Aliza Abraham
email: aliza.abraham@univ-amu.fr

Andrés Castillo-Castellanos

Thomas Leweke

Simplified model for capturing helical vortex interactions with applications to asymmetric rotor wakes

Introduction

The wakes of rotors, such as those found on helicopters, wind turbines, and propellers, are characterized by helical vortices. The interaction between these vortices can lead to various types of instabilities, including displacement instabilities, the focus of the current study. Displacement instabilities occur when the vortex core is shifted from its baseline position, causing adjacent vortices to group together (pairing). When the entire helix is shifted, global pairing occurs. This type of instability can be caused by asymmetry in the rotor generating the helical vortex system, as demonstrated for a two-vortex system by Quaranta et al. [START_REF] Quaranta | Local and global pairing instabilities of two interlaced helical vortices[END_REF]. Most rotors in industrial applications (and their laboratory-scale counterparts) have three or more blades, substantially increasing the complexity of the interlaced helical vortex system. Furthermore, global pairing occurs frequently in laboratory experiments (e.g., [START_REF] Felli | Mechanisms of evolution of the propeller wake in the transition and far fields[END_REF]), likely due to small asymmetries that are unavoidable in scaled-down experiments. This phenomenon has not been thoroughly investigated due to this increased complexity.

The current study proposes a simplified model to develop a more complete understanding of the effect of rotor asymmetry on the development of the helical vortices in the wake. The model is based on the behavior of an infinitely repeating periodic strip of point vortices, which represents a crosssection of an infinite helical vortex system. Though highly simplified, a previous study by Delbende et al. [START_REF] Delbende | Nonlinear dynamics of two helical vortices: A dynamical system approach[END_REF] for a two-vortex system shows that point vortices can be used to represent helical vortices for low values of helical pitch, as is usually the case for rotor wakes. In addition, comparisons with experiments show that the point vortex model captures rotor wake behavior remarkably well. With this simplified model, the broad parameter space required to fully characterize rotor asymmetry (i.e., variations in length, axial position, and pitch of all blades) can be explored in detail.

Methods

Point vortex model

The representation of helical vortices as point vortices is based on the assumption that, for small values of helical pitch relative to the radius of the helices, the effects of curvature and torsion are small [START_REF] Delbende | Nonlinear dynamics of two helical vortices: A dynamical system approach[END_REF]. Under these conditions, the interlaced helices can be "unrolled" and represented as an array of straight parallel vortices subject to periodic boundary conditions dictated by the helical geometry. These straight vortices can in turn can be represented by periodically-repeating point vortices in two dimensions, whose non-linear dynamics can be calculated easily using the induced velocity of neighboring vortices. For a strip of N point vortices repeated periodically along the x-axis, where N represents the number of helices in the original system, the following formula governs the displacement of the basic strip [START_REF] Aref | On the equilibrium and stability of a row of point vortices[END_REF]:

dz * α dt = 1 2Li N ∑ β =1 β ̸ =α Γ β cot π L (z α -z β )
where z α = x α + iy α is the complex position of the point vortex α, * represents the complex conjugate, and L is the length of the basic strip. If the point vortices are identical and evenly spaced, there will be no displacement. However, the system is unstable, so any asymmetry will perturb the vortices along intertwining trajectories determined by the equation above. Once the trajectories of the point vortices within the xy plane are determined, the helical wake can be reconstructed. To transform from the temporal evolution of the helical system to the spatial evolution representing a rotor wake, the point vortices advance along a helical path determined by the advection speed and rotational speed of the rotor. The perturbation deforms the helices, with point vortex displacements in the y-direction corresponding to radial displacements in the helical system, and x-direction point vortex displacements having components in the axial and azimuthal directions of the helix.

Experimental set-up

To investigate the accuracy of the point vortex model, water channel experiments visualizing the wake of asymmetric rotors are conducted. The water channel test section is 150 cm × 38 cm × 50 cm (length × width × height). Two-and three-bladed rotors with radii of 8 cm and 9 cm, respectively, are used to generate helical vortex wakes. The vortices are visualized by painting the rotor blade tips with fluorescent dye and illuminating the test section with a laser or LED panel. These visualizations are captured on video for further analysis. The rotation rate and flow speed of the channel are varied to achieve different values of helical pitch. For the two-bladed rotor, asymmetry is introduced via radial offset relative to the shaft, as described in detail by Quaranta et al. [START_REF] Quaranta | Local and global pairing instabilities of two interlaced helical vortices[END_REF]. For the three-bladed rotor, all blades are 3D printed and can be removed and replaced individually.

