Stéphan Astier
email: stephan.astier@laplace.univ-tlse.fr

Guillaume Fontes

Catherine Azzaro-Pantel
email: catherine.azzaropantel@ensiacet.fr

Design of sustainable energy systems : a new challenge for Engineering Education

Keywords: Education, Sustainable development, Energy, Process Systems Engineering, Electrical Engineering

This paper presents the main features of the masterlevel programme in "EcoEnergy" offered as a full-time one year course at "Institut National Polytechnique of Toulouse" in order to provide engineers with a state-of-the-art education in the area of advanced energy technologies and systems. It is based on an original and equilibrated combination of process systems engineering and electrical engineering disciplines, with an interdisciplinary problem-solving approach necessary for identifying sustainable solutions in the energy sector. More precisely, the students learn how to design, develop and implement energy systems and technologies in various industrial sectors for which efficient management of energy issues is vital to remain competitive.

I. INTRODUCTION AND MOTIVATION

The energy sector represents up to 50% of the whole ecological footprint of humanity. The main Development of sustainable energy system solutions constitutes a real challenge as a result of the global warming problem together with depletion of fossil fuel resources. This constitutes an important technical challenge to the engineering community. In that context, there is a clear need to educate engineers who can respond to these challenges by considering factors beyond the traditional process, product, or enterprise.

Electrical engineering, along with other disciplines, needs to focus on the sustainability of its activities. Indeed, electricity production is the first factor of artificial carbon dioxide emission by mankind on Earth. On another hand, electricity exhibits a lot of assets for an improved penetration of energy sectors, due to its low direct emissions, high efficiency and flexibility and also as a favoured vector for renewable and nuclear sources. So it is necessary to manage new processes of electricity production and treatment with low emissions from renewable energy sources but also from fossil and nuclear as well. Moreover electrical engineering have the advantage of a great ability in holistic or systems approach; it has developed many types of energetic models which is very useful for understanding complex systems.

Chemical engineering is also implied by such a goal, particularly processes which are inherently involved in mass and energy transformations, in energy production and storage and for the treatment of fossil or renewable fuels. Moreover, among all the specialities of chemical engineering, process systems engineering (PSE) is perhaps best positioned to address the challenges of sustainability, since PSE also adopts a holistic or systems view, which is essential for understanding and modelling the complex interactions between industry, society and ecosystems. Such methods will become increasingly important for both new and existing technologies at all stages of their research, development, and use.

It must be emphasized that traditional course programmes (MSc or Engineer level) are generally based on either environmental engineering for quantifying environmental impacts, or on energetic topics involving mainly thermal energetic processes, or on electrical engineering with electricity-oriented energetic processes, or on chemical and process engineering focused on mass and energy transformation.

All these factors participate to a situation which presents unprecedented challenges and exciting opportunities for both Electrical Engineering and PSE to play a crucial role in the quest for sustainable energy systems.

In that context, the aim of the master-level programme in "EcoEnergy" offered as a full-time one year course at "Institut National Polytechnique of Toulouse" is to provide engineers with a state-of-the-art education in the area of advanced energy technologies and systems. The key feature of the programme is based on an original and equilibrated combination of process systems engineering and electrical engineering disciplines, based on an interdisciplinary problem-solving approach necessary for identifying sustainable solutions in the energy sector. As shown on "Fig. 1" for example, the fuel cell inherently illustrates the motivation to use and combine concepts of both disciplines to cover the chain of electricity production (mainly electrical engineering oriented) from a portfolio of various sustainable process alternatives (mainly process systems engineering oriented).

More generally, the students learn how to design, develop and implement energy systems and technologies in various industrial sectors for which efficient management of energy issues is vital to remain competitive. The assessment of both current and potential future energy systems is covered and includes topics on resources, extraction, conversion, and enduse, with emphasis on energy needs in the 21st century in a sustainable manner. Different renewable and conventional energy technologies are presented and their attributes described within a framework that aids in evaluation and analysis of energy technology systems.

The remaining sections of this paper present the learning objectives, the teaching strategy, the state of development and career opportunities induced by the the "EcoEnergy" programme [1].

II. LEARNING OBJECTIVES

A first motivation of the "EcoEnergy" programme was to practice an interdisciplinary approach between two engineering disciplines, namely Process Systems Engineering and Electrical Engineering to tackle the sustainable energy issue, "Fig. 2". For this purpose, a prerequisite was to provide the students with the key subjects of both disciplines that are typically relevant with the specific energy subjects that will be the core of the programme. Of course, the chemical process engineering students will not become specialists of electrical engineering and conversely. The integrated prerequisite subjects are presented in Fig. 2. Let us mention that this period is strongly interconnected to the other common courses so that the students can be mixed as earlier as possible to favour interdisciplinary dialogue. Since this programme may be accessible from students of other disciplines (e.g. fluid mechanics or biochemical engineering), the courses are not arranged in parallel.

