (𝑘 𝑒𝑥𝑝 2𝜋𝑁𝑟) 2 (IV.1)
For example, during the circulation of water in the RVF module, the radial velocity at R1 is around 0.028 m/s at 50 L/h, and the impeller angular velocity is equal to 0.823 m/s at 5

Hz. Under this condition, the ratio between radial and angular velocities is limited to 3%. At the highest feeding flowrate (300 L/h), this ratio reaches more than 20%. It indicates that the contribution of feeding is more important with the lowest radii and mixing rates, as described by Eq. (IV.1).

Mixing rate

The mixing rate effect on the k values also can be explained by Eq. (IV.1). In a constant It can be found that at R5 and R7, the impeller rotation direction has no effect on the k value.

Curiously, at low radii (R2 and R4), the clockwise rotation of the impeller, its k-value is significantly higher than that with the counter-clockwise rotation. The effect of flowrate on k also can be observed at a lower radius during counter-clockwise rotation.

Viscosity

It is of interest to observe the variation of k-value when altering the viscosity of the fluid.

Instantaneous pressure

Data convergence

As preliminary verification, the evolutions of 𝑃 ̅ (𝑁, 𝑟), 𝜎 𝑃 , S and F as a function of sampling number in Fig. IV.17 demonstrate that statistical convergence of raw data is reached at m>1000. The sampling number m (2 15 ) may be sufficient to be analysed with the following methods. very different for each condition (N, r and impeller shape).

Interestingly, Imp 1 and 2 have similar steady pressure values, both higher than Imp 3.

In addition, the magnitudes of pressure fluctuations follow the order: Imp 1>Imp 3>Imp 2. In

Turbulent regime

The pressure fluctuation can be analyzed with SA, PDF, FFT and modeled to illustrate the fluctuating intensity and frequency of the signal. Same treatments are carried out to compare the fluctuations with three different impellers.

SA

The s P (mbar) Compared to the amplitude at 3N, there is an increase in the radius for Imp 1, even reaching up to 100 mbar at R8. Imp 3 also shows the same behaviour but with a lower amplitude.

R1 R2 R3 R4 R5 R6 R7 R8 Q F =50 L/h a b Q F =50 L/h R1 R2 R3 R4 R5 R6 R7 R8 c Q F =50 L/h R1 R2 R3 R4 R5 R6 R7 R8 d Q F =50 L/h β (/) N (Hz) R1 R2 R3 R4 R5 R6 R7 R8 e Q F =50 L/h N (Hz) R1 R2 R3 R4 R5 R6 R7 R8 f Q F =50 L/h N (Hz) R1 R2 R3 R4 R5 R6 R7 R8
Whereas the amplitude for Imp 2 is almost constant at all the radii. (IP, mbar), the fluid flow resonates under the periodic rotation of the impeller. On the membrane surface, the periodic pressure fluctuations evolve similarly to the response amplitude U() of a second-order linear system to a periodic input force 𝐹 = 𝐹 0 sin (𝜔𝑡) [START_REF] Kelly | Mechanical vibrations: theory and applications[END_REF], which follows the equation:

𝑈(𝜔) = 𝐺𝐹 0 √(1 -𝑠 2 ) 2 + (2𝜖𝑠) 2 (IV.2)
where 𝑠 = 𝜔 𝜔 0 ⁄ is the pulsation ratio. Here, we recognise the three parameters of the second-order system: G is the gain, 𝜔 0 is the intrinsic pulsation and 𝜖 the damping coefficient.

However, the input signal 𝐹′ = 𝐹 0 ωrsin (𝜔𝑡) varies as a function of 𝜔 and r in our system;

Eq. (IV.2) was then modified to obtain a new function 𝑈′(𝜔). It can be written as:

𝑈′(𝜔) = 𝐺𝐹 0 𝑟 2 𝑠 2 √(1 -𝑠 2 ) 2 + (2𝜖𝑠) 2 (IV.3)
With slight modifications, a new model based on mixing rate and local radius is proposed as in Eq. (IV.4); the corresponding resonance frequency (Nr) of the system is calculated using Eq. (IV.5). For the random signal, IR is found to be independent of the radius and to increase with the mixing rate slightly. Then a linear regression is used to approximate the variations of random intensity as a function of N, which give a 90% prediction band with IR±3.4 mbar.

𝐼 𝑅 = 0.21𝑁 + 4.8 (IV.6)

Comparison of fluctuating intensity

The signal reconstruction of instantaneous pressure can be seen in Table IV

Laminar regime

In the measuring range, the pressure fluctuations within the laminar flow conditions are much lower than those under the turbulent flow. Although the distribution of fluctuating pressure can be visually characterized by PDF, it is difficult to quantify their intensities. In this section, the pressure fluctuation in laminar flow conditions (BREOX 0.3) will be characterized by SA and FFT.

Modelling

Modelling and quantifying periodic and random contributions of fluctuating pressure have been determined by identifying their amplitude (A) and standard deviation (σ). In Fig.

IV.33a, the total energy evolves with radius (R1 to R8) and the mixing rate (5 to 30 Hz) is presented. Similar to the SA and FFT results, the total energy input is limited to less than 40 mbar, reaching a maximum of 35 mbar at 30 Hz, R5 and R8. Among them, the maximum value of the periodic pressure intensity is 24 mbar, which is higher than the random signal intensity of 13 mbar. (more than 50%) at higher radii (r>45.3 mm) and mixing rates (N>20 Hz).

Viscosity

SA

Fluid viscosity is also an important factor affecting the magnitude of pressure fluctuation.

According to statistical analysis, the standard deviation of pressure was plotted as a function (1) To decompose the local pressure into mixing and fluctuating components;

(2) To evaluate the impeller geometries and operating conditions (N, QF and μ) on local pressure;

(3) To compare the pressure fluctuation based on SA, PDF, FFT and modelling;

(4) To decompose and model the periodic and random intensities of pressure fluctuation.

Contents:

(1) Mean pressure (k values)

Mean pressure is a function of the k value, which is positive to the number of blades, impeller surface area, and feeding flowrate. The effect of flow on the k-value mainly occurs at the entrance of the filtration cell. The average value of k at R6 (Imp 2 and 3) or R7 (Imp 1) can be used to represent the whole cell.

(2) Instantaneous pressure (fluctuating components)

The analysis of instantaneous pressure indicates that the effect of flowrate and back pressure on pressure fluctuation can be neglected; the impeller shape and mixing rate shows to be the main factors. The results are divided into laminar and turbulent regimes.

Turbulent regime:

• The pressure fluctuations show periodic variations;

• The PDF of pressure displayed as unimodal to bimodal distribution;

• The periodic signal occurs at the frequencies of N, 2N, 3N (dominant), 4.25N, and 6N, and their intensity is dominant compared to the random intensity.

• Resonance frequencies were found to be around 20 Hz (water or BREOX 0.1 solution), resulting in a maximum pressure fluctuation of more than 100 mbar. Laminar regime:

• The pressure fluctuation is limited below 30 mbar and increases with the mixing rate;

• The periodic signal occurs at the frequencies of N, 2N, 3N (dominant), 4.25N, and 6N; their intensities constitute more than 50% at higher radii and mixing rates; The magnitude of pressure fluctuation is almost constant under the turbulent regime, while it drops with higher viscosity under the laminar regime.

CFD

The main purpose of CFD simulation is to study in detail the fluid flow within the filtration cell to interpret the performance changes arising from different operating conditions and parameters. The membrane filtration effectiveness depends on the TMP and shear magnitude. The trend of fluid velocity variation needs to be solved, thus helping to answer the pressure and shear fluctuations. to optimize the model, cell geometry, boundary conditions and mesh property. In the laminar regime, 1/3 and the full geometries of the cell have been compared based on the unstructured mesh, and the normal mesh is fine enough to model the pressure. The periodic flow (1/3 of the cell) is well solved for a full disk and a three blades impeller (60°blades). In the turbulent regime, different models have been compared to simulate the pressure. The full disk system has been realised to validate the pressure and velocity. While the simulation converged only in 1/3 of the cells (simplified 60° blades) due to the complex geometry. And we also compared the mesh of the boundary layer in order to get access to the local pressure at the membrane surface.

Laminar regime

In this study, a Newtonian fluid, BREOX solution with a viscosity ranging from 0.05 to 0.6 Pa.s, is assumed to be incompressible and independent of temperature. The back pressure and flowrate were fixed at constant values of 300 mbar and 25 L/h, respectively. The impeller mixing rate varied from 0 to 50 Hz so that the maximum Remixing could reach 18800, which in the laminar regime ( § 1.2). For the impact of impeller geometry on the flow fields (velocity, In order to determine the appropriate mesh size, physical-controlled meshes formed automatically with COMSOL from normal, fine to refine meshes with 299510, 694091 and 1617468 elements, respectively. Their tangential velocity along the z-axis, pressure and shear stress distribution at the membrane surface were compared in Fig. S 3. The finer meshes result in similar velocity, pressure and shear stress distributions to the normal one but take more time to converge. Thus, the simulations in the following part use the normal mesh to solve the fluid dynamics.

Validation of numerical simulation

In order to verify the reliability of COMSOL for the flow simulation within the RVF, we compared the fluid flow velocity and pressure obtained numerically with the experimental results, respectively. Table IV.5 presents the operating conditions for the validation. The velocity profile in the RVF module has been investigated with PIV technology in a previous study [START_REF] Xie | Investigation of Local and Global Hydrodynamics of a Dynamic Filtration Module (RVF Technology) for Intensification of Industrial Bioprocess[END_REF].

Local pressure

The effect of the operating conditions on the pressure variations has been clearly that σP is not increasing monotonically for Imp 1. When r is less than 45 mm, the σP value is limited to 50 mbar for both impellers, then followed by the increase with radius.

Viscosity

The viscous effects on local pressure are illustrated in Fig. IV.46. At R6, the mixing pressures show a minimum value with the viscosity around 0.2 Pa.s. After integration, k values for the laminar regime from 0.05 to 0.6 Pa.s are achieved as 0.69±0.03, which can be assumed as independent of viscosity. However, σP increases with the increasing viscosity, which is opposite to the experimental results. There are several potential explanations for this result: i) increase of temperature in the experiments due to high viscous dissipation, this phenomenon is non-uniform within the cell; ii) cavitation during the mixing that could significantly reduce the apparent viscosity; iii) formation of bubbles in the measuring tube that promotes wrong pressure measurements and iv) dumping effect in the cell as in turbulent regime. Thus, all these considerations appear to interpret the difference between experiments and numerical simulations.

Blades surface area

To compare the effect of impeller surface area on local pressure, Imp 4, already used in the previous section, is the fan-shaped three-blade impeller and has the same thickness (8 mm) as Imp 1. Here its blade surface area varied thanks to angle length, from 0° (no blade) to 120° The variations of ΔPmixing and σP with the angle length of the blades can be seen in Fig.

IV.48. As could be expected, when there are no blades, the additional pressure generated by the rotation of the shaft is small, only 30 mbar at 30 Hz and R6. The existence of the blades significantly increases the additional pressure. It is notable that the increase of the angle length from 20 ° to 75 ° does not significantly change the mixing pressure magnitude.

Asymptotic cases tend to exhibit a lower mixing pressure. At R6, the core velocity coefficient for each case is shown in Table S 1. Moreover, there are no obvious pressure fluctuations with 0° (no blades) and 120° (full disk) of blades. It is also shown that the ΔPmixing and σP strongly increased with the rotation of the impeller. It is found that σP does not vary between 20° and 30° angle length, then decreases with increasing angle length, i.e., blade surface area. At R6, the maximum ratio between σP and ΔPmixing is 22% during the mixing rates of 30 Hz.

If 300 mbar of back pressure is considered, the contribution of pressure fluctuation (10%) can be neglected.

Number of blades

The local pressure for different numbers of blades is investigated. Imp 4 is designed at a 30° angle length but with an increased number of blades, as shown in The impeller with four blades seems to induce the maximum mixing pressure, or we can say that there is a maximum k value. In a rotating disk system, Brou et al. found that a disk with eight vans (4 mm thickness) presents a large k value (0.71) than four vans (0.69) [START_REF] Brou | Dynamic microfiltration of yeast suspensions using rotating disks equipped with vanes[END_REF]. This result is opposite to the k value obtained from our rotating impeller system. There are two possible reasons for this result. One is that the fluid flow between the impellers is different than the one for a full disc, and the second is that the gap between the impeller and the membrane is smaller in the present study. The local k-value at R6 is presented in Table S 2. It is likely that σP is independent of k value and decreases with the number of blades. A twoblade impeller tends to be an optimal device regarding pressure fluctuations. The effect of the number of blades on the pressure fluctuation is also illustrated in Fig.

Local shear stress

It is commonly admitted that the shear stress at the membrane surface is one of the major factors affecting filtration performance. Thanks to the CFD approach, the local shear stress at the membrane surface can be achieved and then compared. In the rotating full disk system, the shear stress at the membrane surface is proportional to the mixing rate in a narrow gap. But this relation is not applicable to the rotating impeller the mean shear stress grows linearly with the radius, and this variation remains consistent with Eq. (II.20). However, at small radii (close to r=25 mm), the calculated shear stress is higher than the CFD simulation results. This may be explained by the sudden increase of the surface area at the inlet, where the fluid generates vortices in this region, and thus the velocity gradient decreases. It is also interesting to note that the calculated values of membrane surface shear stresses are overestimated at low mixing rates (N≤20 Hz) when r is close to the impeller edge. In comparison, the results are completely opposite at high mixing rates (N>20 Hz). As explained at the beginning of this section ( § 3.1.2), the boundary layers that exist at The linear relation between the local shear stress and 𝜌 0.5 𝜇 0.5 (2𝜋𝑘𝑁) 1.5 𝑟 was achieved in Fig. IV.59. When the average k value of 0.69 under laminar flow is used, the calculated slope is 0.96. This value is higher than 0.77, which was proposed in the full disk system and large gap [START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF]. . This means that a smaller gap is not only beneficial for the pressure effect but also creates higher shear stress. However, considering the accessibility of the device manufacturing, a gap of 3 mm seems to be the optimal value. This corresponds to the existing lab-scale RVF module.

Turbulent regime

According to the experiment, water is selected as the model fluid for the simulation in the turbulent regime. The fluid is assumed to be incompressible and independent of the temperature. A constant inlet flowrate (50 L/h) and a uniform outlet pressure (300 mbar) are imposed, and the mixing rate from 0 to 50 Hz is defined.

The convergence and accuracy of the simulation are highly dependent on the quality of the mesh. Considering the complexity of the impeller design, unstructured meshes are constructed based on free tetrahedra. With respect to the physics of turbulent flow, the boundary layers and local grids are both refined. In order to achieve the local stress at the membrane surface, y+<1 is recommended for the simulation. According to the equation:

y + = ρ𝑢 𝜏 𝑦 𝜇
, the velocity 𝑢 𝜏 can be expressed as √ 𝜏 𝑤 𝜌 (𝜏 𝑤 , wall shear stress). Thus, the first node over the membrane surface y at 0.005 mm would be appreciated to fulfil the requirement. This corresponds to the maximum y+ value being slightly higher than 1 (about 1.1).

To validate the model, the simulation results with rotating disk module have been compared with the publications. The structured mesh (Fig. S 7) generated with sweeping surface to simplified the simulation. validate the turbulent model (SST) with experimental data from Iron et al. [START_REF] Itoh | Experiments on turbulent flow due to an enclosed rotating disk[END_REF]. As shown in Fig. IV.66a, the numerical simulation of the angular velocity profile along the z-axis matches correctly at the radius of 0.8R but is slightly higher at 0.4R. This is mainly attributed to the simulation of the device (R=67.5 mm) being much smaller than the experimental one (R=250 mm). It can also be noticed that the location at 0.4R is close to the central part of the device.

Validation of numerical simulation

Another rotating disk module (s/R=0.127, Re=1.6×10 6 ) has been investigated with LDA technology [START_REF] Cheah | Experimental investigation of enclosed rotor-stator disk flows[END_REF], which is related to the gap of 8.6 mm in the RVF module. It can be seen in IV.68), the separation of the boundary layers is also noted, but the magnitude of the velocity at the same radius was lower than the one with the rotating impeller. This explains why the k value of the rotating full disk is lower. Another interesting phenomenon is that the symmetry of flow is lost in the rotating full disk, i.e., the velocity in the upper region (outlet side) of the disk is slightly higher than in the lower region (inlet side), which is not appeared during the feeding flowrate equals to 0. This is not the case if the physical problem is symmetric (neither inlet nor outlet, or without flowrate). On the contrary, it does not occur with the rotating impeller. ). This can also be explained as a result of the unique configuration of the impeller. As for the magnitude of shear stress fluctuation (σs), it is also similar to laminar flow.

However, its relative standard deviation is limited below 10%, which is smaller than that of laminar flow. Due to the limited experimental conditions and time, the CFD simulation is currently limited to 3 mixing rates. More works will be carried out to reconstruct the pressure and shear stress distribution at the membrane surface. In that case, the optimal impeller design will be developed to enhance the dynamic filtration performance. and 3). In the laminar regime, this resonance phenomenon was not observed due to the limitations of the experimental equipment. By using the CFD technique, the simulation is more flexible and can be operated with higher mixing rates and flowrates. The evolution of the fluid boundary layer is fully demonstrated during the rotation of the impeller. The pressure fluctuations at the membrane surface are independent of the feeding flowrate and back pressure. The effect of the mixing rate from the simulations is similar to the experimental measurements, while a divergence appears with viscosity. Based on the magnitude of pressure and shear stress (mean and fluctuating components), a 30° three-blade impeller has been selected. In the turbulent regime, the RANS-based Shear Stress Transport (SST) model has been validated with the rotating full disk system. The flow field induced by a rotating impeller (60° three-blade) was successfully solved. Thus, this model can be used for further optimization of the operating conditions and impeller geometries.

Answer to our initial scientific questions

Researches were dedicated to answering the scientific questions raised in the first part:

(1) How to estimate the global parameters (pumping and mechanical power)?

For global investigation, friction and power consumption curves in laminar and turbulent regimes have been completed and validated with different impeller configurations. The pumping power can be represented as the dimensionless Euler number by the feeding and mixing conditions. Similarly, the motor power can be estimated using the mixing Reynolds number. We also recorded the thermal increase of the RVF module, which allows for evaluating the heat dissipation of the fluid (thermal dissipation on the shell is not considered).

According to the empirical equations regarding the local shear stress, the mechanical power of the impeller can be approximated with the operating conditions.

(2) How to know the local and instantaneous pressure and shear stress, what are their intensity and frequency?

A specially designed porous substrate instrumentation was used to get access to the local and instantaneous pressure at the membrane surface, which provides more accurate measurements, including the mean and fluctuating components. However, the local shear stress was only achieved from the CFD simulation, and the experimental measurements will be implemented in future work.

In the laminar regime, the experimental and simulated local pressures exhibit similar results. The magnitude of the pressure fluctuation is relatively small (<30 mbar) and can be neglected when the TMP is higher than 300 mbar. In contrast, the shear stress increased with the mixing rate, and its fluctuations could reach more than 30%. The frequency of pressure and shear correlates with the number of blades.