Results

Comparisons between predictions from the point vortex model and the experimental results show good agreement. Qualitatively, the key feature of the asymmetric two-bladed rotor wake is the occurrence of leapfrogging, where loops of the two helices swap positions, observed for the experimental case in figure 1(a). When using the values of vortex circulation, helical pitch, and blade asymmetry from the experiment as inputs, the point vortex model reproduces this leapfrogging phenomenon (figure 1b). To quantitatively compare the model to the experiments, the distance z s is defined as in [START_REF] Quaranta | Local and global pairing instabilities of two interlaced helical vortices[END_REF], i.e., the downstream distance where leapfrogging occurs (figure 1a). Quaranta et al. [START_REF] Quaranta | Local and global pairing instabilities of two interlaced helical vortices[END_REF] showed that z s depends on tip speed ratio (λ ), the ratio between the speed of the blade tips and the speed of the axial flow approaching the rotor, as λ affects the strength and geometry of vortices in the wake.

Conclusion and outlook

The point vortex model for the helical vortex system provides a simple way to predict the behavior of asymmetric rotor wakes. Though it neglects many of the components influencing helical vortices (e.g., curvature, torsion, viscosity, spatial evolution), it is shown to accurately capture key features of rotor wake vortex interaction. As different configurations can be tested quickly, this model has a range of applications. For an experiment investigating undeformed helical vortices, a level of acceptable asymmetry for a given region of interest can be determined. To explore the acceleration of coherent structure breakdown and wake recovery, different rotor asymmetries can be tested to determine the combination of perturbations that most effectively achieves this goal. Furthermore, the agreement between the experimental wake visualizations and the point vortex model suggests that, under the conditions of low helical pitch frequently observed in rotor wakes, helical vortex dynamics are dominated by the interactions between a few neighboring vortex loops.

Figure 1 :

 1 Figure 1: (a) Dye visualization of the wake of the asymmetric two-bladed rotor with tip speed ratio λ = 5.4, reproduced from [1]. The white arrow indicates z s , the distance to leapfrogging. (b) Helical vortices reconstructed from the point vortex model using the same parameters as the experiment shown in (a). (c) Comparison between z s normalized by the rotor radius R 0 obtained from the experiments in [1] and the point vortex model for a range of tip speed ratios.

Figure 1 (

 1 c) compares z s values from the experiments to those obtained from the point vortex model

Figure 2 :

 2 Figure 2: (a) Dye visualization of the wake of the asymmetric three-bladed rotor. (b) Helical vortices reconstructed from the point vortex model.

This work was supported by technology transfer company SATT Sud-Est (Marseille).


Annija Lace

Aideen Byrne

Simon Bluett

Laurent Malaquin

Vincent Raimbault

Rémi Courson

Zain Hayat

Breda Moore

Dr Eoin Murray
email: emurray@aquamonitrix.ie

Remi Courson

Ion chromatograph with three-dimensional printed absorbance detector for indirect ultraviolet absorbance detection of phosphate in effluent and natural waters

Keywords: IC, ion chromatography, LED, light emitting diode, SLA, Stereolithography Indirect UV detection / Anion detection / Phosphate / SLA detection cell / Water analysis

An ion chromatography (IC) method employing a low cost, 3D printed UV absorbance detector incorporating a 255 nm light emitting diode (LED) for portable phosphate analysis in environmental and industrial waters has been developed. The optical detection cell was fabricated using stereolithography (SLA) 3D printing of nanocomposite material.