The programme is then based on a 3 components-based platform shown on "fig 4 ": 1. general scientific disciplines to give a global overview on energy electrical networks and converters, electrochemistry, electrical interfaces, electrocatalysis; 2. a methodology framework which highlights systemic approach on energy conversion : analysis and design of complex processes (e.g. process simulation, pinch technology), criteria for assessing the sustainability of energy technologies, integrated processes, Bond Graph modelling, electrochemistry modelling, hybrid architectures, energy storage, optimization tools for decision-making (mutiobjective optimization based on stochastic algorithms, e.g. Multiobjetcive Genetic Algorithms), ecodesign based on e.g. Life Cycle Assessment, and carbon balance, optimal control; 3. specific energy technologies from components to systems: overview of energy supply portfolio, fossil fuels and fossil energy, hydropower energy, nuclear energy, wind power, solar photovoltaic energy, fuel cell and distributed energy, electrochemical components, advanced heat exchanger technologies, solar thermal energy, bioenergy, hydrogen energy, greenhouse effect and CO 2 treatment processes and sequestration….

These underlying objectives can be revisited to give an energy-centred organization: the program builds upon 7 compulsory core courses " A lot of courses are computer-intensive (hybrid systems studied with Bond Graph simulator or SABER, heat integration scenarios performed with ProSim simulator).

A practical case study concerns the fuel cell application: two complementary methodologies of experimental characterization are carried out, dynamic plot of fuel cell voltage as a function of current density and impedance spectroscopy [START_REF] Fontes | Applied work for engineer students: Characterisation and modelling of a PEM fuel cell[END_REF]. This experimental part then leads to the parameter identification of a PEM fuel cell. The behaviour of the PEM fuel cell performance is then studied as a function of disturbance generated by connected static converters.

The validation of the course module is carried out by case study projects referred as CSP performed by multidisciplinary student teams (3 or 4). Their detailed presentation can be found at http://www.ensiacet.fr [1]. Thematic seminars on energy are organized one day a week to favour industrial involvement in the programme. Let us mention that an industrial partnership was initiated at the preliminary design phase of the programme (CEA, IFP, GDF …). Although these seminars are devoted to the presentation of specific topics on energy such as CO 2 process treatments and sequestration (IFP), hydrogen as a future energy vector (CEA), nuclear energy (CEA), gas networks (GDF), wind energy (EdF Energies Nouvelles) and so on…, a large place is given to debate in order to strengthen students' oral communication skills on the given topic. Groups of students have to write alternately a report on these seminars in English and diffuse it rapidly both to the class and to the pedagogical team.

A more general case study project (approximately up to 100 h) is also proposed to multidisciplinary student teams. The project subject is submitted in the second month of the programme to facilitate literature analysis (4h every two weeks) and a progressive knowledge of the subject. Then, an intensive period is scheduled over all the last month so that they can concentrate their attention to the technical choices and design phase. Industrial partners are involved in the definition of the subjects. According to estimations of the European Renewable Energy Council (www.erec-renewables.org) [START_REF]Renewable Energy Target for Europe[END_REF], over 1 million jobs for the Renewable Energy sector are likely to be created by 2010, a number that is to double for the new Renewable Energy sector target of 20% by 2020. Even if it is only a small proportion of these employees who require education at graduate level, it is clear that the demand for technical renewable expertise is growing. We hope optimally prepares graduating engineers for jobs in the energy industry.

V. CAREER OPPORTUNITIES

The EcoEnergy programme is designed to deliver qualified engineers equipped with the latest skills and the right experience for a successful career in the energy industry.

Of course, many traditional energy industry sectors are likely to recruit students graduating from this programme: this is all the more important as companies have to integrate sustainable considerations in their activities. It must be pointed out that the issues surrounding the role of energy extend far beyond the energy sector, since energy use is integral to many chemical and process activities. The concepts developed find here a logical application.

Moreover, the students show a true strong motivation to join such scientific curriculum which clearly deals with environmental concerns and sustainable development.

VI. REFERENCES

Yet not surprisingly, the renewable energy industry seems very attractive to offer motivating career opportunities. As reported by EUREC, the European renewable energy (RE) industry is today one of the fastest growing industry sectors in the EU. The renewable energy industry, because it is labour-intensive, creates employment at much higher rates than many other energy technologies. New research, industrial and craft jobs appear directly in R&D, production, installation and maintenance of renewable energy systems. Backward linkages to other sectors triggering demand for technical RE expertise exist for consultancies (local, departmental or regional communities in France, for instance).

Fig. 1 .

 1 Photovoltaic/ Wind energy

Fig. 2 .

 2 Fig. 2. Prerequisite for the Ecoenergy programme.

Fig. 4 .