In the turbulent regime, we found the resonance phenomenon of pressure fluctuations generated by Imp 1. The resonance frequency is about 20 Hz (water or BREOX 0.1 solution), thus, producing a maximum pressure fluctuation that exceeds more than 100 mbar. This is not negligible under low-pressure microfiltration conditions. This phenomenon was also found for Imp 3, but its pressure fluctuations were much smaller than those of Imp 1 due to decreased surface area and thickness. No significant resonance phenomenon was observed for Imp 2.

(3) What are the best operating conditions (flow regime, mixing rate, flowrate and back pressure)?

Optimal operating conditions not only contribute to lower energy consumption but also accelerate the membrane filtration process. Considering the mass and heat transfer process of low viscosity fluids, more dynamic membrane filtration is applied to dilute fluids (turbulent flow conditions). Therefore, pressure fluctuation is also a key parameter in intensifying filtration performance, especially for resonant frequency applications. Both flowrate and back pressure has been confirmed to show nothing to the local pressure and shear force, including mixing and fluctuating components. Generally, the flowrate in DF can be controlled at a low level as the shear stress is driven by the rotating impeller rather than the feeding flowrate.

Moreover, the back pressure is associated with the TMP, and the appropriate pressure value can be selected according to the filtration type and critical flux.

(4) What is the best filtration cell configuration (membrane/impeller gap and impeller geometry)?

In the laminar flow regime, CFD simulations were performed to obtain the best cell configuration. Based on local pressure and shear stress magnitudes, Imp 1 yielded similar results to the 60° three-blade impeller. Whereas the best impeller design is a 30° three-blade impeller for its high pressure, shear stress and their fluctuations. Reducing the membrane/impeller gap also helps to increase the k-value and shear stress due to the merged boundary layer.

In the turbulent regime, the instantaneous pressures generated by the three impellers were compared. Imp 1 and Imp 2 produced higher mixing pressures, while Imp 2 induced negligible fluctuating pressures. With the pressure fluctuations, resonance is observed for Imp 1 and Imp 3. Therefore, Imp 1 is the best configuration. Further simulation needs to be carried out to optimize the cell geometries.

(5) How do the mean/ fluctuating values of pressure and shear stress impact on filtration performance?

To answer this question, the instantaneous pressure and shear stress should be compared between the rotating impeller and full disk, which will be the future work. Of course, another similar structure may be able to answer this question. In the RD module, a rotating disk with vans yields higher permeate fluxes than a smooth disk, even at the same average shear rate.

(6) How do the microorganisms react to the increase in temperature and mechanical stress inside the filtration cell (cell lysis)?

There are several issues that need to be solved for this question, including RTD, thermal increase and tests in extreme conditions:

In the previous work, RTD was achieved to indicate the mean residence time is dependent on the feeding flowrate rather than the mixing rate in the laminar regime. However, in the turbulent flow regime, mean resistance time varies as a function of the mixing rate, independent of the feeding flow rate.

Due to the heat dissipation, the temperature inside the RVF will increase, which shows to be linear with N 2 . The microorganism will suffer a great thermal increase (more than 10 ℃ at 20 Hz) with high viscous fluid. The temperature can be limited by the increase of flowrate, decrease of viscosity and mixing rate, or by the installation of a cooling system.

Xiaomin has tested the E.coli cell suspension (Prokaryote) react on the extreme mixing conditions (50 Hz). The results indicate that cells were damaged and disrupted under the mechanical shear stress and appeared as clusters and aggregates. Another representative of yeast suspension (Eukaryote) also needs to be applied for the filtration test to acquire their biological behaviour with mixing.

Before selecting the appropriate filtration conditions, the interaction of cells with shear and temperature variations needs to be investigated.

Our highlights and perspectives

Based on the RVF module, as an example, the local hydrodynamic variation during the impeller rotation was investigated in a confined dynamic filtration chamber. It provides the basic and determinant information for bioprocess application. Several results from this PhD work can be highlighted:

(1) Extensive review of DF to raise main criteria and knowledge gap;

(2) Technical strategies and methods to acquire and then treat the time-series pressure;

(3) Investigate and interpret the local hydrodynamics in the RVF module;

(4) Identify pressure resonance phenomena and propose an empirical equation for estimating pressure fluctuations;

(5) Optimize the operating conditions and impeller geometries based on local pressure and shear magnitudes using the CFD approach.

This work provides a better fundamental knowledge for the characterization and the modelling of instantaneous pressure at the membrane surface in a DF module. It highlights the potential of pressure fluctuations as an additional driving force to intensify microfiltration.

Certainly, the identified "resonance phenomena" may not be limited to pressure but also to shear stress. To better utilize and interpret this phenomenon, future work related to DF will be focused on:

(1) Investigation of local and instantaneous shear stress at the membrane surface;

(2) Exploring the contribution of mean and fluctuating values of pressure and shear on filtration performance;

(3) Characterizing the flow field within the RVF under the turbulent regime and optimizing the cell geometries with the aid of the CFD approach;

(4) Extending the application of RVF to bioprocesses, which will involve more complex fluids and more limitations (thermal increase, cell lysis, membrane pore plugging, etc.).

Annexes

Figures:

Fig.

Tables:

Table S 1 Effect of blade surface area on core velocity coefficient.

Fig. I. 1 1 Fig. I. 2 4 Fig. II. 1 10 Fig. II. 2 16 Fig. II. 4

 11241102164 Fig. I.1 Schematic diagram of dynamic filtration module and their investigations. .................. 1 Fig. I.2 Scientific progress and investigation with RVF module. .............................................. 4 Fig. II.1 Comparison between Dead-end filtration (DEF), Cross-flow filtration (CFF) and dynamic filtration (DF). ........................................................................................................... 10 Fig. II.2 Number of publications and citations per year (Source: Core Collection-WoS (Thomson-Reuter), period: 1991 to 2020) ............................................................................... 14 Fig. II.3 Institution's cooperation network. ............................................................................. 16 Fig. II.4 Keywords co-occurrence network. ............................................................................ 17

Fig. II. 5 54 Fig. II. 9 74 Fig. III. 2 75 Fig. III. 3 76 Fig. III. 4 81 Fig. III. 5 90 Fig. III. 8 91 Fig. III. 9 92 Fig. IV. 1 95 Fig. IV. 2 96 Fig. IV. 3 96 Fig. IV. 4 98 Fig. IV. 7 99 Fig. IV. 8 100 Fig. IV. 9 153 AnnexesFig. S 1 180 Fig. S 2 180 Fig. S 3 181 Fig. S 4 181 Fig. S 5 182 Fig. S 6 182 Fig. S 7

 554974275376481590891992195296396498799810091531180218031814181518261827 Fig. II.5 Distribution map of keywords and nodes time-zone associated with DF. ................. 19 Fig. II.6 Application fields and filtration types associated with dynamic filtration. ............... 20 Fig. II.7 Friction curve established with RVF lab-scale module [6] ........................................ 54 Fig. II.8 Power consumption curve established with RVF lab-scale module [6]..................... 54 Fig. II.9 Determination of hydrodynamic performances, evolution of the radial pressure distribution versus the radius and the rotational speed [6] ...................................................... 56 Fig. II.10 Evolution of core velocity coefficient, 𝐾𝜃 as a function of gap-to-radius ratio, z/Rm. Values are reported from literature for DF modules using confined rotating impeller close to the membrane and established under laminar or turbulent regimes [8]. .................................. 58 Fig. II.11 Filtration modes, (a). Single-pass continuous filtration (b). Continuous filtration with partial retentate recycle (Feed & Bleed) .......................................................................... 66 Fig. II.12 Main criteria and knowledge gap in DF application ................................................ 71 Fig. III.1 Schematic diagram of Rotating and Vibrating Filtration module. (a) RVF module; (b) one dismantled filtration cell; (c) and (d) home designed and instrumented porous substrate for local pressure measurements; (e) configuration of filtration cell. ...................................... 74 Fig. III.2 Impeller configuration. ............................................................................................. 75 Fig. III.3 Experimental set-up. ................................................................................................. 76 Fig. III.4 Global measurement with water at 300 L/h and 40 Hz. ........................................... 81 Fig. III.5 The spectrum of instantaneous pressure and data treatment. (a) instantaneous and mean pressure; (b) fluctuating pressure and its standard deviation; (c) probability analysis at 5 and 20 Hz; (d) fluctuating pressure on frequency domain at 20 Hz. ....................................... 85 Fig. III.6 PDF at 20 Hz. Model reconstruction of PDF with periodic and random functions. 88 Fig. III.7 Schematic of RVF cell. (a) is the top view and (b) is the side view. ........................ 90

Fig. I. 1

 1 Fig. I.1 Schematic diagram of dynamic filtration module and their investigations.

Fig. I. 2

 2 Fig. I.2 Scientific progress and investigation with RVF module.

( 1 )( 2 )( 3 )( 4 )( 5 )( 6 )

 123456 How to estimate the global parameters (pumping and mechanical power) with operating conditions? How to know the local and instantaneous pressure and shear stress, what are their intensity and frequency? What are the best operating conditions (flow regime, mixing rates, flowrates and back pressure)? What are the best filtration cell configuration (membrane/impeller gap and impeller geometry)? How do the mean/ fluctuating values of pressure and shear stress impact on filtration performance? How do the microorganisms react to the increase in temperature and mechanical stress inside the filtration cell (cell lysis)? (7) How to enhance the filtration performance during bioprocess (flow regime, operating conditions and device configuration)? 3 Thesis structure PhD work aims to study the local and instantaneous pressure in RVF module to intensify industrial membrane bio-rector (MBR). The time series pressure due to the rotation of the impeller in the RVF is explored intensively using dedicated experiments. CFD simulations on one filter cell of the RVF are also performed. Once validated by experimental results, they are used to scrutinize the local hydrodynamics on a large range of parameters, not only for the pressure, but also for the local shear stress. This manuscript is structured by three main parts: i) an extensive review of DF; ii) methodological development and data treatment and iii) experimental results, data treatment, interpretation, and comparison with CFD simulation. ❖ Chapter Ⅱ: Bibliography (extensive review about dynamic filtration)This chapter provides an extensive review about industrial and laboratory dynamic filtration modules, scientific production, configurations and performances are analyzed and discussed. Firstly, a bibliography analysis of dynamic filtration was performed based on the WoS database; Secondly, all dynamic filtration devices from the lab, pilot to industrial scale were carefully described and classified; Then, an overview of the different methods and techniques to investigate the local hydrodynamics are introduced; Finally, a decision tree based on energy consumption and reported applications was proposed to highlight the knowledge gap for future scientific research and industrial applications.❖ Chapter Ⅲ: Materials and MethodsA dedicated methodology was developed by considering pressure evolution versus time and space associated with impeller shape and rotation. This chapter is devoted to (i) the description of experimental set-up and instrumentation, (ii) the presentation of experimental strategies and operating conditions, (iii) the explanation of data treatment from global to local approaches, and (iv) the construction of CFD model. Data treatment of pressure signals constitutes a challenging step in order to extract all components (mean, amplitude, frequency, periodic and random) through Statistical Analysis, Probability Distribution Function and Fast Fourier Transform, up to signal reconstruction. Finally, the methodology for CFD simulation (COMSOL Multiphysics) within RVF module is detailed in laminar and turbulent regimes.❖ Chapter Ⅳ: Results and DiscussionsThis chapter is dedicated to presenting and comparing the effects of operating parameters in the RVF module. The main scientific questions raised above are answered based on experimental results and CFD simulations. More details are given below:

Fig. II. 1 1 . 2

 112 Fig. II.1 Comparison between Dead-end filtration (DEF), Cross-flow filtration (CFF) and dynamic filtration (DF).

Fig. II. 3

 3 Fig. II.3 Institution's cooperation network.

  Fig. II.4 lists the co-occurrence network of high-frequency keywords (count≥3, representing more than 75% of total keywords) related to DF. Most of these keywords correspond to filtration types (microfiltration, ultrafiltration, nanofiltration and reverse osmosis), DF modules (rotating membrane, perforated disk, overlapping ceramic membrane, …), treated fluids (microalgae, dairy wastewater, biofuel, chicory juice, emulsion…), performances (permeate flux, critical flux, threshold flux, shear stress/ rate…).and CFD simulation.

Fig. II. 4

 4 Fig. II.4 Keywords co-occurrence network.

Fig. II. 5

 5 Fig. II.5 Distribution map of keywords and nodes time-zone associated with DF.

2. 2

 2 Fig. II.6 reports the main domain of DF applications and membrane separation types identified from 150 publications. DF is used in three main domains: Water treatment, Food processing and Bioprocess engineering.

Fig. II. 6

 6 Fig. II.6 Application fields and filtration types associated with dynamic filtration.

  used the zirconium dioxide ceramic MF membrane in HSR-MS to treat shipboard wastewaters (bilge water, blackwater and thermal destruction quench water). They changed different hub sizes resulting in various membrane diameters and different angular speeds of the membrane. For every 100 rpm increase in angular velocity, steady-state flux increased on average by 26 L/(h• m 2 ). While expanding the filter disk diameter also provides excellent performance per disk at a lower rotation speed and reduces the number of discs required.He et al.[START_REF] He | Experimental study of a dynamic filtration system with overlapping ceramic membranes and non-permeating disks rotating at independent speeds[END_REF] modified the configuration of MSD (2 shafts). Previously, each shaft equips with 6 ceramic membranes (0.2 μm). The permeate flux for 12 membranes was 520 L/(h• m 2 ) when filtering 200 g/L of CaCO3, while it was reduced to 503 L/(h• m 2 ) when working with 6 membranes. However, after replacing one of the ceramic membranes on each shaft with a smooth disk or a disk with 8 vans, the permeate flux was further improved to 740 or 816 L/(h• m 2 ), respectively. With the same module, Tu and Ding[START_REF] Tu | Microfiltration of mineral suspensions using a MSD module with rotating ceramic and polymeric membranes[END_REF] replaced the ceramic membrane with nylon membranes of the same size and pore diameter to concentrate CaCO3. Maximum permeate flux was observed for the nylon membrane to reach 850 L/(h• m 2 )

  used this system installed with the MF membrane to filtrate yeast suspension. Results showed no significant difference in flux with three different membranes (PVDF, 0.45 and 1.2 μm pore size for Nylon). Both Nylon membranes reached steady flux earlier than the PVDF membrane, at about 40 min. But 1.2 μm Nylon membrane performed better by 1.4 times higher than the 0.45 μm one according to their concentration factor profile. Moreover, compared with the conventional cross-flow system, steady flux and average shear rate of DMF were 100 L/(h• m 2 )

  modified the loop operation of the RDM module into the retentate recycling process (CRDM) and retentate non-recycling process (DRDM). At rotation speed of 1000 rpm, TMP of 3 bar for MF and 4 bar for UF, results indicated the least flux decline, smallest irreversible fouling and highest permeability recovery after membrane cleaning in CRDM, while DRDM obtained the best leaf protein rejection due to the secondary filtration effect. In the treatment of detergent wastewater, NF was performed after the pre-treatment in UF. The permeate flux in NF increased linearly with TMP to reach 450 L/(m 2 • h) at 40 bar at the rotation speed of 2000 rpm, while it reached a plateau at 350 L/(m 2 • h) above 35 bar without pre-treatment in UF. The rejection of conductivity and COD could be more than 90% when the TMP is up to 20 bar. Increasing feed pH (4.5 to 9.9) and temperature (25 to 45℃)

  , and were often compared to the other DF systems[11, 69, 75, 87, 97, 102, 103, 106-108, 113, 231]. The anti-fouling membrane filtration system (FMX) was produced by BKT Water & Energy (Korea), equipped with high-speed rotating vortex generators. They were veined discs and had two uneven and asymmetric surfaces. Standard class FMX-S and economic class FMX-E were proposed with a filtration area of 95 m 2 and 40 m 2 . In the pilot-scale, FMX-P compacted several membranes on the rotating shaft in series and reached the space between 0.0873 m 2 to 3.16 m 2 [188]. FMX-B only equipped one rotating disk of 145mm diameter and 10mm thickness in the filtration cell (20 mm height). Membrane (surface area of 0.0146 m 2 )

  3 mm thick porous walled cylinder (inner diameter of 25.8 mm) as the filter medium and rotating shaft of 19 mm diameter is placed within a 250 ml high-pressure and high-temperature cell. The mud sample sheared in the annulus formed between the inside diameter of the filter core and the rotating shear shaft. A ceramic filter (5-90 μm) was used in the MF of the drilling fluid. The experimental results fitted with the Boluk-Balavi equation, which could help evaluate the spurt loss volume, the initial rate of fluid volume loss (flux), blocking and cake erosion in DF [201].

3. 3 . 1

 31 Oscillating filtration cell modules3.3.1.1 Oscillating disk cellDisk membranes are placed on the support to permit the collection of permeate and filtration cells oscillated in the azimuthal direction to generate high shear stress. With this knowledge, 2 companies have designed 11 configurations in lab and industrial applications.Commercialized by New Logic (USA), vibratory shear enhanced processing (VSEP)[START_REF] Akoum | An hydrodynamic investigation of microfiltration and ultrafiltration in a vibrating membrane module[END_REF][START_REF] Hapońska | Application of ABS membranes in dynamic filtration for Chlorella sorokiniana dewatering[END_REF][START_REF] Wisniewski | Dynamic vibratory membrane processing for use in water recovery from soluble coffee product manufacturing wastewater[END_REF][START_REF] Takata | Structure of shear-enhanced flow on membrane surface with horizontal vibration and its effect on filtration performance[END_REF][START_REF] Al-Akoum | Casein micelles separation from skimmed milk using a VSEP dynamic filtration module[END_REF][START_REF] Akoum | Concentration of total milk proteins by high shear ultrafiltration in a vibrating membrane module[END_REF][START_REF] Lorente | Microalgae fractionation using steam explosion, dynamic and tangential cross-flow membrane filtration[END_REF][START_REF] Hapońska | Pilot scale dewatering of Chlorella sorokiniana and Dunaliella tertiolecta by sedimentation followed by dynamic filtration[END_REF][START_REF] Zouboulis | Treatment of Tannery Wastewater with Vibratory Shear-Enhanced Processing Membrane Filtration[END_REF] represented the first vibrating filtration device. These filtration bodies, consisting of alternative overlapping membranes or membrane-coated disks in series, are mounted on a torsion bar driven by a motor. It can reach 130 m 2 filtration area per module and scale up by installing more membrane modules. A similar principle was introduced in the vibrating membrane filtration module (PallSep-VMF)[START_REF] Postlethwaite | Flux and transmission characteristics of a vibrating microfiltration system operated at high biomass loading[END_REF]. Industrial VMF biotech modules were available in 0.2, 1 and 5 m² surface areas for more flexibility and easy scale up or scale down[205].

  A linear actuator was used to vibrate the RO membrane desalination cell at the given vibration curve shape, frequency, and amplitude. Feed solution enters from the left feed port at the top plate, flows into the membrane channel, and leaves the desalination cell through the retentate port on the other side of the top plate. The permeate flow is collected by the permeate carrier and flows out through the permeate ports at the bottom plate. The height of the feed channel is 0.78 mm and placed with a feed spacer, which is just above the flat rectangular membrane of 60 cm 2 (20 cm×3 cm) filtration area. With this module, Su et al.[START_REF] Su | Concentration polarization and permeate flux variation in a vibration enhanced reverse osmosis membrane module[END_REF] investigated the desalination of artificial seawater in 3 feeding flowrates related to Reynolds numbers 344, 516 and 688, respectively. Increasing in flowrates led to the decrease of NaCl and CaSO4 concentration polarization (CP) module without vibration, owing to the sweeping effect of flow. In the vibration cases, shear stress was further increased by the vibration; CP modules decreased when the frequency changed from 20 to 50 Hz. Periodic oscillations caused the fluctuation in normalized permeate flux; the higher the vibration frequency is, the higher the permeate flux.