Chromatographic analysis of phosphate was carried out using a CS5A 4×250 mm analytical column in series with CG5A 4×50 mm guard column at a flow rate of 0.75 ml min -1 based on indirect UV detection using a 255 nm LED. Isocratic elution using a 0.6 mM potassium phthalate eluent combined with 1.44 mM sodium bicarbonate was employed. A Linear calibration range from 0.3 to 30 mg L -1 applicable to environmental water analysis was achieved. For retention time and peak area repeatability, RSD value was 0.68 % and 4.09 %, respectively. Environmental water samples were analysed with the optimised IC system and the results were compared to values obtained by an accredited IC system. For environmental samples treated with Dionex Inlet Guard sample preparation cartridge 9×24 mm the relative errors were < 14 %. Recovery analysis was carried out on both freshwater and waste water samples.

Introduction

Phosphorous is an essential nutrient for plant and animal species in aquatic ecosystems. It is mostly found in the form of phosphate [START_REF] Robards | Determination of carbon, phosphorus, nitrogen and silicon species in waters[END_REF]. Increased phosphate presence in water systems can lead to eutrophication which is one of the most common water quality issues worldwide [START_REF] Anderson | Harmful algal blooms and eutrophication: nutrient sources, composition, and consequences[END_REF]. Eutrophication results in increased growth of harmful algae, which during decomposition release toxins and reduces the available amount of dissolved oxygen. This, in turn, deteriorates the water quality and leads to loss of biodiversity [START_REF] Carpenter | Nonpoint pollution of surface waters with phosphorus and nitrogen[END_REF]. The main sources of phosphate in freshwater include wastewater effluents, farm run-off, fertilisers and industrial waste [START_REF] Mainstone | Phosphorus in rivers-ecology and management[END_REF].

To date, the majority of fresh water monitoring is based on manual sampling followed by laboratory analysis using a range of different methods. However, the high cost of sample analysis makes it unsuitable for high frequency monitoring [START_REF] Cleary | Smart Sensors for Real-Time Water Quality Monitoring[END_REF]. In addition, most manual sampling methods are carried out on weekly or monthly samples, which cannot determine seasonal or daily variations in water quality [START_REF] Johnson | Chemical sensor networks for the aquatic environment[END_REF]. Consequently, environmental monitoring using on-site or in-situ methods is needed for data collection at high temporal and spatial frequency [START_REF] Worsfold | Challenges in the Determination of Nutrient Species in Natural Waters[END_REF]. Ideally, the analytical analyser should be compact, robust, cost effective and environmentally compatible with ability to deliver reliable measurements over prolonged periods of time [START_REF] Bowden | Analysis of river water samples utilising a prototype industrial sensing system for phosphorus based on microsystem technology[END_REF]. A wide range of different analytical methods have been applied for in-situ sensor development, including chemiluminescence [START_REF] Gross | Electrochemiluminescence detection in paper-based and other inexpensive microfluidic devices[END_REF], electrochemistry [START_REF] Contreira-Pereira | Compact autonomous voltammetric sensor for sulfide monitoring in deep sea vent habitats[END_REF][START_REF] Pankratova | In-line acidification for potentiometric sensing of nitrite in natural waters[END_REF] and colorimetry [START_REF] Racicot | A Paper-Based Device for Ultrasensitive, Colorimetric Phosphate Detection in Seawater[END_REF][START_REF] Khongpet | A compact multi-parameter detection system based on hydrodynamic sequential injection for sensitive determination of phosphate, nitrite, and nitrate in water samples[END_REF]. Electrochemical sensor prototypes have been developed for phosphate detection in water [START_REF] Barus | Toward an in situ phosphate sensor in seawater using Square Wave Voltammetry[END_REF][START_REF] Jonca | Reagentless and silicate interference free electrochemical phosphate determination in seawater[END_REF]. Despite the fast reaction times and the high sensitivity demonstrated in laboratory-based tests, these methods require further development and extensive field assessment.

Since Manz introduced the idea of miniaturised total analysis systems (µTAS) there has been a growing interest in microfluidic system application to environmental monitoring [START_REF] Manz | Miniaturized total chemical analysis systems: a novel concept for chemical sensing[END_REF].