 4 Fig. 4. Pedagogical strategy in the EcoEnergy programme

  For the sake of illustration, let us mention some projects treated by student teams in 2006-07 and 2007-2008:  Design of the electrolysis zone in a hydrogen production plant using High Temperature steam Electrolysis coupled with a Very High Temperature nuclear Reactor (with CEA, Commissariat à l'Energie Atomique, Cadarache);  Investigation on the electrical system of a Shell ecomarathon fuel cell vehicle (with INSA, Institut National des Sciences Appliquées, Toulouse), [3].  Production of biogas fuel for Toulouse buses.  Solar generator for the future laboratory building in ENSEEIHT The industrial period (4-6 months) is the opportunity for students to apply and further develop the skills acquired in the technology of their programme during a placement in an energy company or a research centre. A tutor from the host company supervises and guides the student during project work, while a second supervisor from the university will supervise the evolution of this industrial period. Typical industrial projects carried out in 2006-07 are following:  Contribution to the development of a wind project (EdF energies nouvelles);  Geothermal energy valorisation in Alsace (in an electric company);  Membrane-based process for hydrogen production and purification from oil-based fuels (ARC Centre for Functional Nanomaterials, The University of Queensland St Lucia, Australia);  Improvement of the energetic and environmental performance of Midi-Pyrénées secondary schools. IV. STATE OF DEVELOPMENT The EcoEnergy programme opened in 2006-07 with 15 students (11 students from electrical engineering, ENSEEIHT, INPT, 4 from ENSIACET INPT). In 2007-08, 22 students attend this programme (8 students from electrical engineering, ENSEEIHT, INPT, 13 from ENSIACET INPT (mainly from process systems engineering department), 1 ERASMUS student from Germany. In parallel, a New Energy Technology Mastere (from "Conférence des Grandes Ecoles" was created in 2007 with the same pedagogical objectives (even if the form may be a little different) and 3 engineers from industry joined this programme.

Table 3 "

 3 (27 ECTS credit units in all). The other ECTS credit units (18) are assigned to English and industrial training periods.

	Course

package Module ECTS Evaluation mode Industrial

  One of the drivers of the programme was to develop teaching/learning methods and strategies closely mixing academic/industry professionals combining lectures, seminars, computer-based work, practical experimental work and projects….

				Report
	Systemic design	Process analysis and design	2	CSP
		Bond Graph systemic modelling	2	CSP
		Optimal control
		Optimal design	2	CSP
	Ecodesign	Life Cycle Assessment	1	CSP
		CO2, greenhouse effect, sequestration	1	CSP
	Electrochemical components	Electrochemical components	3	CSP
		Fuel cells
		Electrochemistry
		Electrified interfaces, electrocatalysis
	Electrical networks and hybridation Electrical networks, static conversion	3	CSP
		Distributed and embedded networks
		System energetic hybridation
		Hybrid vehicle SABER
	Renewable energy	Photovoltaic energy	2	CSP
		Wind energy
		Bioenergy	2	CSP
	Project	Case study	6	Report, oral examination
	TOTAL ECTS		60

period (4-6 months) 31 English 2 Report, oral examination Thematical seminars on energy Fossil fuels and fossil energy, Natural gas transport, Biomass energy Solar energy, Wind energy, Hydrogen Nuclear energy, Industrial and residential buildings, CO2 3

Table. 3. Course organization in Ecoenergy program This table is also in full size at the end of the paper III. TEACHING/LEARNING STRATEGY


H Benabdelhalim

D Brutin

Phase separation and spreading dynamics of French vinaigrette

Phase separation can be observed when vinaigrette is poured on a kitchen plate under certain conditions. The phase separation in vinaigrette, which comprises olive oil, vinegar, and mustard for stabilization and taste, is characterized by the outward spreading of olive oil from the main film. This phase separation and the phenomena that trigger it were investigated in this study. Moreover, the spreading dynamics of the vinaigrette were examined by analyzing the spreading factor and its rate. The spreading of different formulations of the vinaigrette was probed in this regard by varying the mass concentration of vinegar from 10 % to 40 % and the amount of mustard from 0.1 g to 0.5 g. The emulsion films were placed on a white tile substrate with similar characteristics to those of a kitchen plate at 21 °C and a relative humidity of 50 %. The spreading dynamics followed two distinct regimes; increasing the vinegar concentration of mustard-free formulations led to decreases in the spreading factor of the first regime and the spreading rate. The addition of mustard had a similar effect on the spreading factor of the first regime. The variations in these two parameters were related to changes in the system viscosity. The latter was found to be a function of the mustard and vinegar concentrations. Phase separation occurred at vinegar concentrations below 30 % because of a competition between the spreading and the existing instabilities in the vinaigrette. This phenomenon did not affect spreading dynamics.