4. 1 approaches 4 . 1 . 1

 1411 Global Dimensionless analysis4.1.1.1 Reynolds numberThe well-known Reynolds number, Re, is the most common number used in fluid mechanics to characterize the flow regime (laminar, transient or turbulent). It is defined as the ratio between the inertia forces and the viscous forces. For convenience, it is generally written in the form of a length scale, the so-called hydraulic diameter dh, a velocity scale u and the kinematic viscosity v of the fluid, as follows: 𝑅𝑒 = 𝑢𝑑 ℎ 𝑣 . Due to the complex geometry and operating conditions encountered in dynamic filtration devices (enclosed rotating disc/ impeller, static or rotating membrane, oscillating and vibrating module), different expressions of the Reynolds were proposed (see TableII.7). Based on 𝑣 = 𝜇 𝜌 , all equations are given with dynamic viscosity μ, where ρ is the fluid density.

5 ,

 5 destabilize a system, whereas viscous forces tend to stabilize the turbulence. Taylor number (Ta) is defined as the centrifugal force due to rotation of a fluid relative to viscous forces, which is well discussed in Taylor-Couette flow[START_REF] Park | A study on dynamic separation of silica slurry using a rotating membrane filter 1. Experiments and filtrate fluxes[END_REF][START_REF] Kroner | Dynamic filtration of microbial suspensions using an axially rotating filter[END_REF]. Taylor vortices would appear when the Ta reaches specific values. As shown in equation 𝑇𝑎 = ri and ro indicate the radius of the inner cylinder and housing cylinder, respectively, z is the distance between them. When 𝑧/𝑟 𝑖 ≪ 1, it could be simplified with 𝑇𝑎 = 𝜔𝑟 𝑖 0.5 𝑧1.5

4. 1 . 1 . 3

 113 Mass transferDimension analysis of mass transfer (by analogy with heat transfer) lead to establishing the semi-empirical correlation between dimensionless numbers, Sherwood (Sh), f(Sh, Re, Sc)=0, in laminar regime 𝑆ℎ = 𝐴′𝑅𝑒 𝛼 𝑆𝑐 𝛽 ( regime 𝑆ℎ = 𝐴′′𝑅𝑒 𝛼 𝑆𝑐 𝛽[START_REF] Daufin | Equipment Fouling in the Dairy Application: Problem and Pretreatment[END_REF] (D: diffusion coefficient, km: transfer coefficient, dh: hydraulic diameter, L: channel length, : thickness of limiting layer, µ: viscosity, u: velocity, : density).For laminar flow in a thin rectangular channel[START_REF] Porter | Concentration Polarization with Membrane Ultrafiltration[END_REF][START_REF] Hoek | Influence of Crossflow Membrane Filter Geometry and Shear Rate on Colloidal Fouling in Reverse Osmosis and Nanofiltration Separations[END_REF][START_REF] Blatt | Solute Polarization and Cake Formation in Membrane Ultrafiltration: Causes, Consequences, and Control Techniques[END_REF], Sherwood was presented with Graezt-Lévêque's correlation): 𝑆ℎ = 1.62 (𝑅𝑒𝑆𝑐 (

33 .

 33 Both cases share the same exponent of Schmidt and similar Reynolds, but the slop is higher at mixing condition.These relations make it possible to evaluate the mass transfer coefficient, km. It leads to determine how membrane geometry and operating conditions may be selected to improve the filtration flux. These expressions require the identification of diffusion coefficient, D of solutes retained by the membrane in water (solvent). These relations highlight that flux may increase if flowrate increases or the cross-section reduces. From a general standpoint, all hydrodynamics techniques to increase flow velocity and the shear rate at the membrane surface enable to increase flux[START_REF] Porter | Concentration Polarization with Membrane Ultrafiltration[END_REF]. In microfiltration, various recent theories take into account the hydrodynamics: i) lateral migration of particles (tubular pinch effect), ii) axial migration of deposit (flowing cake) or hydrodynamic diffusion generated by shear rate (shear-induced diffusion). To enhance the understanding of the transfer mechanism in the membrane process, it seems essential to investigate and characterize hydrodynamics (velocity field, shear rate, flow regime) at local and global scales.

4. 1 . 2

 12 Friction and power consumption curvesIn a mixing device, the power consumption curve is the representation of the Power number, Np (Eq. (II.10)) against the mixing Reynolds number, Rem (Eq. (II.5)). The characteristic curve integrates the tank configurations, fluid rheological behaviors and operating conditions. The mixing Reynolds number informs about the flow regimes while the Power number Np is associated with power consumption (P).

13 )

 13 The friction (Fig.II.7) and the power consumption (Fig. II.8) curves of the RVF module were previously established[START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF] and aim to predict the pressure drop and energy demand for mixing. Considering Churchill's model, a unique correlation between 𝐷𝑎/𝐷𝑎 𝑁=0 and 𝑅𝑒 𝑄 0.72 /𝑅𝑒 𝑚 1.08 was proposed. It indicated that this friction is related to the mixing rate and flowrate (laminar flow regime: ReQ<3, Rem<2000, transition flow regime: 3<ReQ<50, 2000<Rem<300000 and turbulent flow regime: ReQ>50, Rem>300000). On the opposite, the power number seemed to be independent of the flowrate.

Fig. II. 7 4 . 2 Semi-local approaches 4 . 2 . 1

 742421 Fig. II.7 Friction curve established with RVF lab-scale module[START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF]

  Permeate flux J is calculated according to Darcy's law, ℎ = 𝐿𝑝𝛥𝑃 𝑤𝑖𝑡ℎ 𝛥𝑃 = (𝑃 𝑖𝑛 +𝑃 𝑜𝑢𝑡 ) 2 -𝑃 𝑝 (II.14) where J: flux, Qp: permeate flowrate, S: membrane surface area, ∆P: the transmembrane pressure, μp: the permeate viscosity, Rh: the total hydraulic resistance, Lp: the permeability, Pin, Pout and Pp are respectively inlet, outlet and permeate pressures.

  blade impeller in the gap (membrane to impeller) is different from a full flat disk. This perturbation includes the contribution of rotation speed (N) and additional pressure fluctuation (Pag). Additional pressure Pag deduced by measuring the flux versus the radial position and the rotation speed (Fig. II.9). The flux was measured versus the frequency and compared to the case rotation speed equal to zero (Eqs. (II.17) and (II.18)): 𝐽(0, 𝑅 𝑡𝑜 𝑅 + 𝑑𝑅) = 𝛥𝑃 µ 𝑝 𝑅 ℎ (II.17) 𝐽(𝑁, 𝑅 𝑡𝑜 𝑅 + 𝑑𝑅) = (𝛥𝑃 + 𝛥𝑃 𝑎𝑔 (𝑁, 𝑅))

Fig. II. 9

 9 Fig. II.9 Determination of hydrodynamic performances, evolution of the radial pressure distributionversus the radius and the rotational speed[START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF]

28 )

 28 Bouzerar et al.[START_REF] Bouzerar | Influence of Geometry and Angular Velocity on Performance of a Rotating Disk Filter[END_REF] obtained the same expression of Eqs. (II.[START_REF] Mallubhotla | Flux enhancement during dean vortex tubular membrane nanofiltration. 10. Design, construction, and system characterization[END_REF]) and (II.28) for laminar and turbulent flow for investigating the RDM system. By assuming a thinner gap between the rotor and membrane, boundary layers merged. The narrow gap, s represents the layer thickness, Eqs. (II.25) and (II.26) give the shear rates for rotor and stator, respectively[START_REF] Bouzerar | Concentration of ferric hydroxide suspensions in saline medium by dynamic cross-flow filtration[END_REF][START_REF] Murkes | Crossflow filtration: Theory and practice[END_REF][START_REF] Bouzerar | Filtration dynamique dans un module plan à disque rotatif : Application à des suspensions miné rales[END_REF]. Bendick et al.[START_REF] Bendick | Using a high shear rotary membrane system to treat shipboard wastewaters: Experimental disc diameter, rotation and flux relationships[END_REF] assumed that steady-state flux Jss evolves as a function of γ and Re in the rotating membrane system HSR-MS. They confirmed the Jss-Re and Jss-γ relationships and extended the model for further prediction with larger membranes. With this theory, shear rates on the rotating membrane surface with a membrane diameter of 267 mm were characterized using Eq. (II.23) in laminar flow and Eq. (II.27) in a turbulent flow.Vogel et al.[START_REF] Vogel | Controlled shear filtration: A novel technique for animal cell separation[END_REF] considered the average shear rate γav in the gap between the conical rotor and the membrane in the CSF system. It could be estimated by the angular velocity ω, the radius of the rotating cone r, the distance between the cone and the membrane h, and the inclination angle of the cone α as Eq. (II.29) shown.𝛾 𝑎𝑣 = 𝜔𝑟 ℎ + 𝑟𝑡𝑎𝑛𝛼 (II.29)Lee et al.[START_REF] Lee | Control of scale formation in reverse osmosis by membrane rotation[END_REF] calculated the shear rate in an annulus of coaxes cylindrical RO membrane system as Eq. (II.30) shows, where f was a velocity factor and depended on the flow regime. They considered the circumferential velocity was uniform in the center of the annulus at about riω/2. The maximum shear rate was generated close to the rotating inner cylinder.𝛾 𝑚𝑎𝑥 = 𝑓 ( 𝜔𝑟 𝑖 𝑟 0 -𝑟 𝑖 ) (II.30)Atsumi et al.[START_REF] Atsumi | Frictional resistance of grooved rotor in cylindrical dynamic filter chamber without permeation or throughflow[END_REF] described the shear rate in an annulus of a coaxed cylinder. The Couette-Taylor flow has been studied intensively and the wall shear stress, τ is given below: 𝜏 = 𝑓𝜌𝜔 2 𝑟 𝑖 2 /2 for 0.03≤d/ri≤1.0 (II.31)where ω was angular velocity, ri was the radius of the inner cylinder, d was the gap between two cylinders, f denoted the friction factor, was determined by the flow and could be described as the following equation Eqs. (II.32) and (II.33). Reynolds number is given in Eq.(II.3), while ReC stands as the critical Reynolds number at which the Taylor vortex begins.

34 )

 34 𝛾 𝑤 (𝑟, 𝑡) = 𝑟 𝑅 2 𝑑 𝑟 (𝜋𝐹) 1.5 𝑣 -0.5 (cos(2𝜋𝐹𝑡) -sin(2𝜋𝐹𝑡)) (II.35) With 𝐺(𝑡) = cos(2𝜋𝐹𝑡) -sin(2𝜋𝐹𝑡) , wall shear stress represented as Eq. (II.35),

  Fig. II.11 Filtration modes, (a). Single-pass continuous filtration (b). Continuous filtration with partial retentate recycle (Feed & Bleed)

  ; n.a: not available at present time.The lab-scale RVF module[START_REF] Xie | Local hydrodynamic investigation by PIV and CFD within a Dynamic filtration unit under laminar flow[END_REF][START_REF] Fillaudeau | Investigation of rotating and vibrating filtration for clarification of rough beer[END_REF] (Fig. III.1 a, b) consists of two filtration cells with a total volume of 1.5 L (0.2×2+1.1 L). Four disk membranes (0.012 m 2 filtration area per membrane) can be mounted on the porous substrates, which collect permeate drained to lateral ducts. Each cell includes two crown membranes with a gap of 14 mm, between which is located an impeller that rotates with the central shaft (Fig. III.1 e). And it is driven by a motor that can be operated up to 50 Hz. The feeding fluid comes inside RVF from the inlet at the bottom and flows through the module along with the central shaft, finally leaving from the retentate outlet at the top.

Fig. III. 1

 1 Fig. III.1 Schematic diagram of Rotating and Vibrating Filtration module. (a) RVF module; (b) one dismantled filtration cell; (c) and (d) home designed and instrumented porous substrate for local pressure measurements; (e) configuration of filtration cell.

thickness; shape 2

 2 has decreased surface area and thickness) are applied in the tests, as shown in Fig. III.1 b and c. Imp 1 equips with three blades (shape 1); Imp 2 and 3 have six and three blades (shape 2), respectively. The surface area of the blades for three impellers follows the order: Imp 1> Imp 2> Imp 3.

Fig. III. 2

 2 Fig. III.2 Impeller configuration.

Fig. III. 3 ;

 3 it includes a feed tank, a circulation loop and the RVF module, as shown in Fig. III.1. In the circulation loop, water was pumped from a double-jacket tank (10 L), including thermal regulation at flowrate up to 300 L/h. Flowrate was controlled by a volumetric pump and acquired with a mass flowmeter; it enabled the measurement of mass flowrate, density and temperature (associated with outlet temperature). The inlet temperature was recorded from the conductivity sensor, Cond, in the feeding tank. The back pressure in RVF was adjusted by a counter-pressure valve coupled with a pressure gauge (PG, 0/4 bar) and two relative pressure sensors (PR1 and PR2) located at the inlet and outlet. Before the experiments, the back pressure was maintained at 300 mbar to avoid cavitation caused by the high mixing rate. A Tachymeter was used to adjust the mixing rate (N) from 0 to 50 Hz. Both current (CU) and tension (TEN) of the motor were recorded for all the conditions. The differential pressure sensors (DP) were used to determine the pressure drop and local pressure of RVF. The relative pressure (PR3, maximum acquisition frequency 5 kHz) was measured at the membrane surface. All sensors and equipment used in the experiments are shown in

Fig. III. 3

 3 Fig. III.3 Experimental set-up.

2 Experimental strategies and operating conditions 2 . 1

 221 . III.3). Global measurements along the circulation loop correspond to differential pressure (DP1 and DP2), flowrate, temperature, current and tension. All the sensors were connected to Agilent 34972A (Agilent Technologies, Loveland, USA) with a multiplexer acquisition card (34901A, 20 channels). The Bench View system (Keysight Technologies, Santa Rosa, California, USA) is used for data acquisition and monitoring during the experiments. Instantaneous pressure was measured with PR3 (shown in the blue line in Fig. III.3) at 1000 Hz, connected to the local radius. The pressure signal was recorded with NI USB-6009 (National Instruments, USA, 1 kHz) at a sampling frequency of 1000 Hz. Experimental strategies Two types of measurements were performed without permeate: (i) global measurement and (ii) instantaneous and local pressure measurement. Global measurements were conducted with 2 min stabilization, and then recorded at a 5 s time interval for 3 min; Instantaneous pressure was acquired with the NI instrument at the sampling frequency of 1000 Hz for 40 s, and the operating conditions were controlled with Agilent (3 s/sample). The relevant parameters are listed in the following Table III.4.

20 ℃

 20 , the density of water is 𝜌 = 998.2 kg/m 3 , specific heat capacity at constant pressure Cp=4181.8 J/(kg°C), viscosity =1.0 Pa.s. (under 100 kPa). 2.2.2 BREOX solutions In order to change the fluid viscosity, a water-soluble Newtonian fluid with stable properties, called BREOX (BREOX® Polyalkylene Glycol 75 W 55000, BASF), whose dilutions were used as the model fluid. Their thermal-physical properties at different temperatures are shown below versus the mass concentration C (w/w, %). { 𝐶𝑝 = 𝑎𝑇 + 𝑏 𝑎 = -14.8𝐶 2 + 16.3𝐶 -1.5 (𝑅 2 = 0.9735) 𝑏 = -1202𝐶 2 -948𝐶 + 4113 (𝑅 2 = 0.9997) (III.1) { 𝑙𝑛𝜇(𝑇) = 𝑙𝑛𝜇(20℃) + 4 × 10 6 𝑐 2 + 2811.3𝑐 -0.0161 (𝑅 2 = 0.9905) ) = -8.90 × 𝐶 2 + 18.03𝐶 -6.17 (𝑅 2 = 0.9998) (III.2)

  III.4 a. The pressure drop of the RVF module can be estimated with DP 1; DP 2 indicates the mixing pressure at the membrane surface, which shows to increase with radius. Other global parameters are displayed in Fig. III.4 b. The mixing of the impeller resulted in the thermal increase, the experiments were carried out at the temperature between 20 and 40℃.

Fig. III. 4

 4 Fig. III.4 Global measurement with water at 300 L/h and 40 Hz.

  (-𝑃)𝑛 𝑖 𝑈 𝑖 3 𝑖=1 𝑑𝑠 𝐴 = ∭ 𝜌𝜀 𝑉 𝑑𝑣 𝐷 (III.8) 1 st term: necessary pumping power to drive the fluid in the circulation loop; 2 nd term: external viscous forces (surface shear stress) on the impeller; 3 rd term: external forces of the pressure on the impeller; 4 th term: total power dissipation in the cell.

5

  Fig. III.5 The spectrum of instantaneous pressure and data treatment. (a) instantaneous and mean pressure; (b) fluctuating pressure and its standard deviation; (c) probability analysis at 5 and 20 Hz; (d) fluctuating pressure on frequency domain at 20 Hz.

(III. 18 )

 18 -267]. In our condition, a total number of sampling (m=215 ) is acquired at a constant time interval (1 ms), as illustrated in Fig. III.5b. The mean pressure 𝑃 ̅ (𝑁, 𝑟) and standard deviation 𝜎 𝑃 are expressed as the moment of first order and the square root of the central moment of second order, respectively. Their mathematical definitions for continuous and discrete functions are given in Eq. (III.15) and (III.[START_REF] Cheryan | Ultrafiltration and Microfiltration Handbook[END_REF]). The coefficient of variation, 𝛽 is defined as the ratio between 𝜎 𝑃 and 𝑃 ̅ (𝑁, 𝑟), and give the relative standard deviation.The normalised central moment of the third order, known as skewness (S), determines the symmetry of the signal in the probability distribution, and zero means a symmetrical distribution. 𝑃(𝑁, 𝑟, 𝑡 𝑖 ) -𝑃 ̅ (𝑁, 𝑟))3 𝑚 𝑖=1The flatness (F) is represented by the normalised central moment of the fourth order, indicating the sharpness of distribution. 𝑃(𝑁, 𝑟, 𝑡 𝑖 ) -𝑃 ̅ (𝑁, 𝑟)

into 100 classes considering 2

 2 15 of raw data. The probability of each class can be calculated based on its occurrence. In Fig. III.5c, the probability is illustrated against the fluctuating pressure. The unimodal (dominant random contribution) distribution of probability is observed at 5 Hz while extended to bimodal (dominant periodic contribution) at 20 Hz. These PDF widths are defined by peak-to-peak differences divided by 2, (P2-P1)/2, finally resulting in the pressure intensity of 55.5 mbar at 20 Hz.

  𝑓) 2 (III.21) The time-dependent fluctuating pressure can be converted into the frequency domain with FFT [265, 266, 268-270]. 2 15 sample points were chosen to get a sufficient precision of the fluctuated signal. The amplitude and frequency, driven by the rotating impeller, are discussed in the next part. Fig. III.5d shows the typical result of FFT at 20 Hz. The peak amplitude (A) is defined as the intensity of fluctuation pressure.