Microfluidic or lab on chip detection systems have many advantages over large scale chemical sensors, including reduced reagent consumption, low power requirement and increased sample turnover time [START_REF] Whitesides | The origins and the future of microfluidics[END_REF]. To date, the majority of lab on chip methods have been based on colorimetry due to their simplicity and applicability to microfluidic detection systems [START_REF] Nightingale | Trends in microfluidic systems for in situ chemical analysis of natural waters[END_REF]. However, development of colorimetric reagent-based sensing devices is challenging as they require effective operating fluidic components, electronics, power board and communications. To date, production of detectors is costly, time consuming and requires inter disciplinary expertise. Therefore, there is a need for improved incorporation of fluidic and electronic components at a reduced overall cost [START_REF] Donohoe | Development of a costeffective sensing platform for monitoring phosphate in natural waters[END_REF].

In recent years, numerous researchers have developed autonomous lab on chip phosphate analysers based on colorimetric detection which have been deployed in range of environmental waters with complex matrices. Grand et al. [START_REF] Grand | A lab-on-chip phosphate analyzer for long-term in situ monitoring at fixed observatories: optimization and performance evaluation in estuarine and oligotrophic coastal waters[END_REF] developed a lab on a chip sensor based on molybdenum blue method. The measurements were not affected by high salinity or presence of coloured dissolved organic matter. The phosphate analyser was deployed in estuarine water for 56 days period demonstrating good infield accuracy for the first month of deployment. Similarly, Clinton-Bailey et al. [START_REF] Clinton-Bailey | A lab-on-chip analyzer for in situ measurement of soluble reactive phosphate: improved phosphate blue assay and application to fluvial monitoring[END_REF] generated a lab on a chip analyser for phosphate detection in environmental water using phosphate blue method. The solar powered sensor operated on a stop-flow regime. The analyser demonstrated high accuracy during nine-week infield deployment.

Duffy et al. [START_REF] Duffy | PhosphaSense: A fully integrated, portable lab-on-a-disc device for phosphate determination in water[END_REF] developed a fully integrated lab on a disc analyser for phosphate detection in water using molybdenum blue method. The device used centrifugal force by rotation of the disc to mix reagents and samples. The detection system included an LED-photodiode detector which measured absorbance of light at 880 nm. The device was applied for river water and waste water treatment plant effluent analysis, showing a good agreement with spectrophotometric method. However, further work on detector's hardware is needed; while portable, this lab on a disc approach also cannot be applied to in-situ continuous measurement due to necessity of manual sampling and filtering before loading in the analyser. Despite the encouraging results obtained with portable colorimetric sensors, the manufacture of reagent-based detection systems is very challenging and expensive [START_REF] Donohoe | Development of a Cost-Effective Sensing Platform for Monitoring Phosphate in Natural Waters[END_REF]. In addition, the life time of portable colorimetry-based methods is significantly limited due to reagent stability [START_REF] Pol | Microfluidic lab-on-a-chip platforms for environmental monitoring[END_REF].

In this paper we propose a novel phosphate detection system-based ion chromatography with indirect UV detection. Several indirect UV detection methods have been reported for phosphate determination in water [START_REF] Connolly | Fast ion chromatography of common inorganic anions on a short ODS column permanently coated with didodecyldimethylammonium bromide[END_REF][START_REF] Ohta | Simultaneous separation of common mono-and divalent cations by ion chromatography with indirect photometric detection using an unmodified silica gel column and tyramine-oxalic acid-15-crown-5 as eluent[END_REF][START_REF] Small | Indirect photometric chromatography[END_REF], however, up to date there are no reports on portable indirect UV detection systems. The work described in this paper is aimed towards the development of a portable in-situ analyser for phosphate in both freshwater and wastewater matrices. The analyser is based on ion chromatography using 0.6 mM potassium phthalate eluent. The detection system incorporates indirect UV LED based optical detection for phosphate determination. Freshwater and wastewater samples along with blind freshwater samples were analysed, and the analytical performance of the developed method and configuration was compared to an accredited lab-based ion chromatograph.

Materials and methods

Reagents and materials

All chemicals used within this study were of analytical grade. All solutions were prepared using high purity deionised water (Milli-Q). Sodium tetraborate and potassium phthalate eluent was prepared using Na2B4O7×10H2O (Sigma Aldrich) and C8H5KO4 (Iabkem), respectively. Sodium bicarbonate buffer was prepared using sodium bicarbonate and sodium hydroxide (Sigma Aldrich). Phosphate stock was prepared using KH2PO4 (PanReac AppliChem).