I. INTRODUCTION

The formulation and preparation of salad dressings and sauces are of crucial importance on various scales ranging from industry to kitchens. These processes play a role in product performance parameters, such as stability, viscosity, texture, appearance, taste, and flavor. Generally, food mixtures are emulsions of two or more immiscible liquids in continuous and dispersed phases, with the dispersed phase consisting of small droplets. The thermodynamic instability of these emulsions necessitates the addition of a chemical or natural stabilizer (emulsifier) to suppress or impede phase separation. Emulsion science combines different disciplines such as physics, chemistry, biology, and engineering [START_REF] Mcclements | Food emulsions: principles, practices, and techniques[END_REF] , and is primarily concerned with ensuring the stability and handling of emulsions, and optimization of formulations. The processes and technologies related to the preparation and characterization of salad dressings and sauces have been thoroughly described by Ford et al. [START_REF] Ford | Dressings and sauces[END_REF] , Sikora et al. [START_REF] Sikora | Sauces and dressings: a review of properties and applications[END_REF] , and Campbell [START_REF] Campbell | Current emulsifier trends in dressings and sauces[END_REF] . Several researchers have exhaustively reviewed food emulsions [START_REF] Mcclements | Food emulsions: principles, practices, and techniques[END_REF][START_REF] Hasenhuettl | Food emulsifiers and their applications[END_REF][START_REF] Friberg | Food emulsions[END_REF] and emulsions in a general manner in terms of their formation, stabilization, and various properties [START_REF] Tadros | Emulsion formation and stability[END_REF][START_REF] Mittal | Emulsions, foams, and thin films[END_REF][START_REF] Sjöblom | Emulsions: a fundamental and practical approach[END_REF] .

The complex composition, structure, and dynamics of emulsions present various challenges that should be addressed by research; this has led to significant interest in understanding their properties. Food emulsions can be classified according to their distributions: oil droplets dispersed in an aqueous phase (denoted as O/W emulsions) or water droplets dispersed in oil (W/O emulsions). The distribution of W/O emulsions is similar to that of the salad dressing investigated in this study (vinaigrette), in that vinegar a) Electronic mail: houssine.benabdelhalim@gmail.com b) Electronic mail: david.brutin@univ-amu.fr can be viewed as a substitute for water (denoted as V/O herein).

The conversion of two immiscible liquids into an emulsion can be achieved by providing mechanical energy manually or via a high-speed mixer. In his book [START_REF] Mcclements | Food emulsions: principles, practices, and techniques[END_REF] , McClements has provided details regarding the selection of the mixing method in terms of the energy required to disperse droplets in the continuous phase. However, straightforward mixing of two immiscible liquids and ensuring their long-term homogeneity are difficult, because of the rapid phase-separation tendency of the two phases into two distinct areas with different densities for minimizing the system energy and migrating to a stable thermodynamic state.

In these systems, the droplets tend to merge with their neighbors. The driving force behind this process pertains to the thermodynamically unfavorable contact between the water and oil molecules, resulting in unstable emulsions. The physical mechanisms responsible for this instability after homogenization are flocculation, coalescence, creaming or sedimentation, and Ostwald ripening [START_REF] Mcclements | Food emulsions: principles, practices, and techniques[END_REF] . Chemical mechanisms that react to the nature of the components also exist.

A kinetically stable (metastable) emulsion can be created for a specific period by adding an emulsifier, a surface-active molecule with an amphiphilic character, that is, polar and nonpolar regions in the same molecule. The role of the emulsifier is to adsorb to the droplets of the dispersed phase formed during homogenization to create a film that prevents direct contact between the droplets. Emulsifiers are characterized by the hydrophilic-lipophilic balance (HLB), which represents their ability to dissolve in water (low HLB), oil (high HLB), or both (medium HLB). Emulsifiers are typically added to improve the stability of a product and provide a satisfactory shelf life. Moreover, other ingredients such as thickening agents, gelling agents, weighting agents, and ripening inhibitors can be employed to stabilize emulsions. The use of one or more stabilizers depends on the instability of the emulsion and the desired texture of the product. Vinaigrette is a mixture of oil, vinegar, mustard, and various spices. Olive oil and vinegar typically represent the continuous and dispersed phases, respectively, with mustard being added to ensure stabilization of the emulsion and to provide a slightly spicy taste. The emulsifying character of yellow mustard, which is used in industry as a stabilizer or emulsifier, is due to mucilaginous materials [START_REF] Cui | Chemical and physical properties of yellow mustard (sinapis alba l.) mucilage[END_REF] . Mustard mucilage reduces the surface tension of water molecules. Moreover, the consistency of vinaigrette is attributed to these materials [START_REF] Weber | Functional characteristics of mustard mucilage[END_REF] . Cui et al. [START_REF] Cui | Yellow mustard mucilage: chemical structure and rheological properties[END_REF] showed that this mucilage behaves as a shear-thinning fluid. Milani et al. [START_REF] Milani | The physicochemical influences of yellow mustard paste-comparison with the powder in mayonnaise[END_REF] examined the influence of yellow mustard on the viscosity and stability of mayonnaise sauce, and found that increasing the mustard concentration led to an increase in the mixture viscosity and an improvement in stability.

Lozano-Gendreau et al. [START_REF] Lozano-Gendreau | Physicochemical and flow characterization of a mustard-vinaigrette salad dressing[END_REF] characterized and analyzed the physicochemical properties and flow behavior of a new vinaigrette formulation. The concentrations of oil and mustard, and storage time were found to significantly affect the stability and rheological behavior of the emulsion. The rheological behavior was described using a modified Herschel-Bulkley model, and the vinaigrette was determined to be a yield stress fluid whose threshold was a function of the three studied parameters. These results, in particular, can be used to develop new formulations with longer shelf lives for satisfying customer requirements.