6 . 1 regime 6 . 1 . 1

 61611 Fig. III.6 PDF at 20 Hz. Model reconstruction of PDF with periodic and random functions.

Fig. III. 7

 7 Fig. III.7 Schematic of RVF cell. (a) is the top view and (b) is the side view.

  .8) is generated automatically with COMSOL 5.5 based on the physics. Different element types such as tetrahedral, pyramid, prism, triangular, quadrilateral, edge and vertex elements are then generated, resulting in the 299510 domain cells, 32242 boundary elements and 2401 edge cells for Imp 1.

Fig. III. 8

 8 Fig. III.8 Mesh geometry

  the fluid velocity (Reynolds number) increases, vortices appear in the flow field. Large-eddy simulation (LES) is to solve the filtered N-S equations directly under a large eddy scale grid, and the small eddy is simulated according to their similarity, which needs more time and space for the calculation. The Reynolds-averaged N-S (RANS) equations are based on the time-averaged solution of the flow field, which limits the turbulence fluctuations to some extent but reduces the time for the simulation. The RANS-based model helps us to solve the periodic fluctuations of the flow field induced by the impeller rotation under the turbulent regime.

Fig. III. 9

 9 Fig. III.9 Mesh geometry. (a) 1/36 0f rotating disk and (b) 1/3 of rotating impeller.

1. 1

 1 Pumping power 1.1.1 Pressure drop If energy loss is not considered, the pumping power can be estimated with the pressure drop of the RVF module. Fig. IV.1 shows the evolution of pressure drop with the mixing rate.

Fig. IV. 1

 1 Fig. IV.1 The pressure drop of the RVF module as a function of the mixing rate. (a) the pressure drop for different flowrate (QF: 50-300 L/h); (b) the pressure drop for different viscosity (μ: 0.001-0.6 Pa.s).

  6<Refeeding<9000) and mixing (80<Remixing<1200000) Reynolds numbers are shown in Fig. IV.2.

Fig. IV. 2

 2 Fig. IV.2 Euler number with mixing versus feeding (a) and mixing (b) conditions, respectively.

Fig. IV. 3

 3 Fig. IV.3 Euler number without mixing versus feeding condition (0.001-0.6 Pa.s for Imp 1, 0.001 Pa.s for Imp 2 and 3).

Fig. IV. 4 .

 4 The semi-empirical correlations for three impellers are displayed in

Fig. IV. 4

 4 Fig. IV.4 Friction curve for different impeller configuration. (a) Imp 1 (μ: 0.001-0.6 Pa.s), (b) Imp 2 (μ=0.001 Pa.s) and (c) Imp 3 (μ=0.001 Pa.s).

1. 2 . 1

 21 Fig. IV.5 shows the net power for Imp 1 as a function of the mixing rate. With low viscous fluid, the net power for water and BREOX 0.1 follows the same model, and is

Fig. IV. 5

 5 Fig. IV.5 Net power for Imp 1 as a function of mixing rate. (a) turbulent regime (μ=0.001, 0.01 Pa.s); (b) laminar regime (μ=0.05, 0.2, 0.6 Pa.s).

Fig. IV. 6 .

 6 Two separate regimes are observed at the Remixing equal to 30000, which is consistent with the investigation of flow conditions in the rotating dynamic filtration module. In the laminar regime (Remixing<30000), Np is proportional to Remixing -0.57 , with the viscosity of fluid from 0.05 to 0.6 Pa.s. During the Remixing superior to 30000, Np tends to be constant whatever the mixing rates, and shows 0.09, 0.006 and 0.005 for Imp 1, Imp 2 and Imp 3, respectively.

Fig. IV. 6

 6 Fig. IV.6 Power consumption curves for three impellers from laminar to turbulent regime.

1. 3 . 1

 31 Fig. IV.7 shows the thermal increase of the lab-scale RVF module as a function of the mixing rate. The relationship between ΔT and N can be represented by the parabolic representation. In the turbulent regime, Fig. IV.7a demonstrates that ΔT drops with the increase of feeding flowrate. The slight changes of ΔT can be observed at a constant flowrate (100 L/h) for three impellers, and it follows the order: Imp 2> Imp 1> Imp 3. By increasing the viscosity (Fig. IV.7), ΔT for water (0.001 Pa.s) and BREOX 0.1 (0.01 Pa.s), in the turbulent regime, are almost constant at the same flowrate. However, ΔT is higher in the laminar regime (BREOX 0.2, 0.05 Pa.s) at the same mixing rate. For high viscous fluid (BREOX 0.4, 0.6 Pa.s), only 12 L/h of flowrate can be reached with our equipment, and the thermal increase can reach more than 10℃ at 20 Hz. The variation of fluid temperature is correlated with the flowrate, and it can be further explained by the thermal balance.

Fig. IV. 7

 7 Fig. IV.7 Thermal increase of the fluid in the RVF as a function of mixing rate. (a) Different flowrate (water) for Imp 1 and 100 L/h for Imp 2 and 3; (b) different fluid (μ: 0.001-0.6 Pa.s) for Imp 1.

Fig. IV. 8

 8 Fig. IV.8 Thermal dissipation in the RVF as a function of mixing rate for Imp 1. (a) Different flowrate (water, μ: 0.001 Pa.s, QF: 50-300 L/h,) and impeller; (b) different flowrate (QF: 12-200 L/h) and viscosity (BREOX solution, μ: 0.01-0.6 Pa.s).

Fig. IV. 9

 9 Fig. IV.9 Comparison of thermal dissipation and mechanical power as a function of net power for Imp 1. (a) turbulent regime (μ=0.001 Pa.s, N: 0-50 Hz) (b) laminar regime (μ=0.6 Pa.s, N: 0-30 Hz).

Fig. IV. 10

 10 Fig. IV.10 Mixing pressure as a function of mixing rate and radius for three impellers. (a) Imp 1, (b) Imp 2 and (c) Imp 3. Operating conditions: μ=0.001 Pa.s, N: 0-50 Hz, QF=50 L/h.

  the viscosity increases. However, from a global perspective, the mixing pressure of each regime can be represented by a single equation, respectively.

Fig. IV. 11

 11 Fig. IV.11 Mixing pressure as a function of mixing rate at R5. (a) turbulent regime (μ: 0.001, 0.01 Pa.s, N: 0-50 Hz, QF: 50-300 L/h, Imp 1, r: 53.9 mm); (b) laminar regime (μ: 0.05, 0.2, 0.6 Pa.s, N: 0-40 Hz, QF: 12-130 L/h, Imp 1, r: 53.9 mm).

Fig. IV. 12

 12 Fig. IV.12 Mean core velocity coefficient for three impellers. (a) Imp 1, (b) Imp 2 and (c) Imp 3.Operating conditions: water, μ: 0.001 Pa.s, N: 0-50 Hz, QF: 50-300 L/h, r: R1-R8.

Fig.

  Fig. IV.12ashows the regression of mixing pressure in water for Imp 1 as a function of N 2 r 2 from 50 to 300 L/h. The great correlation indicates a core velocity coefficient equal to 0.65, which is lower than 0.71, as reported by Fillaudeau et al.[START_REF] Fillaudeau | Etude hydrodynamique d'un module de filtration dynamique[END_REF]. Previously, the mixing pressure at a defined radius was measured with the permeable crowns. With large gaps(5 mm)

Fig. IV. 13

 13 Fig. IV.13 Core velocity coefficient for different flowrates. (a) Imp 1, (b) Imp 2 and (c) Imp 3.Operating conditions: water, μ: 0.001 Pa.s, N: 0-50 Hz, QF: 50-300 L/h, r: R1-R8.

  flowrate, the contribution of angular velocity increase with the mixing rate, which indicates the experimental k values will be closer to the theoretical one. The local k values for three impellers are presented in Fig. IV.14. An increase of k can be observed at a lower radius due to the highest contribution of radial velocity at the entrance of the cell (close to the shaft). However, the changes of k at R8 (close to the external wall) are not yet known.

Fig. IV. 14

 14 Fig. IV.14 Core velocity coefficient for different mixing rates. (a) Imp 1, (b) Imp 2 and (c) Imp 3. Operating conditions: water, μ: 0.001 Pa.s, N: 0-50 Hz, QF: 50 L/h, r: R1-R8.

Fig. IV. 15

 15 Fig. IV.15 Core velocity coefficient for the different rotation directions. Operating conditions:water, μ: 0.001 Pa.s, N: 0-50 Hz, QF=50 L/h, r: R2, R4, R5, R7.

Fig.

  Fig. IV.16a shows that the k-value decreases with increased viscosity when r is close to the rotation shaft; the result is exactly the opposite when it is close to the impeller outer edge. Especially at high viscosity conditions, the k shows to increase with r, even reaching 0.7 at R7. Another point worth mentioning is that in the middle part of the membrane surface (R5), the change of viscosity shows little effect on the k value. The same data are represented in Fig. IV.16b, with the laminar and the turbulent flow as the distinction. In the turbulent regime, k tends to decrease with viscosity. But the mean k values are almost constant in the laminar regime among the test range, and the standard deviation of k shows to increase with viscosity due to the large range of k for different radii.

  Fig. IV.16 Core velocity coefficient of different fluids. Operating conditions: μ: 0.001-0.6 Pa.s, N: 0-50 Hz, QF: 12-50 L/h, r: R2, R4, R5, R7.

Fig. IV. 17

 17 Fig. IV.17 Statistical convergence of raw data.

2. 2 . 2

 22 Raw data Instantaneous pressures were locally measured at eight radii (R1 to R8) and different mixing rates from 0 to 50 Hz. They are shown in Fig. IV.18, indicating the increase of steady or mean pressure versus N and r for three impellers. But their magnitudes of fluctuation are

Fig

  Fig. IV.18d, it can be observed that the instantaneous pressure for Imp 1 varies with a period around 60 Hz, which is consistent with three times the mixing rate. This can be attributed to the number of blades. Whereas in Fig. IV.18f, the periodic amplitude of Imp 3 at 20 Hz is relatively small, its period is also in accordance with 3N. For Imp 2 at 20 Hz, the periodic variation cannot be achieved from Fig. IV.18e, and the pressure fluctuations are much weaker.

Fig

  Fig. IV.18 Raw data analysis for three impellers with water. (a), (b) and (c) are the evolution of instantaneous pressure versus mixing rate for three impellers at R6; (d), (e) and (f) are the evolution of instantaneous pressure versus local radius for three impellers at 20 Hz.

Fig. IV. 19

 19 Fig. IV.19 Raw data analysis for different fluids with Imp 1. (a), (b) (c) and (d) are the evolution of instantaneous pressure at R6 and mixing rate of 10, 20, 30 and 50 Hz, respectively.

  standard deviation σP has been used to describe the fluctuation intensity of the signal. As shown in Fig. IV.20, σP is independent of back pressure and flowrate, but influenced by mixing rate. On the contrary, the local pressure P0 is influenced by these parameters. Of course, the change in these parameters will affect the mean local pressure.

Fig. IV. 20

 20 Fig. IV.20 Standard deviation of instantaneous pressure for Imp 1 at different conditions (flowrates,mixing rates and back pressures) with water.

FigFig

  Fig. IV.21a, b and c present the evolution of σP under different conditions. For Imp 1, a large increase of σP with N can be observed below 20 Hz and followed by a decrease until 50 Hz. The maximum σP varies in the range of mixing rate between 20 and 25 Hz. It increases with local radius and even reaches more than 100 mbar at R8. For Imp 2, σP exhibits a constant value below 20 mbar, and then slightly increases with a mixing rate from 40 to 50 Hz. While the increase of σP occurs at 20 Hz with Imp 3, it is relatively lower than Imp 1. With the same shape of blades, the highest deviations for Imp 2 and 3 are limited to a value below 50 mbar, almost negligible when compared with Imp 1. It can be concluded that more blades contribute positively to a higher mixing pressure but negatively to the generation of pressure fluctuations. Comparing the standard deviation of instantaneous pressure relative to steady pressure, the coefficients of variation  are shown in Fig. IV.21d, e and f. It can be noticed that the β value of Imp 2 is limited to less than 7%; Imp 3 shows an increase, reaching 13% at R4. However, these values are inferior to Imp 1, which achieved 25.3% of local pressure at R8 and 20 Hz. It indicates that the pressure fluctuations cannot be neglected with Imp 1 in microfiltration applications. An intensive fluctuating area with high-pressure fluctuations at the membrane surface is promoted at the range of mixing rate from 15 to 30 Hz.

FigFig

  Fig. IV.22 High order items distribution. (a), (b) and (c) are the skewness distribution for three impellers; (d), (e) and (f) are the flatness distribution for three impellers. The dashed line indicates the S and F in a normal distribution.

Fig

  Fig. IV.24 PDF analysis for Imp 1. (a) the probability distribution of fluctuating pressure at R6; (b) the evolution of PDF width (peak-to-peak/2) versus mixing rate.

  Fig. IV.25 Frequency domain analysis with FFT at 20 Hz. (a), (d), (g) and (j) are Imp 1; (b), (e), (h) and (k) are Imp 2; (c), (f), (i) and (l) are Imp 3.

Fig. IV. 26

 26 Fig. IV.26 shows the cumulative amplitude of pressure fluctuations at the frequency of N, 2N, 3N, 4.25N and 6N at R6 for the three impellers. This type of representation appears to be very useful for exploring the dominant frequencies, i.e., the frequencies associated with the higher amplitudes in FFT analysis plotted in Fig. IV.25. It can be seen in Fig. IV.26a that the cumulative amplitude increases significantly with the mixing rate until 22.5 Hz, and then decreases for Imp 1. This behaviour is similar to one of the standard deviations plotted in Fig. IV.21a. The dominant frequencies are 6N below 10 Hz and 3N above 10 Hz. For Imp 2 (Fig. IV.26b), the cumulative amplitude is very weak, below 10 mbar. We find that the dominant frequencies are 6N from 5 to 15 Hz, change to 3N from 17.5 to 35 Hz, and finally to be N from 40 to 50 Hz. It indicates that there is an increase in the contribution of the frequency N (one-blade effect) at higher mixing rates. Furthermore, it should be noted that the cumulative amplitude does not increase at 50 Hz as it appears in σP, which means that this increase of pressure fluctuations is generated by a random component instead of a periodic signal. For Imp 3 (Fig. IV.26c), with the increase in mixing rate, the dominant frequencies evolve from 6N (5-10 Hz) to 3N (12.5-30 Hz) and 2N (35 Hz), finally by N (40-50 Hz). The cumulative

Fig

  Fig. IV.26 Cumulative amplitudes at R6. (a) Imp 1; (b) Imp 2; (c) Imp 3.

Fig

  Fig. IV.27 Total energy input IP+IR (a, b, c) and periodic contribution IP/(IP+IR) (d, e, f) as a functionof mixing rate and radius for Imp 1, Imp 2 and Imp 3, respectively.

2

  and ϵ are constants, N0 is the intrinsic frequency of the fluid in the cell. After the regression, N0 is equal to 20.6 Hz, which is slightly lower than the resonance frequency (21.1 Hz). Meanwhile, the values of K and ϵ are solved as 1.5 and 0.15, respectively.

Fig. IV. 28

 28 Fig. IV.28 Fluctuating intensities for Imp 1 as a function of mixing rate and radius. (a) periodic intensity; (b) random intensity.

  Fig. IV.[START_REF] Mercier | Influence of the flow regime on the efficiency of a gas-liquid two-phase medium filtration[END_REF]. From a global perspective, the deviations of the curves almost share the same trends with increasing mixing rates. The results from PDF are higher than other methods, around 1.04 (±0.17) times of σp above 15 Hz. Nevertheless, the former case contains information about fluctuations in all ranges, which can be useful in signal reconstruction.Meantime, the amplitude from FFT at 3N indicates 0.72 (±0.18) times of σp. This ratio increases to 0.9 if the contributions of other peaks (N, 2N, 4.25N and 6N) are considered.When it comes to the model, fluctuating intensity is composed of the period and random contributions. The total energy input is higher than σp and reaches 126%. As shown as a grey zone in Fig.IV.29, the intensive fluctuation occurs in the range from 15 to 30 Hz.

Fig. IV. 29 2 . 2 . 3 . 4 .

 292234 Fig. IV.[START_REF] Mercier | Influence of the flow regime on the efficiency of a gas-liquid two-phase medium filtration[END_REF] The evolution of pressure fluctuations (standard deviation, peak-to-peak/2, amplitude from FFT at 3N and total energy from modelling) as a function of mixing rate.

2. 2 . 4 . 1 SA

 241 The standard deviation (σP) of pressure fluctuation versus mixing rate and radius is shown in Fig. IV.31. The variation of pressure is almost negligible (below 20 mbar) during the mixing rate inferior to 15 Hz and r<40 mm. The highest value is observed at 30 Hz and R5, which is approximately one-fourth in the turbulent regime.

Fig

  Fig. IV.31 Standard deviation of pressure fluctuation at different mixing rates and radii.

Fig. IV. 32

 32 Fig. IV.32 Evolution of cumulative amplitude from FFT versus mixing rate.

  Fig. IV.33b shows the map of the ratio between periodic and total energy input for the pressure fluctuation. It indicates that the periodic signal is dominant

Fig. IV. 33

 33 Fig. IV.33 Spectrum of total energy input and periodic contribution as a function of mixing rate andradius.

  of viscosity in Fig. IV.34. Below 10 Hz, σP is almost independent of viscosity both at R6 and R8, the values of which are limited below 20 mbar. With the increase in mixing rate, especially at 20 Hz, σP reaches the maximum in the turbulent regime (μ: 0.001, 0.01 Pa.s) and is poorly influenced by viscosity. When it comes to 30 Hz, similar trends of σP can be observed with low viscosity fluid. However, in the laminar regime (μ: 0.05, 0.2 and 0.6 Pa.s), σP can be neglected with respect to the mean pressure value. It can be observed that σP decreases with increasing viscosity at a mixing rate superior to 20 Hz, while the change in mixing rate then becomes less influential on σP instead.

  Fig. IV.34 Viscous effect on the standard deviation of pressure fluctuation. Operating conditions: μ: 0.001-0.6 Pa.s, N: 0-30 Hz, r: R6 and R8.

Fig. IV. 35

 35 Fig. IV.35 Viscous effect on the amplitude at 3N of pressure fluctuation. Operating conditions: μ: 0.001-0.6 Pa.s, N: 0-30 Hz, r: R6 and R8.

Fig

  Fig. IV.36 Explorations and actions in CFD approach within RVF module (L: laminar regime, T:turbulent regime)

  pressure and shear stress), new-designed impellers (Imp 4, Fig. S 1 and Fig. S 2) with different configurations were achieved with Auto CAD (2021), then performed with the same simulation.

  The magnitude of the horizontal velocity component (xy plane) along the z-axis, which is mainly in the  direction, is shown in Fig. IV.37. Different  positions were explored regarding the impeller position: leading, middle and trailing. The horizontal velocity significantly increases when close to the blades. Considering the PIV measurements as the reference, the velocity is well calculated by the CFD model at the leading edge, while it is slightly overestimated between two blades and at the trailing edge. It should be noted that the numerical results also show large deviations in the impeller zone (-4<z<4 mm). This can be explained by the influence of the impeller on the laser during the PIV measurement, where the velocity values can only be determined between the two blades. Nevertheless, it can be claimed that the numerical velocity profiles are in great agreement with the experimental results if the deviations in the laser installation process are taken into account.