For the interference study nitrate, nitrite, carbonate, chloride, iodate, sulphate, bromide and fluoride stock solutions were prepared using NaNO3(Sigma Aldrich), NaNO2 (Sigma Aldrich), Na2CO3 (Sigma Aldrich), NaCl (Fisher Chemicals), KIO3 (PanReac AppliChem), Na2SO4 (Sigma Aldrich), KBr (Merck) and NaF (Sigma Aldrich), respectively. Working standards were prepared by diluting the stock solutions.

UV Optical Detector

The optical detector was based on a z-shape format and was fabricated using SLA printing.

The detector is shown in figure 1. The fluidic design of the detector was based upon the design previously reported by Murray et al. [START_REF] Hmso | The Determination of Anions and Cations, Transition Metals, Other Complex Ions and Organic Acids and Bases in Water by Chromatography[END_REF]. The cell was 56.2 x 32.4 x 15.6 mm in size and 11,38mL in volume Cells were fabricated with a 3D stereolithographic system DWS 29J+ in DL260 from DWS Systems (Italy). The system uses a 405 nm laser source and provides a 30µm writing resolution(Ref : 10.1016/j.aca.2017.11.062). DL260 is a nanoceramic composite material with a density of 1.3g/mL, a flexural modulus of 1,8GPa and a static water contact angle of 77°+/-3°. The parts were printed with a constant slice thickness of 30µm and a laser hatching value of 30µm. The detector cell was printed with a laser speed set to 2800 mm/s for the first 62 layers composing the basal part of the design and increased to 5800 mm/s for the remaining layers. All other printed parts were obtained with a 5800mm/S laser speed. All parts were developed in ethanol in an ultrasonic bath for 1 min. Microfluidic channels were further developed by manually injecting 5mL of ethanol using a plastic syringe connected to the device inlet. The total fabrication time, comprising 3D printing and device development, was 2h30 min per chip.a microfluidic z-shaped channel with a diameter of 500 µm and optical path of 2.15 cm was micro-milled. The internal volume of the z-cell channel was 11 µL, the square-shaped microchannels being 500µm wide. Fused silica glass windows are assembled to the 3D printed detector using TESA 61210 double sided-tape, which is cut by xurography using a Graphtec FC8600-60 cutting plotter. This adhesive features good chemical resistance to polar and non-polar chemicals, and is resistant toward UV light, ensuring good sealing of the assembly over time. Question : Shall we provide the design, at least, the internal architecture of the chip (part n°5) as well as the fluidic connectors ? and eventually parts N °2 and 6 ? Shall we also give information about the connectors ?

We could also show the final 3D printed device (some. examples below, we can show better images if needed)

IC Configuration

The automated portable phosphate analyser described in this paper was based on the IC system reported by Murray et al. [START_REF] Murray | Low cost 235 nm ultra-violet light-emitting diode-based absorbance detector for application in a portable ion chromatography system for nitrite and nitrate monitoring[END_REF]. The phosphate analyser fluidic configuration is shown in figure 2. The syringe pumps were manufactured from low-cost components coupled with a 3D printed base and a pusher block. Sample and eluent were pumped using 1 ml gas tight luer lock glass syringes (Sigma Aldrich, Wicklow, Ireland). A 6 port 2-position injection valve (VICI AG, Schenkon, Switzerland) with automated hybrid stepper motor (Radionics, Dublin, Ireland) was used. Syringes were flushed and filled using 12 V brushed geared DC motors (Pololi, Las Vegas, USA). Efficient and fast separation was achieved using a 4×250 mm in series with 4×50 mm IonPac CS5A guard column. Indirect UV detection was carried out using 255 nm UV-LED (Crustal IS, Green Island, NY, USA) and UVC photodiode. For eluent storage. Inline check valves and tubing connectors were purchased from Kinesis (Altrincham, UK) and Sigma Aldrich (St. Louis, MO). The analytical system was housed within a 1510 M Peli Case (Peli Products, Clare, Ireland). Cost?