As mentioned earlier, the preparation of an emulsion requires the contribution of agitation-induced mechanical energy. The speed and duration of agitation influence the stability of the emulsion; these aspects were examined by Chen et al. [START_REF] Chen | An experimental study of stability of oil-water emulsion[END_REF] , who found that stable emulsions could be achieved at high mixing speeds. This can lead to the dispersion of more droplets via minimization of their size, thus suppressing (or hindering) coalescence and flocculation. In addition, exceeding a particular limit was noted to result in detachment of the emulsifier from the droplets; this behavior also applied to the mixing time [START_REF] Chen | An experimental study of stability of oil-water emulsion[END_REF] .

The phase separation of V/O emulsions during their spreading on a horizontal substrate was investigated in this study. Phase separation occurs when one component stops spreading, and the other continues. Pouring a given quantity of vinaigrette leads to the outward spread of the oil from the main film. This phase separation occurs under specific formulation conditions depending on the concentration of vinegar and the presence or absence of mustard. Therefore, spreading experiments of vinaigrette with different formulations were performed on a substrate with identical characteristics to that of a plate at 21 °C and a relative humidity of 50 %. Humidity control was targeted because of its considerable influence on the spreading dynamics and the final surface at equilibrium [START_REF] Bou-Zeid | Effect of relative humidity on the spreading dynamics of sessile drops of blood[END_REF][START_REF] Benabdelhalim | Phase separation during blood spreading[END_REF] .

Although the spreading dynamics of fluids and emulsions have been rigorously investigated, certain issues persist. This phenomenon is omnipresent in the culinary, cosmetic, and construction materials industries, as well as in biomedical and forensic sciences. The spreading dynamics of food sauces and salad dressings have not been reported to date. Elucidation of this phenomenon can enable the development of new formulations and the optimization of the process of preparation on an industrial scale and in kitchens.

Classically, the spreading of a fluid on a horizontal and non-porous substrate can be described by the balance of the existing inertial, gravitational, capillary, and viscous forces. Several regimes appear during this spreading, with each regime being described by the competition between two dominant forces: a driving force and a dissipative one. The balance of these two forces yields a power-law evolution of the radius, R(t) = ct n , where the spreading factor, n, is a function of the driving force and the nature of the dissipation. In addition to these forces, several instabilities that intervene depending on the nature of the fluid and the external parameters must be considered because of the complicated nature of the spreading dynamics. Several phenomena such as the inversion of the emulsion, coalescence, and the formation of a complex pattern were observed therein. Phase inversion and destabilization are related to the rate of spread and non-Newtonian behavior of emulsions.

The emulsion droplets impact and spreading have already been investigated by considering the surface energy at the liquid-liquid interface and rheological characteristic [START_REF] Choi | Effect of interactions between multiple interfaces on the rheological characteristics of double emulsions[END_REF] . Piskunov et al. [START_REF] Piskunov | Effect of rheology and interfacial tension on spreading of emulsion drops impacting a solid surface[END_REF] showed in their study on Bingham emulsions, that the relationship between the effects of viscoplasticity, yield stress, and capillarity plays a major role in the description of the maximum spreading diameter. Kumar et al. [START_REF] Kumar | Impact of emulsion drops on a solid surface: The effect of viscosity[END_REF] found that the emulsion viscosity increases with the percentage of water, which leads to a decrease in the final spreading diameter. Also, they reported an increase in the droplet contact angle at equilibrium. This study was aimed at elucidating the spreading dynamics of vinaigrette as a function of vinegar and mustard concentrations. The spreading dynamics were analyzed at a fixed room temperature and relative humidity on a white tile substrate. The phase separation and the spreading factor, n, of the vinaigrette were probed under similar conditions.

II. METHODS AND MATERIALS

Experiments were performed using a vinaigrette composed of extra virgin olive oil (ρ o = 820 kg/m 3 ), balsamic vinegar of Modena (ρ v = 964 kg/m 3 ), and Dijon mustard (ρ o = 1124 kg/m 3 ), which were purchased from a supermarket. The high-quality balsamic vinegar of Modena is a Newtonian fluid with constant viscosity. It is mainly composed of sugars (glucose and fructose), organic acids, and volatile components. Its rheological behavior was exhaustively studied by Falcon et al. [START_REF] Falcone | Measuring rheological properties for applications in quality assessment of traditional balsamic vinegar: description and preliminary evaluation of a model[END_REF][START_REF] Falcone | A rheological approach to the quantitative assessment of traditional balsamic vinegar quality[END_REF] . Emulsions were prepared using different formulations by varying the mass concentration of vinegar from 10 % to 40 % with a step of 5 %, and changing the amount of mustard from 0 g to 0.5 g with a step of 0.1 g. Spreading and phase separation behavior were examined on a white tile substrate with similar properties to those of a kitchen plate (roughness of 0.93 ± 12 % µm). This substrate was selected because of difficulties involved in procuring a perfectly horizontal kitchen plate. All experiments were performed inside a glove box at a relative humidity of 50 %, which was regulated using a built-in system, and at room temperature (21 °C). For white tile conditions, we have an equilibrium contact angle of: θ oil = 43.2°± 5 % and θ vinegar = 40.1°± 8 %. Consequently, both liquids have similar wetting proprieties.