Fig. IV. 37

 37 Fig. IV.37 Horizontal velocity profile at z-direction and r=45 mm for PIV measurement and CFD simulation. Operating conditions: μ: 0.81 Pa.s, N: 2 Hz, QF: 45 L/h.

Fig. IV. 39

 39 Fig. IV.39 Velocity field in the filtration cell. Operating conditions: μ: 0.2 Pa.s, N: 20 Hz, QF: 25 L/h.

Fig

  Fig. IV.40a depicts the vertical profiles (z-axis) of the tangential velocity component 𝑈 𝜃 at different locations in the cell relative to the position of the impeller (points A-G can be seen in the figure). At the same radius (points A, B and D, r=60 mm), the tangential velocity varies with the location relative to the position of the impeller. The fluid velocity at the leading edge (point B) remains identical to the impeller velocity close to the centre of the cell (z=0 mm). On the contrary, it reaches its minimum value close to the centre of the cell (z=0 mm) at the trailing edge (point D). In the region of the narrow gap between the membrane and the blade, the vertical profile of the tangential velocity is roughly linearly from the membrane to the blade surface (points C, E, F and G). A perfectly straight line would correspond to a Couette flow. Between the two blades, the velocity profile is almost parabolic (point A). An exact parabolic shape would correspond to a Poiseuille flow. The maximum velocity value is around 7.5 m/s at point B. It is close to the value of 2Nr, which is the linear velocity of the blade at this radial position.

Fig. IV. 40

 40 Fig. IV.40 Tangential velocity along the z-direction. (a) is the velocity distribution at different positions; (b) and (c) are the velocity distribution for different mixing rates at A and C, respectively. A

Fig. IV. 41

 41 Fig. IV.41 Tangential velocity along the z-direction. (a) and (b) are velocity distribution at different positions for Imp 1; (c) is the velocity distribution for the full disk. Operating conditions: μ: 0.05-0.6 Pa.s, N: 20 Hz, QF: 25 L/h, Imp1 and full disk.

  Fig. IV.42 shows the pressure field at the membrane surface and two different angular cross-sectionals (0 and 60°). From the top view (Fig. IV.42a, b and c), the pressure at the membrane surface increases with the mixing rate, and the maximum value occurs between two blades and close to the external wall. The pressure variation increases with the higher mixing rates. It is also seen that the pressure distribution is uniform in the vertical direction (Fig. IV.42d-i) according to the type of flows occurring within the RVF (laminar boundary layer, Couette, Poiseuille) already discussed in § 3.1.2.

Fig. IV. 42

 42 Fig. IV.42 Pressure field for different mixing rates with Imp 1. (a), (b) and (c) are on the membrane surface; (d), (e) and (f) are the cross-section with 0° to x-axis (black dashed line); (g), (h) and (i) are the cross-section with 60° to x-axis (red dashed line). Operating conditions: μ: 0.2 Pa.s, N: 10, 20 and 30 Hz.Two impellers with similar blade surface area (1090 mm 2 for one blade) are compared.The first impeller has the exact shape of Imp 1 used experimentally, while the second impeller called Imp 4-60° is fan-shaped with three blades.The mixing pressure and the magnitude of pressure fluctuation as a function of the

Fig. IV. 43

 43 Fig. IV.43 Pressure distribution as a function of mixing rate. (a) and (b) are the mixing pressure; (c) and (d) are the standard deviation of pressure fluctuation. Operating conditions: μ: 0.2 Pa.s, N: 0-50 Hz, r: R2, R4, R6 and R8, Imp 1 for (a) and (c), Imp 4-60° (three blades) for (b) and (d).

Fig. IV. 44

 44 Fig. IV.44 Pressure distribution as a function of radius. (a) and (b) are the mixing pressure; (c) and (d) are standard deviation of pressure fluctuation. Operating conditions: μ: 0.2 Pa.s, N: 0-50 Hz, r: 25-67.5 mm, Imp 1 for (a) and (c), Imp 4-60° (three blades) for (b) and (d).

Fig. IV. 45

 45 Fig. IV.45 Core velocity coefficient for different radii. Operating conditions: μ: 0.2 Pa.s, N: 0-50 Hz, QF: 25 L/h, r: R1-R8.

Fig. IV. 46

 46 Fig. IV.46 Pressure distribution as a function of viscosity. (a) is the mixing pressure; (b) is the standard deviation of pressure fluctuation. Operating conditions: μ: 0.05-0.6 Pa.s, N: 10-50 Hz, r: R6.

(

  full disk), as shown in Fig. S 1. The pressure field for the different cases is shown in Fig. IV.47. As already found in the previous section, the maximum pressure takes place between two blades. When there is no blade (Fig. IV.47b), a uniform pressure distribution along the  direction is achieved. The same phenomenon can be observed with the full disk (Fig. IV.47 i) but induced higher pressure. In addition, one can see that the pressure distribution in the area below the blade varies with the blade surface area.

  Fig. IV.47 Pressure field at the membrane surface for different impeller geometries. (a) is the geometry 30° blade, which angle length varies from 0 to 120°; from (b) to (h) are the three blades impeller with the increased surface area from 0 to 90°; (i) is the full disk. Operating conditions: μ: 0.2 Pa.s, N: 20 Hz.

Fig. IV. 48

 48 Fig. IV.48 Pressure distribution with the increased angle of blades. (a) is the mixing pressure; (b) is the standard deviation of pressure fluctuation. Operating conditions: μ: 0.2 Pa.s, N: 0-30 Hz, r: R6.

Fig. IV. 49

 49 Fig. IV.49 illustrates the evolution of pressure fluctuation as a function of  at the membrane surface for the different angle lengths of blades, showing irregular sinusoidal waves. A quasi-linear decrease of pressure can be seen above the blade, and the minimum pressure occurs at the trailing edge of the blade.

Fig. IV. 49

 49 Fig. IV.49 Evolution of pressure fluctuation for different kinds of blades. Operating conditions: μ: 0.2 Pa.s, N: 20 Hz, r: R6.

Fig. S 2 .

 2 Eachsimulation is carried out with a geometrical domain of one blade. The pressure fields at 20 Hz for each case are given in Fig. IV.50. As previously described, the maximum value of pressure appears at the leading edge of the blades for all impeller geometry. Among them, the pressure distribution of the two-blade impeller shows a larger fluctuation in the  direction.

  Fig. IV.50 Pressure field at the membrane surface for different impeller geometries. From (a) to (e) are the impeller with the increased number of blades (30°) from 2 to 8. Operating conditions: μ: 0.2 Pa.s, N: 20 Hz.

Fig

  Fig. IV.51 shows the mixing pressure and its standard deviation at the membrane surface.

Fig. IV. 51

 51 Fig. IV.51 Pressure distribution with the increased number of blades. (a) is the mixing pressure; (b) is the standard deviation of pressure fluctuation. Operating conditions: μ: 0.2 Pa.s, N: 0-30 Hz, r: R6.

IV. 52 .

 52 The change in the number of blades does not affect the trend of pressure fluctuation, but its intensity decreases rapidly with the number of blades. As can be seen from Fig. IV.51b, for the two-blade impeller at R6, σP can reach 75 mbar at 30 Hz, while this value for the eight-blade impeller is only 2 mbar.

Fig. IV. 52 Fig

 52 Fig. IV.52 Evolution of pressure fluctuation for different numbers of blades. Operating conditions: μ: 0.2 Pa.s, N: 20 Hz, r: R6.

Fig. IV. 54

 54 Fig. IV.54 Pressure distribution with the different gaps. (a) is the mixing pressure; (b) is the standard deviation of pressure fluctuation. Operating conditions: μ: 0.2 Pa.s, N: 0-30 Hz, r: R6.

3. 1 . 4 . 1

 141 Mixing rate Unlike pressure, local shear stress is proportional to the velocity gradient for a Newtonian fluid. The shear stress fields in different cross-sections of the filtration cell are shown in Fig. IV.55. In the lab-scale RVF module, the gap between the impeller and the membrane is 3 mm, corresponding to a gap ratio of s/Ri equal to 0.04. In this narrow gap, the boundary layer can merge together depending on the magnitude of N, resulting in slight variations of the shear stress along the z-direction (Fig. IV.55g-i). While between the two blades, the large gap (14 mm) allows the separating boundary layer. The shear stress appears to reach the maximum at the membrane surface, and it is obviously about 0 close to the center of the cell between two blades (Fig. IV.55d-f). At the membrane surface (Fig. IV.55a-c), the maximum shear stress occurs at the trailing edge of the blades, which is exactly opposite to the pressure distribution.

  Fig. IV.55 Shear stress field for different mixing rates with Imp 1. (a), (b) and (c) are on the membrane surface; (d), (e) and (f) are the cross-section with 0° to x-axis (black dashed line); (g), (h) and (i) are the cross-section with 60° to x-axis (red dashed line). Operating conditions: μ: 0.2 Pa.s, N: 10, 20 and 30 Hz.

  device. The shear stress variations as a function of the mixing rate are shown in Fig. IV.56, which indicates that the mean shear stress is linear with N 1.5 . As can be seen from Fig. IV.57,

Fig

  Fig. IV.56 Shear stress distribution as a function of mixing rate. (a) and (b) are the mean shear stress; (c) and (d) are the standard deviation of local shear stress. Operating conditions: μ: 0.2 Pa.s, N: 0-50 Hz, Imp 1 for (a) and (c), Imp 4-60° (three blades) for (b) and (d).

Fig

  Fig. IV.57 Shear stress distribution as a function of radius. (a) and (b) are the mean shear stress; (c) and (d) are the standard deviation of local shear stress. Operating conditions: μ: 0.2 Pa.s, N: 0-50 Hz, Imp 1 for (a) and (c), Imp 4-60° (three blades) for (b) and (d).

  the cell (membrane surface and impeller surface) highly depend on fluid properties (viscosity) and operating conditions (mixing rate of the impeller). Recall that the wall shear stress for a Newtonian fluid in the present flow conditions can be expressed as 𝜏 𝑊 = 𝜇 ( walls of the cell. That can be seen in the plots of the velocity profiles presented in the previous section (Fig. IV.39 and Fig. IV.40). The development of the boundary layer is less important in this situation, in particular in the region between two blades. (Fig. IV.40b). In the region above the blade, the shear rate is obviously increased according to the increase of N (Fig. IV.40c). Therefore, increasing N significantly increases the wall shear stress. On the contrary, increasing  leads to a decrease ( walls due to the more important development of the boundary layer (Fig.IV.41a and b). But the corresponding value of the wall shear stress still increases due to the higher value of viscosity that compensates for this phenomenon.

Fig. IV. 59

 59 Fig. IV.59 Estimation of local shear stress at the membrane surface. Operating conditions: μ: 0.05-0.6 Pa.s, N: 0-50 Hz, r: R1-R8.

Fig

  Fig. IV.60 Shear stress field at the membrane surface for different impeller geometries. (a) is the geometry of a blade; from (b) to (h) are the three blades impeller with the increased surface area from 0 to 90°; (i) is the full disk. Operating conditions: μ: 0.2 Pa.s, N: 20 Hz.

Fig. IV. 61

 61 Fig. IV.61 shows the variation of membrane surface shear stress with blade surface area. The local shear stress slightly decreases as the blade's area increases and reaches the minimum when it is a full disc. For shear stress fluctuations, σs reach their maximum value with three blades impeller of 30° and 60°. At R6 and 20 Hz, the relative standard deviation of local shear stress reaches 23.4% with 30° blades, and 25.1% with 60° blades.

Fig. IV. 61

 61 Fig. IV.61 Shear stress distribution with the increased angle of blades. (a) is the mean shear stress; (b) is the standard deviation of local shear stress. Operating conditions: μ: 0.2 Pa.s, N: 0-30 Hz, r: R6.

Fig

  Fig. IV.62 Shear stress field at the membrane surface for different impeller geometries. From (a) to (e) are the impeller with the increased number of blades (30°) from 2 to 8. Operating conditions: μ=0.2 Pa.s, N=20 Hz.

Fig. IV. 63

 63 Fig. IV.63 Shear stress distribution with different numbers of blades. (a) is the mean shear stress; (b) is the standard deviation of local shear stress. Operating conditions: μ=0.2 Pa.s, N: 0-30 Hz, r: R6.

  Fig. IV.64 Shear stress field at the membrane surface with different gaps between impeller and membrane. (a) is the illustration of cell geometry; from (b) to (h) are the increased gap from 2 to 10 mm. Operating conditions: μ=0.2 Pa.s, N=20 Hz.

Fig. IV. 64

 64 Fig. IV.64 and Fig. IV.65 show the effect of the gap, s, between the blade and the membrane surface on shear stress distribution. The maximum shear stress occurs at the gap of 2 mm, further increase in the gap value shows little effect on mean local shear stress. As s increases from 2 to 10 mm, σs is decreasing and are constant with pressure fluctuation observed in Fig. IV.54b. This means that a smaller gap is not only beneficial for the pressure

Fig. IV. 65

 65 Fig. IV.65 Shear stress distribution with different gaps. (a) is the mean shear stress; (b) is the standard deviation of local shear stress. Operating conditions: μ=0.2 Pa.s, N: 0-30 Hz, r: R6.

Fig. IV. 66

 66 Fig. IV.66 Angular velocity profile at z direction. (a) s/R=0.08, Re=10 6 , (b) s/R=0.127, Re=1.6× 10 6 . Operating conditions: μ: 0.001 Pa.s, N: 35/56 Hz, QF: 0 L/h.

First, a rotating

  disk system with structural parameters of s/R=0.08 (s=5.4 mm, R=67.5 mm, corresponds to the increase of gap from 3 to 5.4 mm in the RVF module) and Reynolds number (𝑅𝑒 = 2𝜋𝑁𝑅 2 𝑣 ) of 10 6 is simulated. The objective of this preliminary work is to

Fig

  Fig. IV.66b that the velocity profile at the same position shows a better agreement with the numerical simulation. This result is also similar to the CFD results from Torras et al. for the classical RD model [230].

Fig. IV. 67

 67 Fig. IV.67 Velocity field in the filtration cell. Operating conditions: 60° three-blade impeller, μ: 0.001 Pa.s, N: 20 Hz, QF: 50 L/h.

Fig. IV. 68

 68 Fig. IV.68 Tangential velocity along the z-direction. (a) velocity distribution at different positions (radius, angle) for 60° three-blade impeller; (b) velocity distribution at different radii for the disk. A (between two blades), B (leading edge), C (on the blade) and D (trailing edge) with a radius of 60 mm; E, F and G with a radius of 50, 40 and 30 mm, respectively. Operating conditions: μ: 0.001 Pa.s, N: 20 Hz, QF: 50 L/h.

Fig. IV. 70

 70 Fig. IV.70 Pressure distribution as a function of radius. (a) is the mixing pressure, (b) is the standard deviation of pressure fluctuation. Operating conditions: μ: 0.001 Pa.s, N: 10, 20, 50 Hz, QF: 50 L/h.

Fig. IV. 71

 71 Fig. IV.71 Shear stress field at the membrane surface. Operating conditions: μ: 0.001 Pa.s, N: 20 Hz, QF: 50 L/h.

Fig. IV. 73

 73 Fig. IV.73 Estimation of local shear stress at the membrane surface. Operating conditions: μ:

( 7 )

 7 How to enhance the filtration performance during bioprocess (flow regime, operating conditions and device configuration)?As illustrated in Fig.II.12, the decision tree is proposed to select the appropriate DF module. The basic information (fluid, membrane, and process) associated with the empirical data and hydrodynamics were required before the selection. These knowledge gaps in scientific research should be highlighted.

S 1

 1 Fig. S 1 Impeller geometry with difference surface area. No blades and full disk indicate 0 and 120°, other three impellers equip with three blades and the angle from 20 to 90°.

Fig. S 2

 2 Fig. S 2 Impeller geometry with difference number of blades. The impellers equip with 2 to 8 blades (30°).

Fig. S 3

 3 Fig. S 3 The comparison of velocity, pressure and shear stress for different meshes. (a) tangential velocity along the z-axis; (b) and (c) are the pressure and the shear stress along the  direction.

Fig. S 4

 4 Fig. S 4 Core velocity coefficient for different flowrates. Operating conditions: water, μ=0.001 Pa.s, N: 0-50 Hz, QF: 50-300 L/h, r: R1-R8.

Fig. S 5 Fig. S 6 Fig. S 7

 567 Fig. S 5 Local pressure as a function of back pressure. Operating conditions: μ=0.2 Pa.s, N: 20 Hz, r: R6, QF=25 L/h.

Table IV .