Eluent optimisation

Buffered eluents with controlled pH are required for optimum elution of ions from ion exchange systems. In Methods for the Examination of Waters and Associated Materials analysis, published in 1990 [START_REF] Murray | Fully automated, low-cost ion chromatography system for in-situ analysis of nitrite and nitrate in natural waters[END_REF], an anion exchange chromatography method with indirect UV detection of inorganic anions using potassium phthalate combined with sodium tetraborate was described for phosphate determination. However, when using sodium tetraborate in combination with potassium phthalate as the eluent, a constant eluent pH overtime could not be achieved resulting in poor and unstable chromatography overtime. In order to achieve robust and stable eluent pH a range of different buffers were assessed, including, Tris, Bis Tris, sodium hydroxide and sodium bicarbonate. From these various buffers, sodium bicarbonate was selected due to its non-toxic nature and it enabled stable eluent pH. The stability and performance of potassium phthalate and sodium bicarbonate eluent was assessed by continuous analysis of 10 mg L -1 phosphate sample.

Results and discussion

Eluent assessment

The pH stability of the eluent, consisting of 0.6 mM potassium phthalate and 1.44 mM sodium bicarbonate was assessed by analysing and monitoring the retention time of a 10 mg L -1 PO4 3- standard over twelve days. Three measurements were obtained on a daily basis using the same eluent. The results, including the % RSD values for each day, are outlined in figure 4.

Satisfactory precision was achieved over the twelve-day analysis with RSD of 3.74 %. The eluent demonstrated sufficient stability for use within the portable phosphate analyser and demonstrates potential when considering future deployment of the analyser in remote environmental locations for extended periods of time.

Figure 4: Within-day(n=3) and between-day (n=10) precision data for 10 mg L -1 PO4 -3 retention time using 0.6 mM potassium phthalate combined with 1.44 mM sodium bicarbonate buffer. Overall average retention time was 8.12 min and the between day % RSD was 3.74.

Analytical performance

The optimised IC method enabled phosphate determination under 10 min run time which is comparable to commercial phosphate analysers [31,32]. Satisfactory resolution was achieved and a sufficiently wide linear calibration plot was obtained ranging from 0.3 to 30 mg L -1 (R 2 = 0.999). The phosphate linear curve generated by the analyser is shown within Figure A1 of the ESI. The limit of detection was calculated using a signal-to-noise ratio (S/N) = 3 which corresponded to 0.322 mg L -1 . The limit of quantification (LOQ) was 1.07 mg L -1 which was obtained by using S/N = 10 [Add Ref EM]. The interference of common anions was investigated to ensure that coelution of phosphate with other anions would not be present during environmental sample analysis. In the study, chloride, iodate, fluoride, carbonate, sulphate, bromide, nitrate and nitrite were selected as these anions are commonly found in environmental waters. An anion mixture containing 10 mg L -1 of these nine commonly found anions along with phosphate was analysed using the portable IC set up. As can be seen in figure 3, selective detection of phosphate was achieved and the determination of phosphate was not affected by the presence of other anions.

Figure 3:

Chromatogram of nine-anion standard containing 10 mg L -1 PO4 -3 , SO4 -2 , CO3 -2 , IO3 -, Br -, F -, Cl -, NO2 -and NO3 -. The standard was analysed using a 75 µL sample loop and 0.6 mM potassium phthalate eluent at a flow rate of 0.75 mL min -1 with a Dionex CG5A 4×50 mm guard column and Dionex CS5A 4×250 mm analytical column employing the 3D printed detector with 255 nm LED and photodiode for detection.

Chromatographic repeatability

To assess the repeatability of the portable IC platform, 52 sequential chromatograms were produced for a nine-anion standard solution. Prior to the first injection, the system was equilibrated with the eluent for approximately 20 min and automatic injection was configured. The 10 mg L -1 phosphate standard solution was injected every 10 min. The repeatability of the retention times and peak areas are presented in figure 5. The relative standard deviation (RSD) of peak area and retention time for the 52 successive runs was 4.07 % and 0.68 % respectively. These repeatability results highlight a suitable robustness associated with the method and the portable platform when considering phosphate quantification in environmental water samples.