Three steps were followed to prepare the vinaigrette. The first step involved manually mixing the vinegar and mustard with a spatula for 1 min. The mustard was well dissolved in the vinegar in this step. The second step involved progressive addition of the olive oil while manually mixing to disperse the vinegar droplets in the continuous phase (oil). In the third step, the vinaigrette was mixed at 4500 rpm using a vortex mixer for 10 s. The selection of the mixing time is discussed in the following section. Fig. 1 shows a schematic of the emulsion preparation protocol. Immediately after its preparation, 4.16 g ± 2.2 % of the emulsion was poured on the substrate, which was placed on a balance (Mettler Toledo, MS6002TS) to ensure the use of identical initial amounts in the experiments. A fresh emulsion was prepared for each experiment (5 g of oil and vinegar + mustard). The spreading and phase separation behavior were monitored using a digital camera (Canon EOS 7D), with photographs being acquired every 5 s during the first 5 min and every 1 min until the end of the two-hourlong experiment. This experimental duration was selected to ensure that the equilibrium regime, during which the film stops spreading, was achieved. We chose components concentrations and films area that enable a clear phase separation. The separation phenomena would have been observed for smaller or larger films. The film size is not the main parameter of this paper.

A. Effects of mixing time on phase separation during spreading

The first set of experiments was performed to determine the influence of the mixing time (third step) on the texture and phase separation of a mustard-free emulsion. Various mixing times-2, 4, 8, 10, 20, and 60 s-were employed with four V/O mass concentrations: 10 %, 20 %, 30 %, and 40 %.

Fig. 2 shows photos of an emulsion poured on the white tile substrate, which were acquired 2 h after their placement. The effects of the mixing time were monitored at concentrations of 10 % and 20 %. Phase separation decreased with time until it disappeared at 60 s. Longer durations of mixing clearly led to superior dispersion of vinegar as small droplets, which mitigated or impeded the instabilities that resist the flow (flocculation and coalescence), resulting in the oil readily dragging the droplets during its spread. The coalescence achieved at a concentration of 20 % was more pronounced than that at 10 %, because of the presence of more vinegar. Verbish et al. [START_REF] Verbich | Evaluation of stability ratio in oil-in-water emulsions[END_REF] reported that increasing the homogenization period leads to a decrease in the droplet diameter of the dispersed phase, which improves the emulsion stability. Phase separation was not observed at vinegar concentrations of 30 % and 40 %, because of close packing of the droplets. The excess oil that was not encapsulated spread outward, forming a crown at the edges of the emulsion. This effect appeared in all the experiments conducted with varying mixing times.

Similar emulsions containing the emulsifier (mustard) were subsequently examined. Mustard is used for stabilization in the classic vinaigrette recipe. A mixing time of 10 s was selected based on previous studies. Chen et al. [START_REF] Chen | An experimental study of stability of oil-water emulsion[END_REF] examined the stability of a W/O emulsion with an emulsifier, and noted the existence of a possible risk related to the detachment of the emulsifier from the oil-water interface at long mixing times. However, the stability of the emulsion increased with time below a threshold homogenization time [START_REF] Chen | An experimental study of stability of oil-water emulsion[END_REF] . Although emulsion stability was not directly analyzed, phase separation was related to it. This is comprehensively described in the next section.

III. RESULTS AND DISCUSSIONS

The effects of vinegar and mustard concentrations on phase separation during the spreading of vinaigrette are discussed herein. First, the visual aspect of this separation is analyzed and linked to the emulsion stability. The second part describes the characterization of the spreading dynamics of the vinaigrette.

A. Visualization of the phase separation

Emulsions such as vinaigrette are often prepared domestically. These products are also prepared on an industrial scale following precise formulation protocols to obtain stable emulsions. Mustard was used in this study to stabilize the vinaigrette. Recipes of this product was designed to provide an excellent taste, desired texture, and stable emulsions for specific periods.

Pouring a vinaigrette (homemade or industrial) onto a plate results in its spreading until it reaches an equilibrium state. During this spreading, the two phases that constitute the dressing can separate depending on the concentrations of vinegar and mustard. The formulations investigated in this study were designed to explain this phenomenon and prevent phase separation. Fig. 3 shows the different emulsion films obtained after equilibrium, which represents the complete stoppage of spreading. Emulsions with V/O concentrations of 35 % were not presented because they behaved similarly to those with concentrations of 30 % and 40 %. Fig. 4 shows the spreading of a vinaigrette prepared using 25 % vinegar and 0.1 g of mustard on the white tile substrate. The plate was horizontal with an accuracy of ± 0.05°. The anisotropy of the film spreading come from the inherent irregularities on the plate. Phase separation occurred 1 min after the formation of the film. The vinegar droplets formed aggregates and sediments during spreading. In addition, the spreading velocity decreased over time, and the flow could no longer drag the vinegar. Consequently, olive oil separated and spread outward from the main film.