 IV Table II.1 Top 5 most productive journals considering the number of articles and citations(source: WoS) ........................................................................................................................... 14Table II.2 Top 9 most productive institutions (source: WoS). ................................................. 15 Table II.3 Clusters of research hotspots. .................................................................................. 17 Table II.4 Top 10 keywords with the strongest citation bursts. ............................................... 18 Table II.5 Classification of DF modules according to the movement and shape..................... 23 Table II.6 Classification and specification of DF modules (d: membrane diameter, S:membrane surface area, N/F: maximum rotating, vibrating and/or oscillating speed/ frequency, 2 Numerical coefficient for the thermal dissipation based on the equation: Ф𝑇 = 𝑎𝑁2. ....................................................................................................................................... 100 Table IV.3 Information on the data treatment. ....................................................................... 119 Table IV.4 Signal reconstruction for Imp 1 at R6, with the value of the two parameters to estimate the instantaneous pressure. A and σ are calculated from the convolution of PDF functions. ................................................................................................................................ 121 Table IV.5 Validation of CFD simulation based on velocity and pressure field. ................... 127

	OPEX C PT U	operational expenditure concentration total power tangential velocity	/ W m/s
	PAAS Cp Pin u Abbreviation AVM PDF D Pout uz BDF BOD BSA CAPEX CFD CFF CFD COD Cond CP CR CRD CRDM CSAF CSF PEG PES d Pp 𝑢 ̅ PG dh Δp v PR di ΔP v0 PVDF PIV PMA PMMA PTFE PTV RCF RDM RD-M R-HFM RO dm ΔPag y do 𝑃 𝑃 ̃(𝑡) z Da 𝑃 𝑅 ̃(𝑡) E 𝑃 ̅ (𝑁, 𝑟) Greek letter Ek Eu EP(x) 𝑃 ̃(𝑁, 𝑟, 𝑡) α Q β ϵ ER(x) Qc σP F Qf στ f Qp φ G Qr γ CTF RVF H r γav CU DCF DEF DF SA SBM h Rh γmax SBR I Rm γR SS IP rh γS SSDF IR ri δ	poly acrylic acid sodium specific heat capacity inlet pressure velocity probability distribution function diffusion coefficient outlet pressure axial flow velocity axial vibration membrane biodruck-filter biological oxygen demand bovine serum albumin capital expenditure computational fluid dynamics cross-flow filtration computational fluid dynamics chemical oxygen demand conductivity concentration polarization cross rotational compact rotating disc filter retentate recycling process controlled shear affinity filtration polyethylene glycol diameter permeate pressure mean velocity of fluid polyether sulfones hydraulic diameter pressure drop kinematic viscosity pressure gauge inner diameter transmembrane pressure amplitude of velocity relative pressure polyvinylidene difluoride particle image velocimetry copolymer of maleic acid and acrylic acid polymethyl methacrylate Polytetrafluoroethylene particle tracking velocimetry rotating cross-flow rotating disk module rotating disk-membrane rotating hollow fiber membrane reverse osmosis rotor diameter additional pressure gap outer diameter periodic signal gap between rotor and membrane, or between two cylinders Darcy number random signal Specific energy demand mean time pressure Ekman number Euler number periodic PDF fluctuating pressure inclination angle flowrate relative standard deviation of pressure dumping factor random PDF circulation flowrate standard deviation of pressure oscillating/ vibrating frequency, flatness feeding flowrate standard deviation of shear stress velocity factor, friction factor permeate flowrate phase gain of the system retentate flowrate shear rate controlled shear filtration rotating and vibrating filtration vertical distance radius average shear rate Couette-Taylor flow current dynamic cross-flow filter dead-end filtration dynamic filtration statistical analysis rotor height hydraulic resistance Maximum shear rate spinning basket membrane tension rotor radius shear rate at rotor surface styrene butadiene rubber periodic intensity hydraulic radius shear rate at membrane surface single stirred signal shaft disk filter random intensity inner radius limiting layer thickness	J/(kg.℃) m/s Pa m 2 /s Pa m/s m m/s Pa m Pa m 2 /s m Pa m Pa m m mbar m m mbar / mbar kWh/m 3 / / ° mbar mbar m 3 /s / mbar -1 m 3 /s mbar mbar -1 Pa m 3 /s Hz m 3 /s  / / s -1 m 3 /s m s -1 m m s -1 m -1 A m s -1 mbar m s -1 mbar m m
	DMF DP DRDM FFT FMX HF SST TEN TMP UF UHT URV J Jss K ro Δ Re μ k km L Rea μp Refeeding ρ Remixing τ ω	dynamic membrane filter differential pressure retentate non-recycling process fast Fourier transform anti-fouling membrane unit hollow fiber Shear Stress Transport tension transmembrane pressure ultrafiltration ultra-high temperature processing Rovira Virgili University Flux steady-state flux numerical coefficient outer radius minimum cumulative error Reynolds number dynamic viscosity core velocity coefficient transfer coefficient channel length Reynolds number for axial flow in annulus permeate viscosity Reynolds number for feeding density Reynolds number for mixing shear stress angular velocity	m/s m/s / m Pa.s / / / / m Pa.s / kg/m 3 / Pa / rad/s
	HSR-MS USVM Lp ReQ η	high shear rotary membrane system uniform shearing vibration membrane permeability Reynolds number in the tube mechanical efficiency	m/(s• Pa) / /
	IREC UTC m Rer ФM	Catalonia Institute for Energy Research University of Technology of Compiè gne sampling number Reynolds number in rotating system mechanical power	/ / W
	ISBM LDA VCF N Res ФN LDV LLR MBR MF MMV VHM VMBR VMF VRM VSEP P0 Sc P Sh Nr s Np S VERO N0 Rev ФT	intermeshed spinning basket membrane volume concentration factor mixing rate Reynolds number for rotating cone net power laser doppler anemometry Log-likelihood Ratio membrane bioreactors microfiltration magnetically induced membrane vibration vibrating hollow fiber microfiltration vibratory shear enhanced processing Schmidt number pressure without the rotation of impeller vacuum rotation membrane power consumption Sherwood number vibrating membrane filtration resonance frequency characteristic length scale, gap vibrating membrane bioreactor Power number membrane surface area, skewness laser doppler velocimetry vibration enhanced reverse osmosis intrinsic frequency Reynolds number in oscillating/ vibrating system thermal power	Hz W / mbar / / W Hz m / m 2 Hz / W
	MSD WoS P(f) T	multi-shaft disk web of science pressure at frequency f period, temperature	mbar Hz
	MSDF MTV NF OFSM P(N,r,t) t Δt Latin letter A PM Ta a, b PP U	modular span disk filtration molecular tagging velocimetry nanofiltration oscillatory flat surface membrane instantaneous pressure time time interval amplitude mechanical power Taylor number numerical constants pumping power current	s mbar s W / m / W V
		XXVII

A: amplitude, displacement or vibrating angle, TMP: maximum operating transmembrane pressure) ................................................................................................................................... 24 Table II.7 Dimensionless numbers used to describe hydrodynamic within Dynamic Filtration device (d: diameter, u: velocity, Q: flowrate, r: radius, dh: hydraulic diameter, rh: hydraulic radius, do: outer diameter; di: inner diameter, uz, axial flow velocity, N: mixing rate, dm: rotor diameter, k: core velocity coefficient, : angular velocity, h: rotor height, α: inclination angle of conical rotor, s: characteristic length scale, F: oscillating/ vibrating frequency, H: vertical distance). .................................................................................................................................. 50 Table II.8 Four flow pattern in rotating system. ...................................................................... 51 Table II.9 Core velocity coefficient of different DF filters. ..................................................... 57 Table II.10 Shear rate of four flow regimes in a rotation system. ........................................... 59 Table II.11 Specific energy demand in different modules. ...................................................... 69 Table II.12 Resume of available data about hydrodynamics and applications with the different types of DF modules. ............................................................................................................... 72 Table III.1 Radial distribution of pressure taps at the membrane surface (porous substrate). . 74 Table III.2 All sensors used in the experiment. ........................................................................ 77 Table III.3 All equipment used in the experiment. ................................................................... 77 Table III.4 Data acquisitions in the experiments. .................................................................... 79 Table III.5 Operating conditions for global and local pressure measurements. ....................... 79 Table III.6 Signal decomposition into periodic and random contributions (PP(t): periodic signal, PR(t): random signal, A: amplitude, f: frequency, φ: phase, σ: standard deviation, EP(x) and ER(x) are the PDF.). ........................................................................................................... 87

Table IV.1 Established friction curves for three impellers. ...................................................... 97 Annexes Table S 1 Effect of blade surface area on core velocity coefficient. ...................................... 183 Table S 2 Effect of blade number on core velocity coefficient. ............................................. 184 Table S 3 Effect of impeller/membrane gap on core velocity coefficient. ............................. 184 XXIII Nomenclature

Table II .1 Top 5 most productive journals considering the number of articles and citations (source: WoS) Journal TA (P) TC (P) Category

 II

	published by 26 journals among 23 WoS subject categories. The five most productive
	journals with the number of articles and categories of journals are shown in Table II.1. Total
	articles and citations rate in each journal follows the same trend with a dominant position for
	the Journal of Membrane Science.
	2.1.2 Research institutions and scientific cooperation
	Table II.2 shows the top 9 most productive institutions with the same indicators. The
	leading institution is University of Technology of Compiè gne, UTC (France), which
	published the most articles accounting for 30.0% of the total, and almost half of them were in
	cooperation. Afterward, Rovira Virgili University, URV (Spain), Jadavpur and Calcutta
	University (India) and Nagoya University (Japan) published relatively few articles, but they
	all exceeded five. Then followed by IREC (Spain) and Tamkang University (China).
	JOURNAL SCIENCE	OF	MEMBRANE	31 (20.7)	1143 (43.5)	ENGINEERING; SCIENCE	POLYMER
	DESALINATION		20 (13.3)	298 (11.4)	ENGINEERING; RESOURCES	WATER
	SEPARATION AND PURIFICATION TECHNOLOGY	14 (79.3)	203 (7.7)	ENGINEERING
	BIOTECHNOLOGY BIOENGINEERING	AND	7 (4.7)	165 (6.3)	BIOTECHNOLOGY & APPLIED MICROBIOLOGY
	CHEMICAL RESEARCH DESIGN	ENGINEERING	6 (4.0)	32 (1.2)	ENGINEERING
	TA: Total article; TC: Total citation; P: percentage (%)
	According to the Citation report for 150 selected results, the articles related to DF were

Table II .

 II 2 Top 9 most productive institutions (source: WoS).

	last four years.
	Institution	TA(P)
	UNIV TECHNOL COMPIEGNE	45 (30.0)
	UNIV ROVIRA VIRGILI	9 (6.0)
	JADAVPUR UNIV	8 (5.3)
	UNIV CALCUTTA	7 (4.7)
	NAGOYA UNIV	6 (4.0)
	IREC	5 (3.3)
	TAMKANG UNIV	5 (3.3)
	DALIAN UNIV TECHNOL	4 (2.7)
	UNIV TOULOUSE	4 (2.7)
	TA: Total article; P: percentage (%)
	113 institutions (academics or private companies) and 99 collaborative links were
	illustrated by the cooperation network (Fig. II.3). The size of the nodes represents the
	scientific activity, and the links inform the cooperation between the academic institutions
	and/ or private companies. As for the major network, the dominant position is led by UTC
	(France) from the 7 most massive clusters, which published 45 articles and linked with other
	12 institutions, but mainly concentrated from 2000 to 2010. Another major one emerged at
	University of Toulouse. It has 5 collaborators, among 4 of them are connected. Furthermore,
	the bilateral national cooperation in India, Korea, and China, the international collaborations
	between Tamkang University (China) and Nagoya University (Japan), URV (Spain) and UTC
	(France) indicates a high degree of cooperation. In Fig. II.3, the color informs about the
	production year. Most productive institutions have come from China, France and Korea in the

Table II .3 Clusters of research hotspots. Cluster ID Size Top Terms (LLR)

 II

	summarized in 4 dominants:
		• DF technologies, such as rotating disk, vibratory disk, rotating membrane filter,
		shear enhanced filtration and vibration;
	0		particle size, clean-bed, membrane separations, yeast cells, ferric hydroxide
	1		rotating disk, dairy effluent, nanofiltration, vibratory disk, ceramic membranes
	2		flux behaviors, alfalfa juice, dynamic cross-flow filtration, turbulent flow, rotating membrane filter
	3		concentration polarization, number, concentration polarization (cp), mass transfer, vibration enhanced reverse osmosis (vero)
	4		microalgae, dynamic membrane filtration, perforated disk, shear stress, dewatering
	5		shear enhanced filtration, beta-lactoglobulin, milk fractionation, alpha-lactalbumin and beta-lactoglobulin transmissions, alpha-lactalbumin
	6		dynamic simulation, back transport flux, rotating disk uf membrane, cell pore-plugging model, mathematical modelling
	7		algae dewatering, ceramic microfilter, vibrating membrane system, algae microfiltration, membrane dewatering impact factor
	8		ceramic membrane, solid-liquid separation, rotary filter, filtration, membrane
	9		ultrafiltration module, dean vortice, fluidized bed, co2 transfer, variable secondary flow
	10	8	bundle configuration, hollow fibers, vibration, analytical solution, shear rate
	11	7	vibratory disk, particle size, dynamic cross-flow filtration, ceramic membranes, dynamic simulation
		Based on keyword co-occurrence analysis, network relationships were simplified into a
	relatively small number of clusters. Table II.3 lists 12 clusters with the top 5 terms by using
	the Log-likelihood Ratio (LLR). The majority of the keywords are cross-linked and can be

  .4 presents the top 10 keywords citation bursts about DF between 1991 and 2019.

	It is noticeable that all keywords alternate between technologies, applications and
	performances. Dynamic filtration ranked the first position with strength was bursting from
	2000 to 2005. Meantime, skim milk, ultrafiltration, performance and crossflow
	microfiltration also stood as the hot pots before 2010. Afterward, the scientific interest
	evolves from the description of fouling mechanisms (concentration polarization, permeate
	flux and threshold flux) to new applications (microalgae) and technological developments.

Table II .

 II 4 Top 10 keywords with the strongest citation bursts.

	Keywords	Year Strength Begin End	1991-2019
	dynamic filtration	1991 4.2973	2000	2005 ▂▂▂▂▂▂▂▂▂▃▃▃▃▃▃▂▂▂▂▂▂▂▂▂▂▂▂▂▂
	skim milk	1991 2.5107	2004	2009 ▂▂▂▂▂▂▂▂▂▂▂▂▂▃▃▃▃▃▃▂▂▂▂▂▂▂▂▂▂
	ultrafiltration	1991 3.1852	2004	2009 ▂▂▂▂▂▂▂▂▂▂▂▂▂▃▃▃▃▃▃▂▂▂▂▂▂▂▂▂▂
	performance	1991 2.7155	2008	2010 ▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▃▃▃▂▂▂▂▂▂▂▂▂
	cross flow microfiltration 1991 2.4962	2009	2010 ▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▃▃▂▂▂▂▂▂▂▂▂
	concentration polarization 1991 2.5581	2011	2012 ▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▃▃▂▂▂▂▂▂▂
	permeate flux	1991 3.0425	2011	2013 ▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▃▃▃▂▂▂▂▂▂
	microalgae	1991 2.9145	2014	2019 ▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▃▃▃▃▃▃
	technology	1991 2.3293	2015	2019 ▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▃▃▃▃▃
	threshold flux	1991 3.0737	2015	2017 ▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▃▃▃▂▂

Table II .

 II [START_REF] Xie | Investigation of Local and Global Hydrodynamics of a Dynamic Filtration Module (RVF Technology) for Intensification of Industrial Bioprocess[END_REF] Classification of DF modules according to the movement and shape.

	Movement

form Movement part Shape of movement part Shape of membrane Type

	Table II.6 Classification and specification of DF modules (d: membrane diameter, S: membrane surface area, N/F: maximum rotating, vibrating and/or Type Manufacturer Configuration Membrane Status size (
		oscillating speed/ frequency, A: amplitude, displacement or vibrating angle, TMP: maximum operating transmembrane pressure)
	Type	Manufacturer		Configuration	Status	Membrane size (mm)	S (m 2 )	N/F (rpm, Hz), A (mm, °)	TMP (bar)	Fluid	Ref
		Spintek, Huntington Beach, CA,	Spintek ST II	Industrial	d=340	0.05-2.3	1200 rpm	10	/	[154]
		USA		Spintek ST IIL	Lab	d=203 (2)	0.05	1800 rpm	3.1	Cutting oil emulsion	[155]
				High shear rotary
		Spintek, Los Alamitos, CA, USA	membrane system, HSR-	Lab	d=74-267	0.0492	1750 rpm	5.17	Wastewater, O/W emulsion	[156-161]
				MS
		Novoflow GmbH, Rain/Lech, Germany	Single shaft disk filter, SSDF-312 SSDF-500+ Compact rotating disk filters CRD	Industrial Industrial Lab	d=312 (75-100) d=550 (75) d=152 (3)	40 50 0.108	/ / 1800 rpm	/ / 1	/ / Oily wastewater	[162] [73]
		Diva Envitec Pvt. Ltd., India	Modular spin disk filtration, MSDF	Industrial	/	1-100	/	/	/	[163]
		Fraunhofer IGB, Germany, membrane supplier: KERAFOL	Rotating disk filter	Industrial	/	/	/	0.5-1.2	/	[164]
	1	Mio Vigneto Products, Automatic Filter System	Rocket M7	Industrial	(35)	7	/	/	/	[165]
		ANDRITZ KMPT GmbH, Vierkirchen, Germany	Rotational dynamic filtration, DCF 152/S	Lab	d=152	/	1150 rpm	/	Water/ ethanol	[62]
		HUBER (Berching, Germany), Vacuum Rotation Membrane VRM® Bioreactor	Vacuum rotation membrane bioreactor, VRM 20/36 VRM	Industrial Industrial	/ d=4500	108 540	1.8 rpm /	0.3 /	Wastewater /	[166] [167]
		Hitachi, Japan		AQUA UFO	Industrial	/	/	/	/	/	[4]
		ANDRITZ KMPT (Vierkirchen, Germany), membrane supplier: KERAFOL	Dynamic cross-flow filter, DCF	Lab	d=152 (6)	0.138	1110 rpm	5.5	Microalgae	[118, 119]
		Westfalia Separator, Aalen, Germany	Multi shafts disks, MSD, two-shaft laboratory pilot MSD, eight-shaft pilot	Lab Industrial	d=90 (12) d=31.2	0.121 80	2000 rpm /	2.5 /	CaCO3 /	[86, 89, 168] [38]
		Gurpreet Engineering Works,	Spinning basket membrane, SBM	Lab	130×55 (4)	0.0286	600 rpm	9.7	PEG 6000, BSA, Polyving alcohol	[51, 59, 148, 169]
	2	Kanpur, UP, India		Intermeshed spinning basket membrane, ISBM	Disk Lab	105×55 (8)	Disk 0.046	1 480 rpm	9.7	BSA	[149]
		Membrane Key Laboratory of Industrial Ecology and Environmental Engineering, Dalian University of	/ /	Rectangular Lab 300×30 (2) Cylinder Lab 230×20 (2)	Rectangular 0.018 Cylinder 0.0092	160 rpm 2 3 /	0.065 /	Kaolin, yeast, CaCO3 Halogenated compounds in water	[170] [48]
	Rotating			Hollow fiber Disk	Hollow fiber Disk	4 5
			Mechanical device	Impeller		Disk	6
					Cylinder		Cylinder	7
			Mechanical device + Membrane	Disk + Membrane Disk	8
			Filtration module	Cylinder Rectangular	Disk Rectangular	9 10
	Oscillating	Membrane		Rectangular Cylinder	Rectangular Cylinder	11 12
					Hollow fiber	Hollow fiber	13
			Spacers		Rectangular	Rectangular	14
	Oscillating + Vibrating	Membrane		Hollow fiber	Hollow fiber	15
	Vibrating	/