Water sample analysis

Water samples obtained from various locations, including a visitor center, effluent from residential care facility and industrial food processing effluent were analysed by the portable IC system. In addition, blind artificial fresh water samples were prepared and analysed. Prior to analysis, all samples were filtered using 0.2 µm nylon filters and Whatman Grade 1 filter paper to remove suspended particles. All samples were analysed in triplicate. The performance of the portable IC detection system was assessed by comparing the obtained results to an accredited IC system. Accuracy of the portable IC configuration was obtained by calculating the relative % error between the portable and accredited IC system. Samples were treated with Dionex InGuard Na sample preparation cartridge 9×24 mm which was installed within the analyser to remove interfering transition metals from the water sample. Table 2 shows the phosphate concentrations determined within each sample using the portable IC system versus the accredited lab-based IC system. Examples of chromatograms generated by the portable IC system are shown in figure 6.

Concluding Remarks

A portable IC configuration and method for the determination of phosphate in water has been developed and demonstrated in a laboratory. The method employed isocratic elution using buffered potassium phthalate eluent with a CS5A 4×250 mm analytical column in series with a CG5A 4×50 mm guard column. Indirect UV detection of phosphate was achieved using a 3D printed detection cell with a 255 nm LED and photodiode. Question: We could mention the advantages of 3D printing : mechanically robust monolithic device, direct integration of connectors, low cost and fabrication time compatible with medium scale production. The IC set up demonstrated good performance in terms of repeatability and precision. In addition, a LOD of 0.3 mg L -1 PO4 3-and a linear detection range between 0.3-30 mg L -1 PO4 3-applicable to a wide range of environmental waters was achieved. Environmental samples were analysed using the portable IC system and the results were compared to an accredited IC system with relative errors ˂ 15 % obtained. Recovery assessment was successfully carried out for both fresh water and waste water samples. Overall, the developed phosphate detection method shows a great potential for phosphate monitoring in both freshwater and waste water. Further work will be focused on development of an embedded system and communications to enable complete automation of the analyser for remote in situ phosphate monitoring in the field.

Figure 1 :

 1 Figure 1: Design of 3D printed UV LED absorbance detector fabricated using SLA. Legend: (1) UV photodiode and electronic board; (2) 3D printed photodiode holder; (3) fused silica glass UV-transparent windows (12.5 × 2 mm); (4) chemical resistant double-sided tape ; (5) 3D printed detector cell; (6) UV LED holder; (7) surface mount UV LED and electronic board; (8) detector cell holder.

Figure 2 :

 2 Figure 2: Schematic representation of portable chromatographic set up for phosphate analysis. The flow path of water sample through the sample reservoir is shown in blue. An aliquot of sample taken from the reservoir is drawn through a cation trap cartridge and is introduced into the system via the sample loop of the six-way valve, this flow path is shown in green. The flow path of the buffered potassium phthalate eluent is shown in black.

Figure 5 :

 5 Figure 5: Repeatability of peak area and retention time values determined using the portable analyser, analysing 10 mg L -1 PO4 standard over 50 sequential runs and associated RSD values.

Figure 6 :

 6 Figure 6: (Left) Chromatogram of industrial process effluent sample; (Right) chromatogram of spiked river water sample. Samples were analysed using a 75 µL sample loop and 0.6 mM potassium phthalate eluent at a flow rate of 0.75 mL min -1 with a CG5A 4×50 mm guard column and CS5A 4×250 mm analytical column employing the 3D printed detector with 255 nm LED and photodiode.

Table 2 :

 2 Phosphate concentrations obtained using portable IC configuration versus phosphate concentrations generated using accredited IC (n=3).

	Sample	Portable IC (mg L -1 PO4 3-)	Accredited IC (mg L -1 PO4 3-)	Relative error (%)
	Residential care facility effluent	1.3	1.5	13.3
	Visitor center water sample	24	28	14.3
	Industrial food processing effluent	7.2	7.8	7.7
	Freshwater A	6.8	6.6	1.9
	Freshwater B	3.5	3.8	7.8

Table 3 .

 3 Average recovery for environmental samples spiked with phosphate ranged between 98.4-115.69 % which lies within the recommended recovery range for ion chromatography methods set by EPA method[34].