This phase separation can be explained based on the competition between the spreading flow and the characteristic instabilities of emulsions (flocculation, coalescence, and sedimentation or creaming); the latter factors cannot be appropriately visualized on a thin film, which varied between 0.55 mm and 3.4 mm in thickness in this study. Sedimentation is a common instability that is encountered in food emulsions [START_REF] Robins | Emulsions-creaming and rheology[END_REF] because of differences in the densities of the dispersed and continuous phases. The densities of oil and vinegar used in this study were 820 kg/m 3 and 964 kg/m 3 , respectively. The vinegar droplets with their higher densities move downward via "sedimentation" because of gravitational forces acting on them [START_REF] Hiemenz | Principles of Colloid and Surface Chemistry[END_REF] . The speed at which an isolated drop of vinegar moves can be expressed using Stokes' law:

ν Stokes = 2gr 2 (ρ vinegar -ρ oil ) 9η ( 1
)
where η is the continuous phase viscosity and r is the droplet radius. Equation [1] is obtained by balancing the downward force owing to gravity, F g = 4/3πr 3 (ρ vρ o )g), and the upward force due to hydrodynamic friction, F f = -6πηrν, acting on the droplet. As a rule of thumb, an emulsion with a sedimentation rate lower than 0.5 mm.day -1 is considered stable [START_REF] Mcclements | Food emulsions: principles, practices, and techniques[END_REF] . Stokes' law indicates that sedimentation can be impeded by decreasing the droplet size, which could result in a longer shelf life and stability. It should be noted that equation [1] is an approximation, and the experimental measurements of sedimentation likely exhibit considerable differences in this regard. This is because of the omission of droplet fluidity and the no-slip assumption of the Stokes' equation with respect to the interface between the droplet and the surrounding fluid [START_REF] Dickinson | Properties of emulsions stabilized with milk proteins: overview of some recent developments[END_REF] . In addition, dilution of the system leads to a higher sedimentation or creaming velocity than that of a concentrated emulsion [START_REF] Chanamai | Dependence of creaming and rheology of monodisperse oil-in-water emulsions on droplet size and concentration[END_REF] . The decreasing sedimentation velocity in concentrated emulsions is due to the dropletdroplet interactions and the crowding effect 30 . Flocculation, which refers to the association of two or more droplets in the dispersed phase, can be either advantageous or disadvantageous in terms of emulsion stability. In vinaigrette, flocculation accelerates the process of sedimentation by the creation of larger aggregates, which increases the viscosity. However, a vinaigrette with desirable texture can be achieved by controlling this phenomenon. Droplet collisions occur owing to the presence of movements that are induced by Brownian motion, gravitational separation, or an applied mechanical force [START_REF] Mcclements | Food emulsions: principles, practices, and techniques[END_REF] .

Coalescence, a process during which one or more droplets merge [START_REF] Sanfeld | Emulsions stability, from dilute to dense emulsions-role of drops deformation[END_REF][START_REF] Tcholakova | Comparison of solid particles, globular proteins and surfactants as emulsifiers[END_REF] , is considered to be the primary phenomenon by which emulsions achieve their thermodynamically stable states, owing to a reduction in the contact area between vinegar and oil.

Similar to flocculation, coalescence accelerates sedimentation. Moreover, coalescence can occur only when the droplets are sufficiently close, and the film that separates them is broken.

The use of an emulsifier, the generation of small droplets, and the selection of an appropriate concentration can assist in the prevention of sedimentation or creaming, flocculation, and coalescence. These phenomena were not characterized and measured according to the different formulations. However, their definitions were used to explain the phase separation that occurred during the spreading of vinaigrette.

At V/O mass concentrations below 30 %, phase separation was pronounced and started disappearing above a specific mustard concentration threshold Fig. 3. Increasing the concentration of mustard (emulsifier) hindered the forces generated by flocculation and coalescence, leading to the disappearance of the resistant forces, and straightforward dragging of vinegar by the oil. Toward the end of these experiments, that is 2 h after the preparation of the vinaigrette, the vinegar was noted to adhere to the substrate in scenarios involving low concentrations of mustard. This adhesion is related to sedimentation; hence, this particular instability affects phase separation. An additional morphological change was induced by the increase in mustard concentration, which is related to changes in texture and an increase in viscosity. These resulted in a creamy emulsion in which the excess oil spread outward and formed a crown at the edge of the emulsion, similar to scenarios involving V/O concentrations above 30 %. This phenomenon was previously observed by Forester et al. [START_REF] Forester | Spontaneous spreading of emulsions on solid surfaces: Morphology and dynamics[END_REF] and was explained by the fact that the droplets diameter of the dispersed phase is larger than the thickness of the precursor film, which causes the precursor film to spread out ahead of the interline demarcating the dispersed phase. At vinegar concentrations above 30 %, phase separation no longer occurred in the mustard-free samples. However, the addition of mustard prevented the formation of the crown during the spreading because of the sufficient amount of vinegar for encapsulating the oil and the high viscosity due to the presence of the mustard. Fig. 3 enables visualization of the effects of mustard on the morphologies of the final films. In the mustard-free emulsions with low concentrations of vinegar, the vinegar droplets aggregated because of attractive forces related to coalescence and flocculation. At low vinegar concentrations and increasing mustard concentration, the lack of aggregates was observed owing to the emulsifying quality of mustard. However, the excess mustard that was not dissolved in the vinegar appeared as small fragments scattered in the thin films. Beyond a certain amount of mustard, its "thickening" quality was observed, which led to a change in texture, resulting in a creamy emulsion. B. Vinaigrette spreading dynamics Fig. 5.a shows the evolution of the film area, "A," normalized by the initial area "A 0 " over time (that is, the spreading rate) of mustard-free formulations with different mass concentrations of vinegar ranging from 10 % to 40 % with a step of 5 %. Because the film area was not perfectly circular, the evolution of the surface was monitored instead of the radius. A 0 represents the initial area obtained immediately after pouring the emulsion. At equilibrium, an increase in the dispersed phase concentration led to a decrease in the spreading rate because of an increase in emulsion FIG. 6: Spreading factor of mustard-free vinegar-oil emulsions (m = 4.16 g ± 2.2 %) as a function of the vinegar concentration at 21 °C and a relative humidity of 50 %.