mm) S (m 2 ) N/F (rpm, Hz), A (mm, °) TMP (bar) Fluid Ref

	Type	Manufacturer	Configuration	Status	Membrane size (
		Technology, China
		Hemascience, Santa Ana, CA, USA	Plasmacell filter	Industrial	/	/	/	/	/	[171]
	3	Faculty of Engineering, University of Regina, Canada	/	Lab	/	/	10000 rpm	0.25	Oily-wastewater	[172]
		Membrex Inc. Fairfield, USA	Benchmark Biopurification system	Lab	/	0.02	2000 rpm	1.4	Yeast	[133]
		Department of Chemical	/	Lab	2π×15×500	0.0471	1500 rpm	1.51	PMMA	[81]
		Engineering, Nagoya University, Japan	/	Lab	2π×15×320	0.03016	5000 rpm	1.51	PMMA, O/W	[77, 78, 83]
		Department of Mechanical
		Engineering, Northwestern	Rotating reverse osmosis	Lab	2π×241×127	0.0192	180 rpm	10	CaSO4, model wastewater	[63, 72]
		University, USA
		Millipore Co.	/	Lab	2π×26×670	0.1094	600 rpm	/	SiO2	[92, 94]
		Department of Chemical
		Engineering, Universitie de	/	Lab	2π×5×45	0.0014	7000 rpm	1	Al2O3	[95]
		Technologie de Compiegne, France
		Suker AG, Winterthur, Switzerland	Biodruck-filter, BDF-01	Lab	2π×33×200	0.04	3000 rpm	0.7	Yeast	[173]
	4	Facultad de Ciencias-Seccion de Quí mica, Universidad La Laguna, Spain	Rotating hollow fibre membrane, R-HFM	Lab	/	0.047	330 rpm	0.4	Anaerobic suspensions	[47]
		University of Technology of Compiegne, France	Rotating disk module, RDM-1	Lab	d=154	0.019	3000 rpm	10	CaCO3, yeast, skim milk, juice, broth, dairy effluent, microalgae, PAA-Cd complex	[11, 14, 15, 33, 43, 66, 67, 70, 71, 74, 75, 87, 88, 99, 106, 108, 110, 114, 115, 141, 174-184]
			RDM-2	Lab	d=260	0.046	1500 rpm	2	Skim milk	[183]
		School of Chemistry and Chemical
		Engineering, Central South	Rotating disk module	Lab	d=176	0.0242	3000 rpm	2.5	Cd 2+ , Zn 2+	[185, 186]
		University, China
	5	Department of Chemical and Materials Engineering, Tamkang University, Taiwan, China	Rotating-disk dynamic filter-1 Rotating-disk dynamic filter-2	Lab Lab	d=38 d=155	0.00112 0.0377	3000 rpm 3000rpm	1 1	Microalgae, PMMA, artificial seawater Microalgae	[57, 82, 93, 121] [124]
		Pall Corp., Dreieich, Germany	Dynamic membrane filter, DMF LAB6 system	Lab	d=151	0.0137	3450 rpm	2	Yeast, coli	[134, 145, 153, 187]
		Grundfos BioBooster, Bjerringbro, Denmark	Rotating cross-flow, RCF MBR	Lab	d=312	0.12	350 rpm	15	/	[7]
		BKT Water & Energy, Korea	Anti-fouling membrane filtration system FMX-S FMX-E	Industrial Industrial	/ /	94.9 40	270 rpm 270 rpm	15 5	/ /	[188]
			FMX-P	Industrial	/	0.0873-3.16	290-350 rpm	30	/

mm) S (m 2 ) N/F (rpm, Hz), A (mm, °) TMP (bar) Fluid Ref

	Type Type	Manufacturer Manufacturer	Configuration Configuration	Status Status	Membrane size (mm) Membrane size (mm)	S (m 2 ) S (m 2 )	N/F (rpm, Hz), A (mm, °) N/F (rpm, Hz), A (mm, °)	TMP (bar) TMP (bar)	Fluid Fluid	Ref Ref
		CAPEC, Department of Chemical	FMX-B VSEP series P	Lab Lab	d=150 /	0.0146 1.57	1600 rpm /	1 40	Microalgae /	[123, 126, 128]
		Miltenyi Biotec, Germany Engineering, Technical University	Life 18 disk separator VSEP series B HF membrane filter	Industrial Lab Lab	/ / /	/ 0.0111 0.0256	/ / 30 Hz, 1.175mm	/ 10 0.25	/ / Enzyme, yeast	[189] [13, 136, 221, 222]
	14	Michael Smith Laboratories, Canada of Denmark, Denmark Gesellschaft für Biotechnologische Forschung mbH, Biochemical Engineering Division, Germany Nanyang Environment and Water Research Institute, Nanyang Technological University, Singapore	Controlled shear affinity filtration (CSAF) VSEP series P-50 Controlled shear filtration, CSF VSEP series i18 VSEP series i36 VSEP series i84 Vibrating membrane Spacer vibration of submerged flat sheet membranes	Lab Lab Lab Lab Lab Lab Lab	d=30 / d=90 / / / 50×70×2	0.0014 4.65 0.0515 13.9-26.9 41.8-55.7 up to139 0.007	/ / / 35-49 Hz 38-55 Hz 43-55 Hz 2 Hz, 12 mm	/ 40 / 38 38 38 0.4	/ / BHK cell / / / Bentonite and alginate solution	[190] [144] [223]
	6 15	Bokela GmbH, Karlsruhe, Germany Metso Paper Co, Raisio, Finland Pall Filtration, East Hills, NY, USA School of Chemical Engineering, The University of New South Wales, Australia Department of Nephrology, San Bortolo Hospital, Italy Department of Mechanical Engineering, Texas A&M University, College Station, TX, School of Chemical Engineering, The University of New South Wales, Australia USA Chemical and Biochemical Engineering Department, Western University, London, Ontario, School of Water Resource and Civil Engineering, Northeast Agricultural University, China	Dynotest DYNO Cross Rotational (CR)-Filter, CR 200/1 CR 250/2 CR 500/5 CR 550 / 15 to 30 filtration, VMF-PALLsep PS 10 Transverse vibrating hollow fibre membrane VMF-PALLsep Biotech Module Shaking HF membrane module Vibration enhanced reverse osmosis (VERO) membrane Rotational vibrating hollow fibre membrane CR 1000/ 26 to 60 Oscillatory flat surface membranes, OFSM Vibration hollow fibre membrane	Lab Industrial Lab Lab Industrial Industrial Lab Lab Industrial Lab Lab Lab Industrial Lab Lab	/ / d=200 (1) d=250 (2) d=500 (5) d=550 (15-30) / / / / 30×20 / d=1000 (26-60) 89×68 /	0.013 0.13-12 0.054 0.18 1.75 7.5-15 0.2 / 0.2-5 / 0.0006 0.0131 35-84 0.006 0.0045	/ / / 470 rpm / 55-55.75 Hz 58 Hz, 5 mm / 20 Hz, 20 mm (20 °) 60 Hz, 1.2 mm 10.3 Hz, 18.3-55° / 25 Hz, 30 mm 2 Hz, 180 °	7 6 / 10 2.7 / 2 0.2 3.5 / 55 0.8 / 0.6 0.6	Alpha-lactose monohydrate suspension / Paper mill waste BSA Yeast, milk / / Simulated seawater Yeast Yeast Microalgal	[150] [191] [192-194] [195] [196] [204] [138, 224] [205] [225, 226] [56, 64] [32] [39] [39] [137, 139, 206-209] [132]
		Canada Institute of Oceanic and	CR 1000/10	Industrial	d=1000 (10)	13.5	365 rpm	1		[193]
		RVF Filtration, Paris, France Katholieke Universiteit Leuven, Faculty of Bioscience Engineering, Tongji University, China Technology, China State Key Laboratory of Pollution Control and Resource Reuse, Environmental Chemical Engineering, Zhejiang University of	CR 1010/70 to 100 Rotating and vibrating filtration, RVF membrane vibration, Magnetically induced USVM Uniform shearing vibration membrane, Pendulum type oscillation, PTO	Industrial Lab Lab Lab Lab	d=1010 (70-d=142 (4) / 100) / /	0.024 per cell (1 to 5 cells) 0.016-0.0215 60 Hz, 20 mm 50 Hz 98-140 / 0.02 5 Hz, 20 mm 0.2 70 rpm, 50 mm	3 0.3 / 0.7 /	Beer, wine, viscous, solution anaerobic sludge, Wastewater, microalgae, Microalgae Oily wastewater	[46, 211-215] 198] [6, 8, 111, 112, 197, [39] [210] [227]
		Belgium Fann Instrument Company, Houston, Texas, USA State Key Laboratory of Pollution Control and Resource Reuse, Tongji University, China	RVF 5 MMV Fann 90 Dynamic HPHT® Filtration System Axial vibration membrane, AVM	Industrial Lab Lab	d=800 (10) / /	1 per cell (1 to 5 cells) / 0.02	30 Hz 300 rpm 15 Hz, 40 mm	20 7 0.7	lignocelluloses hydrolysate Waste water, chemical sludge [199, 200] Drilling fluid [201] Microalgae [216-218]
	7	Department of Nuclear Methods in Process Engineering, Dorodna, Warsaw, Poland Department of Chemical Engineering, University of Engineering & Technology	Helical Couette-Taylor flow (CTF) filtration module Oscillating membrane module	Lab Lab	/ /	0.04 /	2800 rpm 0-100 Hz, 0-10 mm	0.7 0.4	Radioactive wastes, wastewater Oil in water emulsion	[52, 53] [79]
	8	Gurpreet Engineering Works, Kanpur, UP, India Peshawar, Pakistanb Krauss-Maffei DCF, Andritz KMPT GmbH, Vierkirchen, Germany Chemical Engineering Department, Loughborough University, Leics, UK IMI Institute for R&D, Israel Chemicals Group, Israel	Rotating disk-membrane, RD-M Dynamic cross-flow Azimuthal and axial oscillation filtration filtration, DCF Vibratory shear enhanced Vibrating hollow fibre microfiltration, VHM	Lab Lab Lab Lab	/ d=152 (4) / /	0.00246 0.14 / 0.0057	Membrane:600 rpm stirrer: 1000 rpm 1000 rpm 100 Hz, 3 ° 10 Hz, 40mm	10 5 0.3 /	BSA, PEG6000, kraft black liquor Skim milk Suspension of calcite Skim milk, simulated tannery Yeast	[41, 42, 58, 60, 147] [105] [219] [34, 44, 65, 84, 100, [220]
		School of Civil and Environmental	processing, VSEP series L	Lab	d=135	0.05	55-60.75 Hz	15	wastewater, microalgae, latex	101, 127, 131, 181,
	9	New Logic, CA, USA Engineering, Nanyang Technological University,	101 VSEP series LP Vibrating submerged hollow fibre membranes	Lab Lab	/ /	1.53 /	/ 0-15Hz, 0-12mm	40 0.4	solution Microalgae Bentonite	202] [122] [80]
		Singapore	VSEP series L	Lab	/	0.446	/	40	/	[203]

Table II .

 II 7 Dimensionless numbers used to describe hydrodynamic within Dynamic Filtration device (d: diameter, u: velocity, Q: flowrate, r: radius, dh: hydraulic diameter, rh: hydraulic radius, do: outer diameter; di: inner diameter, uz, axial flow velocity, N: mixing rate, dm: rotor diameter, k: core velocity coefficient, : angular velocity, h: rotor height, α: inclination angle of conical rotor, s: characteristic length scale, F: oscillating/ vibrating frequency, H: vertical distance).

	Mode						Formula	Equation
	Tube	Re =	ρdu 𝜇	or Re 𝑄 =	ρQ 𝜇𝜋𝑟	(II.1)
	Equivalent tube	Re =	ρd ℎ u 𝜇	or Re 𝑄 =	ρQ 𝜇𝜋𝑟 ℎ	(II.2)
	Annulus tube	Re =	ρ(𝑑 𝑜 -𝑑 𝑖 )u 𝜇	(II.3)
	Axial flow in annulus	Re 𝑎 =		2ρdu 𝑧 𝜇	(II.4)
	Rotating system (mixing)	Re 𝑚 =	2 ρNd 𝑚 𝜇	(II.5)
	Rotating system*	Re 𝑟 =	kρω𝑟 2 𝜇	(II.6)
	Rotating cone	Re s =	𝜌ω(h + rtanα) 2 μ	(II.7)
	Gap based Ekman number	Ek =	1 𝑅𝑒 𝑠		=	μ 𝜌𝜔𝑠 2	(II.8)
	Oscillating/Vibrating system	Re 𝑣 =		2πF𝐻 2 𝜌	(II.9)

Table II .

 II [START_REF] Xie | Local hydrodynamic investigation by PIV and CFD within a Dynamic filtration unit under laminar flow[END_REF] Four flow pattern in rotating system.

	Rer	z/Rm	Flow regime	Pattern
	<2-3×10 5	<0.05	Laminar	I
	<2-3×10 5	>0.05	Laminar	II
	>2-3×10 5	<0.05	Turbulent	III
	>2-3×10 5	>0.05	Turbulent	IV

Table II .

 II [START_REF] Chaudhuri | Permeate flux decrease due to concentration polarization in a closed roto-dynamic reverse osmosis filtration system[END_REF] Core velocity coefficient of different DF filters.

	Module	Rotor	z (mm)	z/Rm	Flow regime	Testing fluid	k	Ref.
	Rotating infinite disks	One disk rotates	/	/	/	Reynolds Re=l0 4 numbers	0.3131	[245]
	RDM (154 mm housing)	Plexiglas flat disk (smooth) PVC flat disk Disk with mesh Smooth flat disk	10	0.13 0.13	Turbulent Turbulent Turbulent Turbulent	CaCO3 suspension, 60 kg/m 3	0.32 0.35 0.43 0.44	[174]
		Disk with 8 pairs of 2mm rods	10	0.14	Turbulent		0.62
	RDM (154 mm housing)	Smooth flat disk Disk with 8 pairs of 6mm vans	8	0.11 0.11	Turbulent Turbulent	Water	0.45 0.84	[11]
		Smooth flat disk			Turbulent		0.42
	RDM (154 mm housing)	Disk with 8 pairs of 2mm vans Disk with 8 pairs of 4mm vans	15	0.21	Turbulent Turbulent	Water	0.65 0.71	[183]
		Disk with 8 pairs of 6mm vans			Turbulent		0.79
	RDM (176 mm housing)	Flat disk Disk with 6 of 2mm rectangular vanes	14 12	0.17 0.14	Turbulent Turbulent	Water	0.44 0.79	[185]
		Smooth flat disk	17	0.23	Turbulent		0.45
		Disk with 8 pairs of 2mm vans	15	0.21	Turbulent		0.65
	RDM (154 mm housing)	Disk with 4 pairs of 4mm vans Disk with 8 pairs of 4mm vans	15 15	0.21 0.21	Turbulent Turbulent	Baker yeast suspension, 3g/L	0.69 0.71	[15]
		Disk with 8 pairs of 6mm vans	15	0.21	Turbulent		0.84
	RVF mm housing) (154	3 blades impeller	3	0.04	Turbulent Laminar Laminar	Water PIV CFD	0.71 0.3 0.35	[111] [8]
	RCF (352.6 mm housing)	Plastic flat disk	5	0.04	Laminar Turbulent	CFD CFD	0.895 0.795	[7]

Fig. II.10 Evolution of core velocity coefficient, 𝐾 𝜃 as a function of gap-to-radius ratio, z/Rm. Values are reported from literature for DF modules using confined rotating impeller close to the membrane and established under laminar or turbulent regimes

  .2.2.1 Rotating systemsIn rotating systems, flow is governed by centrifugal forces generated by rotors, and it induces different flow patterns near the rotor and the stator. Considering the boundary theory, four different flow regimes were presented, according to azimuthal Reynolds number and the gap to radius ratio z/Rm, and shear rates at rotor (γR) and membrane (γS) surfaces were defined in TableII.10:

	Regime				Rotor				Stator
	I	𝛾 𝑅 =	𝜔𝑟 𝑧				(II.21)	𝛾 𝑆 =	𝜔𝑟 𝑧	(II.22)
	II	𝛾 𝑅 = 1.81	(𝑘𝜔) 𝑣 1 2 3 2 ⁄ 𝑟 ⁄		(II.23)	𝛾 𝑆 = 0.77	(𝑘𝜔) 3 2 ⁄ 𝑟 𝑣 1 2 ⁄	(II.24)
	III	𝛾 𝑅 = 0.008	(𝜔𝑟)	7 4 ⁄ ( 𝑣 𝑧 ⁄ ) 𝑣	1 4 ⁄	(II.25)	𝛾 𝑆 = 0.0115	(𝜔𝑟)	7 4 ⁄ ( 𝑣 𝑧 ⁄ ) 1 4 ⁄ 𝑣	(II.26)
	IV	𝛾 𝑅 = 0.057	(𝑘𝜔) 𝑣	9 5 ⁄ 𝑟 4 5 ⁄	8 5 ⁄	(II.27)	𝛾 𝑆 = 0.0296	(𝑘𝜔)

Table II.10 Shear rate of four flow regimes in a rotation system.

  Gomaa et al.[START_REF] Gomaa | Intensification of membrane microfiltration using oscillatory motion[END_REF] investigated a flat vertical vibrating membrane unit with turbulence promoters. They gave a surface shear rate expression in Eq. (II.38) and the maximum shear rate in Eq. (II.39).

	𝛾(𝑡) =	𝐴𝑤 1.5 2𝑣 0.5 (cos 𝜔𝑡 +	𝜋 4	)	(II.38)

  Hz and amplitude of 1.175 mm, it could reach up to approximately 2000 s -1 with the permeate flowrate of 68 L/(m 2 h).

	𝛾̅ 𝑠 = 𝛾 𝑚𝑎𝑥1 ∑ 𝛾 𝑚𝑎𝑥2 = 1000 |𝛾 𝑠 (𝑡 = 𝑖/1000)| 𝑖=0 1000 𝑑 1 𝑑 2 ( 1.5 𝜔 1 𝜔 2 )	(II.42) (II.43)

  For laboratory or industrial DF devices, energy demand is rarely reported and resumed in TableII.11. Specific energy varies to a large extent from 0.29 to more than 1000 kWh/m 3 due to the different configurations and scales. Other parameters such as disk design, fluid concentration and temperature also affect power consumption. Consequently, the comparison of DF modules is hardly reliable or feasible.

			Table II.11 Specific energy demand in different modules.
	Module		Fluid	Membrane	N (Hz, rpm)/ A (mm)	S (m 2 )	J (L/m -2 h)	TMP (bar)	E (kWh/m 3 )	Ref.
	RDM	1:2 diluted skim milk	NF	2000 rpm	0.0176	350	40	170	[176]
	RDM	1:2 diluted skim milk	NF	1000 rpm	0.0176	135	40	303	[176]
	RDM	1:2 diluted skim milk	UF	2000 rpm	0.019	/	/	65	[183]
	RDM	1:2 diluted skim milk	UF	2000 rpm	0.019	/	/	30	[183]
	RDM	Baker yeast	MF	2000 rpm	0.019	200	/	15	[15]
	MSD	CaCO3	MF	1930 rpm	0.06	/	3	1.7	[87]
	MSD	CaCO3	MF	1930 rpm	0.033	/	3	2.9	[87]
	VSEP	Skim milk	RO	60.2 Hz	100	55	40	1.63	[69]
	VSEP	Skim milk	UF	60.4 Hz	151	56	/	1.05	[101]
	OFSM	baker's yeast	MF	25 Hz/ 1.5 mm 0.006	500	0.6	0.3	[139]
	SBM	PEG 6000	UF	400 rpm	0.0286	411	5.884 80	[59]
	MMV	Activated sludge	MF	/	0.016	16	/	12.2	[212]
	MMV	Activated sludge	MF	/	0.096	16	/	2.03	[212]
	VHM	Yeast	MF	1.7 Hz	0.0057	46	/	0.29	[220]
	VERO	Silica colloids and sodium chloride	RO	/	0.006	/	/	~10 3	[64]
	𝑇 𝑄 𝑓	≈	𝑃 𝑀 𝐽𝑆𝜂						(II.50)

Table II .

 II [START_REF] Zsirai | The impact of mechanical shear on membrane flux and energy demand[END_REF] Resume of available data about hydrodynamics and applications with the different types of DF modules.

		Empirical data							Hydrodynamics investigation
		Application / Performances			Global approach		Semi-local approach (Membrane or rotor surface)	Local approach (Filtration cell volume)
	Type	Water treatment	Food processing	Bioprocess engineering	Dimensionless	analysis	Dimensionless	correlation	Pumping power	Mechanical power	Core velocity coefficient, k	𝑃 ̅ (𝑥, 𝑦, 𝑧)	γ(x,y,z)	U(x,y,z,t)/ γ(x,y,z,t)

Table III .