Table 3 :

 3 Concentrations determined within fresh and spiked environmental water samples determined with portable phosphate analyser (n=3).

	Sample	Portable IC (mg L

-1 PO4 3-) Spike (mg L -1 PO4 3-) Average recovery (%)

	Residential care sample	1.28	5	98.48
	Waste water treatment plant (Baltinglass)	0.99	5	108.80
	Industrial food processing effluent	9.98	5	115.69
	River water sample	< 0.5	5	95.48

Acknowledgements

The authors would like to acknowledge financial support through the H2OMon project from the EU Horizon 2020 Research and Innovation programme under grant agreement number 880886. The authors would also like to acknowledge financial support from the Holifab project, EU Horizon 2020 Pilots Programme under grant agreement number 760927.

This work was partly supported by LAAS-CNRS micro and nanotechnologies platform (member of the Renatech french national network) and by the MultiFAB project funded by FEDER European Regional Funds and French Région Occitanie (grant agreement number 16007407/MP0011594)


Marta Avalos Fernandez
email: marta.avalos-fernandez@u-bordeaux.fr

Samia Mehouachi

ORGANISATIONAL LEARNING STRATEGIES OF INTRODUCTORY STATISTICS COURSES IN AN ONLINE MPH: SLOW AND STEADY WINS THE RACE

PURPOSE

The first year of the Master of Public Health (MPH) program at the University of Bordeaux (France) has been organized in Open and Distance Learning (ODL) since 2007. The courses are aimed exclusively at French-speaking professionals working in the health field or in the social and solidarity economy sector, whether in the private or public sector. In 15 years, almost 300 people have been trained, about half of whom come from Africa and about half from French-speaking countries in Europe, overseas, and French-speaking countries abroad. The program aims to meet a growing demand in public health from active professionals whose mobility and/or time for training is limited. The basics of statistical reasoning, methods, and computing are introduced.

In addition to direct interactions throughout the year, each semester an anonymous satisfaction survey is sent to students. Analyzed together with the results of course assessments, the survey constitutes a valuable source for the evolution of practices. This feedback has led to an individualized organization of training according to each student's personal background, professional or family workload, and projects. We are able to organize the training over one or two years and to validate the university diplomas beforehand (i.e., institution-specific degrees equivalent to certain Master's courses). This is the case for the university diplomas "Statistical Methods in Health" and "Methods and Practices in Epidemiology," which allow the validation of part of the statistics courses of the Master's degree. We aimed to analyze the success or failure of the training by organizational profiles.

METHODOLOGY

We considered all the people enrolled in the first year of the MPH program at the University of Bordeaux over the period from 2007 to 2021. The data considered are: gender, age, nationality, country of residence, and year(s) of enrolment. We consider three organizational profiles: with prior validation of university diplomas in statistics and epidemiology and without prior validation in one or two years. We calculated the dropout rate from the number of students who failed to graduate.

RESULTS

Between 2007 and 2021, 294 students enrolled (53% women). The number of students per year ranged from 16 to 41. The average age of the students at the beginning of the training was 37 years (ranging from 23 to 57 years). Of the students, 55% were African and 40% French. Concerning the organizational profiles, 25% of the students obtained the university diplomas in statistics and epidemiology before entering the program, 62% of the students planned their training over one year, and 13% over two years. The yearly dropout rate ranges from 3% to 31% (average 13%). The dropout rate among students with prior validation of the university diplomas was 7%. Among the others, this figure doubles for those who planned their training over two years (14%) and increases to 25% for students who planned over one year.

IMPLICATIONS FOR THEORY AND PRACTICE

Introductory statistics courses require good skills in scientific reasoning, mathematical calculation, computer manipulation, etc. These courses can be particularly stressful and sources of failure for continuing education students in the MPH who had long since left university and have started again in ODL. Multiple factors (not accounted in this study) can have an impact on dropout; yet orienting vulnerable candidates (those with weak scientific backgrounds or substantial professional workloads) to the prior validation of statistics courses seems to be a good strategy to prevent failure.

ORIGINALITY AND VALUE

The 15-year study period provides some robustness for the observed results.