 III In Fig.III.1 c and d, a home-designed and instrumented porous substrate was used to measure the local pressure at the membrane surface. Eight pressure taps (2 mm) were connected to stainless tubes, with one extremity welded to the porous support and the other extremity located on the outer cell wall. The pressure taps were distributed between 26.2 mm (R1) up to 64.9 mm (R8), as indicated in TableIII.1.

	Radial position	Radius (mm)	Radial position	Radius (mm)
	R1	26.2	R5	45.3
	R2	29.3	R6	53.9
	R3	34.8	R7	63.4
	R4	38.2	R8	64.9

1 Radial distribution of pressure taps at the membrane surface (porous substrate).

  Table III.2 and Table III.3.

Table III .

 III 2 All sensors used in the experiment.

	Sensor	Ref	Measure	Range-precision	Application Global Semi-local Local Cell
	Relative pressure sensor, Bourdon-Haenni E913	PR 1	Pinlet	0-10 bar, ±0.2%	×	×	×	×
	Relative pressure sensor, Bourdon-Haenni Y913	PR 2	Poutlet	0-6 bar, ±0.2%	×	×	×	×
	Relative pressure sensor, KELLER, PR 23	PR 3	P(N,r,t)	-1-1 bar, ±0.1%	/	/	×
	Conductivity meter Conducell 4USF-PG325	Cond Tinlet	1-500000 μS/cm, ±1%; -20-150 ℃, ±0.5 ℃	×	×	×
			Toutlet	0-130 ℃, ±1 ℃	×	×	×
	Mass flowmeter, KROHNE MFS-7050-S06	MF	ρ	500-2000 kg/m3, ±2 kg/m 3	×	×	×
			QF	0-950 kg/h, ±0.1% Liq, ±0.5% Gas	×	×	×
	Differential pressure sensor, Honeywell STD 120 DP 1	ΔPRVF	0-2.5/ 1000 mbar, ±0.075%	×	/	/
	Differential pressure sensor, Honeywell STD 120 DP 2	ΔP(N,r,t) 0-2.5/ 1000 mbar, ±0.075%	/	×	/
	Ammeter AT 20 B 10 LEM KR 02	CU	I	Input: 20 A, Output: 0-10 V, precision ±0.3 A	×	/	/
	Voltmeter Camille bauer Ref: SINEAX U 504	TEN	U	Tech. Info. Input: 0-250 V, 50 Hz, Output: 0-20 mA, R: 750 , precision ±0.2V	×	/	/

×: means selected; /: indicates not used.

Table III .

 III [START_REF] Daufin | Recent and Emerging Applications of Membrane Processes in the Food and Dairy Industry[END_REF] All equipment used in the experiment.

	Devices	Information	Notes
	Tank	8 L double-jacket glass tank	With a thermal regulation
	Pump	Head: TUTHILL CO., series A54739, Drive: GROSCHOPP CO., series PM8014, 3800 rpm, DC motor control unit: DART 250G series	Feeding pump
	Rotor	94358 electronic, Heidolph	Mixing the fluid in the tank
	Thermal balance	9105-BB, Polyscience, serial 615342, temperature range: -45-150 ℃, reservoir capacity: 13 L	To maintain the temperature
	Pressure gauge	Manometer, 0-6 bar	To control the counter pressure in the outlet
	Motor	LSFMV80L, LEROY SOMER	To enhance the filtration in the RVF
	Tachymeter	Testo 460, Germany, 100-29999 RPM, ±0.02% of mv, resolution 0.1 RPM (100-999.9 RPM) 1 RPM (1000 to 29999 RPM)	To measure the rotating speed of motor

Table III .

 III 4 Data acquisitions in the experiments.

	Sensor	Measure	Global Agilent	Instantaneous and local Agilent	NI
	PR 1	Inlet pressure, Pinlet	×	×	/
	PR 2	Outlet pressure, Poutlet	×	×	/
	PR 3	Instantaneous pressure, P(N,r,t)	/	/	×
	Cond	Inlet temperature, Tinlet	×	×	/
		Outlet temperature, Toutlet	×	×	/
	MF	Density, ρ	×	×	/
		Flowrate, QF	×	×	/
	DP 1	Pressure drop, ΔPRVF	×	/	/
	DP 2	Mixing pressure, ΔPmixing	×	/	/
	CU	Current, I	×	/	/
	TEN	Tension, U	×	/	/

×: means selected; /: indicates not used.

Table III .

 III [START_REF] Xie | Investigation of Local and Global Hydrodynamics of a Dynamic Filtration Module (RVF Technology) for Intensification of Industrial Bioprocess[END_REF] Operating conditions for global and local pressure measurements. flowrate, mixing rate, radius, back pressure and impeller configurations on the local pressure were introduced. The detailed information is shown in TableIII.5.

	Fluids	Parameters QF (L/h) N (Hz) r (mm) Poutlet (mbar) Imp 1 R-Imp 1 Imp 2 Imp 3 Impellers
	Water (0.001 Pa.s)	50-300	0-50	R1-R8	0-500	×	×	×	×
	BREOX 0.1 (0.01 Pa.s)	50-200	0-50	R1-R8	310	×	/	/	/
	BREOX 0.2 (0.05 Pa.s)	50-130	0-40	R1-R8	440	×	/	/	/
	BREOX 0.3 (0.2 Pa.s)	25-40	0-30	R1-R8	630	×	/	/	/
	BREOX 0.4 (0.6 Pa.s)	12	0-20	R1-R8	890	×	/	/	/

The model fluids (water and BREOX solutions) were used for global and local measurements, with the flow from laminar to turbulent regimes. Several parameters, including feeding

  In theory, the continuous model of pressure fluctuation distribution results from the convolution of EP(x) with ER(x), as reported in Eq.(III.22). Comparison between experimental data and model is realized by identifying amplitude, A for periodic component, and standard deviation (σ) for a random term. Considering the statistical convergence, phase lag has no effect on PDF building. Both optimal parameters, A and σ are obtained by minimizing the cumulative error function, Δ with Eq. (III.23), thanks to Excel solver (Suite Office Microsoft 2013, Excel, GRG non-linear) for each operating condition. Fig. III.6 illustrates the experimental and simulated PDF at R6 and 20 Hz.

	Table III.6 Signal decomposition into periodic and random contributions (PP(t): periodic signal, PR(t):
	random signal, A: amplitude, f: frequency, φ: phase, σ: standard deviation, EP(x) and ER(x) are the
			PDF.).
	Contribution	Function	Parameters	PDF (mbar -1 )		Energy input (mbar)
	Periodic Random	𝑃 𝑃 (𝑡) = 𝐴𝑠𝑖𝑛(2𝜋𝑓𝑡 + 𝜑) 𝑃 𝑅 (𝑡)~𝑁(𝑥̅ , 𝜎 2 )	A, f=3N, φ 𝑥̅ = 0, σ	𝐸 𝑃 (𝑥) = 𝐸 𝑅 (𝑥) =	1 𝜋√𝐴 2 -𝑥 2 1 𝜎√2𝜋 𝑒 -1 2 ( 𝑥-𝑥̅ 𝜎	) 2	𝐴 √2 ⁄ σ

  Table IV.1:

		10 4						a	10 4					b	Water-50 L/h Water-100 L/h
														Water-150 L/h
														Water-300 L/h
	(/)	10 3							10 3 (/)					BREOX 0.1-50 L/h BREOX 0.1-100 L/h
	Eu(N)	10 2							10 2 Eu(N)					BREOX 0.2-100 L/h BREOX 0.1-150 L/h BREOX 0.1-200 L/h BREOX 0.2-50 L/h
														BREOX 0.2-130 L/h
														BREOX 0.3-25 L/h
														BREOX 0.3-40 L/h
		10 1	10 0	10 1	10 2	10 3	10 4	10 1	10 2	10 3	10 4	10 5	10 6	BREOX 0.4-12 L/h
					Re feeding (/)						Re mixing (/)
						10 4
												Imp	1-Water
												Imp	1-BREOX	0.1
												Imp	1-BREOX	0.2
					(/)	10 3						Imp Imp	1-BREOX 1-BREOX	0.3 0.4
					Hz)							Imp Imp	2-Water 3-Water
					Eu(N=0	10 2						Imp	1-model
						10 1
							Eu(N=0	Hz)=3924/Re feeding +14
							R 2	=0.9996
						10 0
							10 0	10 1			10 2	10 3	10 4
									Re	feeding (/)

Table IV .

 IV 1 Established friction curves for three impellers.

	Impeller	Conditions	Equation	R 2
	Imp 1	2000<Remixing<1200000, 30<Refeeding<11000	𝐸𝑢(𝑁) -𝐸𝑢(0 𝐻𝑧) =	1.53 0.0111𝑅𝑒 𝑚𝑖𝑥𝑖𝑛𝑔 𝑅𝑒 𝑓𝑒𝑒𝑑𝑖𝑛𝑔 1.27	0.9934
	Imp 2	90000<Remixing<1200000, 1500<Refeeding<11000	𝐸𝑢(𝑁) -𝐸𝑢(0 𝐻𝑧) =	1.46 0.047𝑅𝑒 𝑚𝑖𝑥𝑖𝑛𝑔 𝑅𝑒 𝑓𝑒𝑒𝑑𝑖𝑛𝑔 1.32	0.9985
	Imp 3	90000<Remixing<1200000, 1500<Refeeding<11000	𝐸𝑢(𝑁) -𝐸𝑢(0 𝐻𝑧) =	1.38 0.157𝑅𝑒 𝑚𝑖𝑥𝑖𝑛𝑔 𝑅𝑒 𝑓𝑒𝑒𝑑𝑖𝑛𝑔 1.36	0.9983

Table IV .

 IV 2 Numerical coefficient for the thermal dissipation based on the equation: Ф 𝑇 = 𝑎𝑁 2 .

	Fluids	QF (L/h)	N (Hz)	Imp 1	Imp 2	Imp 3
		50	0-50	0.1395	0.2565	0.1358
	Water,	100	0-50	0.1386	0.1463	0.1253
	μ=0.001 Pa.s	150	0-50	0.1627	0.1561	0.1259
		300	0-50	0.1786	0.1527	0.141
		50	0-50	0.1295	/	/
	BREOX 0.1,	100	0-50	0.156	/	/
	μ=0.01 Pa.s	150	0-50	0.1743	/	/
		200	0-50	0.1896	/	/
	BREOX 0.2, μ=0.05 Pa.s	50 100 130	0-40 0-40 0-40	0.1916 0.1842 0.1821	/ / /	/ / /
	BREOX 0.3,	25	0-30	0.2453	/	/
	μ=0.2 Pa.s	40	0-30	0.2854	/	/
	BREOX 0.4, μ=0.6 Pa.s	12	0-20	0.4496	/	/
	1.3.3 Energy balance
	Considering the energy balance in the RVF module, the thermal dissipation should equal
	to the power input (pumping and mixing power).

  .3. Since membrane surface pressure includes periodic signals generated by impellers and random signals induced by turbulent flow, coupled with sensor errors, it is not accurate to describe pressure fluctuations by standard deviation only. The different methods are compared below.

Table IV .

 IV [START_REF] Daufin | Recent and Emerging Applications of Membrane Processes in the Food and Dairy Industry[END_REF] Information on the data treatment.

	Method	Mean pressure	Periodic + Random	Fluctuating pressure Periodic	Random
	SA	𝑃 ̅ (𝑁, 𝑟)	σp, S, F	/	/
	PDF	/	Peak-to-peak	/	/
	FFT	/	/	Ai, fi	/
	Model	/	/	A1, f1	σ

Table IV .

 IV 4 Signal reconstruction for Imp 1 at R6, with the value of the two parameters to estimate the instantaneous pressure. A and σ are calculated from the convolution of PDF functions.

	N (Hz)	P0 Constant (mbar)	ΔPmixing k (/)	𝑷 𝑷 ̃(𝒕) A (mbar)	f (Hz)	𝑷 𝑹 ̃(𝒕) σ (mbar)
	10			5.5	3N	6.9
	20			58	3N	9
	30	294.5	0.59	32.3	3N	11.1
	40			24.4	3N	13.2
	50			21.8	3N	15.3
	Fig. IV.30 Signal reconstruction of instantaneous pressure with empirical correlations (continuous
	and fluctuating components at R6). Dots and lines correspond to the experimental and reconstructed
			signal, respectively.

  The dominant contribution of amplitude at 3N was extracted and plotted versus viscosity in Fig. IV.35.These results are similar to σP but slightly decreased.

	2.2.5.2 FFT
	From turbulent to laminar flow, the same frequencies of peak amplitudes can be found
	by FFT, which has been described in sections § 2.2.3.3 and 2.2.4.2.

Table IV .

 IV [START_REF] Xie | Investigation of Local and Global Hydrodynamics of a Dynamic Filtration Module (RVF Technology) for Intensification of Industrial Bioprocess[END_REF] Validation of CFD simulation based on velocity and pressure field.

	Simulation	Fluid properties ρ (kg/m 3 ) μ (Pa.s)	N (Hz)	Operating parameters Pb (mbar)	QF (L/h)
	Velocity	1060	0.81	2	300	45
	Pressure	1060	0.18	0-30	625	25

Table S 2

 S Effect of blade number on core velocity coefficient.

	Operating conditions	Number of blades (/)	k (/)
		2	0.61
	μ=0.2 Pa.s,	3	0.65
	N: 0-30 Hz,	4	0.66
	r=53.9 mm	6	0.59
		8	0.59
	Operating conditions	Angle of blades (°)	k (/)
		0 (no blades)	0.23
		20	0.65
	μ=0.2 Pa.s, N: 0-30 Hz, r=53.9 mm	30 45 60 75	0.65 0.66 0.64 0.64
		90	0.6
		120 (full disk)	0.5

Table S 3

 S Effect of impeller/membrane gap on core velocity coefficient.

	Operating conditions	Impeller/membrane gap (/)	k (/)
		2	0.71
		3	0.65
	μ=0.2 Pa.s,	4	0.64
	N: 0-30 Hz,	5	0.59
	r=53.9 mm	6	0.61
		7	0.59
		10	0.65

X X X X n.a X X X X X X n.a X

X X X X X X X X X X X n.a X

Hz 20 Hz

Chapter III: Materials and Method

The rotating and Vibrating Filtration (RVF) module was used to investigate their global performances (mixing and pumping power), local and instantaneous pressure. On the global scale, the effect of operating conditions was characterized by the thermal increase in the filtration cell, the pressure drop and the power consumption. Local measurements were carried out to quantify the continuous and fluctuating pressure.

The configuration of the RVF module (filtration cell and impeller geometry and number of blades) and its instrumentation were described with a focus on pressure measurement at the membrane surface. Data treatments were performed with Statistical Analysis (SA), Probability Distribution Function (PDF), Fast Fourier Transform (FFT) and then modeling to extract the amplitude and frequency of pressure fluctuation. The experiments were carried out with Newtonian fluids (water and BREOX solutions) in laminar and turbulent regimes.

Afterward, the methodology associated with CFD simulation (COMSOL Multiphysics) was detailed.

Highlights:

(1) Experimental set-up to acquire the local pressure at the membrane surface;

(2) Data treatment of time-series pressure;

(3) Optimization of impeller geometries and operating conditions based on numerical approaches.

Chapter IV: Results and Discussion

Dynamic filtration exhibits high performance by generating wall shear stress (tangential to the membrane) and pressure stress (normal to the membrane) by mechanical movements, such as rotating, oscillating or vibrating systems. The rotating and Vibrating Filtration (RVF) module includes rotating flat blade impellers which generate high and fluctuating shear stress and pressure at the membrane surface.

To optimize the operating conditions, global parameters (power consumption, pressure drop) and driving forces (mean, instantaneous and local pressure at the membrane surface) were characterized. For global approach, friction and mixing power in the RVF module were described by semi-empirical correlations.

❖ Summary of CFD investigation Objectives:

(1) To clarify the operating conditions (QF, Pb, N and μ) on the pressure and shear stress distribution (mean and fluctuating components);

(2) To expand the range of experiments (QF, Pb, N and μ);

(3) To optimize the filtration cell (impeller geometry and gap s).

Contents:

The filtration performances are associated with the local shear stress (𝜏̅ and σs) and TMP (k-value and σP) at the membrane surface, which has been compared based on different operating parameters and cell geometries.

(1) Laminar regime Operating parameters: ➢ Feeding flowrate shows a slight effect on local pressure due to the contribution of radial velocity, which can be neglected in dynamic filtration; ➢ Back pressure has no effect on pressure and shear stress; ➢ ΔPmixing and σP are positively correlated with mixing rate and radius, but the contribution of σP is limited to less than 12% when the back pressure is 300 mbar; ➢ The ratio between σs and 𝜏̅ can reach up to 39%.

Filtration cell geometries:

➢ The optimal impeller geometry is a 30° three blades impeller; ➢ The maximum pressure and shear stress can be achieved with a 3 and 4 blades impeller, but the increase in blade number is negative to pressure and shear stress fluctuation; ➢ Reducing impeller/membrane gap contributes to improving local pressure and shear at the membrane surface.

(2) Turbulent regime ➢ The simulated k value is overestimated; ➢ The increase of σP is quasi-linear as a function of local radius; ➢ The 𝜏̅ can be estimated with the empirical equation, and the contribution of σs is limited below 10%. The simulation in the turbulent regime needs to be further investigated in order to give the optimum cell geometry.

Chapter V: Conclusions and Perspectives 1 Scientific context

In order to investigate the intensification of membrane bioreactors with dynamic filtration (DF), our group has conducted a wide range of studies to characterize the hydrodynamics in RVF modules and their performances in biotechnology. With the knowledge gaps, this doctorate was devoted to gaining insight into the complex hydrodynamics of RVF module at global and local scales, scrutinizing the local and instantaneous measurements of the driving force (pressure), and accessing a better understanding of the limiting mechanisms that take place close to the membrane during the filtration operation.

Firstly, in this framework, an extensive review was realized, describing the DF techniques and the related hydrodynamic investigations, providing the scientific background of this research, and raising its application prospects and limitations.

Secondly, RVF, as shear-enhanced membrane filtration, has demonstrated better performance than DE and CF filtrations. Due to the rotation of the impeller, high shear stress is generated at the membrane surface, uncoupling from the feeding flowrate. The instrumentation and experimental set-up to measure the global parameters (current, tension, pressure drop, temperature and flowrate), local and instantaneous pressure were achieved.

The time series pressure has been treated with SA, PDF and FFT in order to extract the mean and fluctuating (amplitude and frequency) components. Furthermore, the simulation of the same geometry (one cell) with CFD technology (COMSOL Multiphysics) was detailed in the laminar and turbulent regimes.

Thirdly, at the global scale, the empirical correlations to estimate the mixing and pumping power have been established with dimensionless numbers. The laminar and turbulent regimes were identified. For local approach, mean radial pressure and core velocity coefficient were quantified at different flowrates and mixing rates. The local k-value is highly dependent on the contribution of the angular velocity. But in the laminar regime, especially for high viscous fluid, the variation of the boundary layer also needs to be taken into account.

Pressure fluctuations have been treated with several strategies to compare their amplitude (periodic and random components) and frequency. In the turbulent regime, a "resonance frequency" close to 20 Hz (21.1 Hz) is clearly identified for Imp 1, at which frequency the magnitude of pressure fluctuation is significantly higher than the other two impellers (Imp 2