viscosity. An increase in concentration implies the presence of more droplets, resulting in more friction with the continues phase. R. Chanamai and D. McClements [START_REF] Chanamai | Dependence of creaming and rheology of monodisperse oil-in-water emulsions on droplet size and concentration[END_REF] have shown that the apparent viscosity of an O/W emulsion increases with increasing concentration of the dispersed phase, and that the viscosity of a diluted emulsion is independent of the shear rate, in contrast to that of a condensed emulsion. Additionally, emulsions with larger droplets were noted to exhibit low viscosities compared to those of emulsions with small droplets. E. Forester et al. [START_REF] Forester | Spontaneous spreading of emulsions on solid surfaces: Morphology and dynamics[END_REF] analyzed the spreading of an emulsion of water dispersed in silicone oil with an emulsifier, and observed a similar phenomenon in terms of a decrease in the spreading rate with increasing concentration of water droplets. However, the phase separation did not influence the spreading dynamics of these formulations, unlike that observed by H. Benabdelhalim and D. Brutin [START_REF] Benabdelhalim | Phase separation during blood spreading[END_REF] , who examined the spreading of human blood pools. However, phase separation is influenced by the concentration of each component.

The spreading dynamics of the vinaigrette with or without mustard follow similar dynamics to those of pure fluids [START_REF] Forester | Spontaneous spreading of emulsions on solid surfaces: Morphology and dynamics[END_REF] ; therefore, they can be described by a power law, A(t)/A 0 = ct n . E. Forester et al. [START_REF] Forester | Spontaneous spreading of emulsions on solid surfaces: Morphology and dynamics[END_REF] examined emulsion drops with an emulsifier, and found that the radius of the drops varied with a spreading factor of 1/10, as is often observed in pure fluids [START_REF] Bonn | Wetting and spreading[END_REF][START_REF] Oron | Long-scale evolution of thin liquid films[END_REF] . This value of 1/10 resulted from the absence of gravitational effects; moreover, the drops formed hemispheres at equilibrium. In the present scenario, the gravitational forces were not negligible, and the final shape was pancake-like instead of hemispherical. The spreading dynamics of an emulsion with 20 % vinegar were characterized by two distinct regimes, as shown in Fig. 5.b; the first regime was driven by gravitational forces and countered by viscous forces with a spreading factor, n, of 0.09, and the second capillary-viscous regime represented the termination of the spreading with a factor of 0.06. The spreading factor of the first regime was examined to analyze the spreading dynamics as a function of the vinegar concentrations, because it perfectly described the influence of viscosity. Fig. 6 shows the evolution of the spreading factor as a function of the vinegar concentration. This factor was determined using a power-law fit. The error bars accounted for the uncertainty of the fit and the errors that occurred during image processing. A decrease in this factor with increasing vinegar concentration was observed. The increase in this concentration presumably delayed the spreading, similar to the spreading rate, because of changes in the viscosity. These results are consistent with those obtained by E. Forester et al. [START_REF] Forester | Spontaneous spreading of emulsions on solid surfaces: Morphology and dynamics[END_REF] . The spreading dynamics of formulations with mustard were subsequently analyzed. First, the influence of mustard on formulations with 15 % vinegar is considered (Fig. 3), followed by a discussion of the other scenarios based on the spreading factor of the first regime. Their visual aspects have been discussed in the first sub-section. Fig. 7.a shows the evolution of the spreading rates over time for different amounts of mustard. The arrangement of the curves does not appear to assist elucidation of the influence of mustard. The addition of mustard certainly creates a layer around the vinegar droplets, which suppresses (or delays) coalescence and flocculation, resulting in a smaller force that slows the flow, and the dragging of the droplets by the continuous phase. This explains the increase in the spreading rate in scenarios involving 0.1 g and 0.2 g of mustard and 15 % vinegar. The use of 0.3 g to 0.5 g of mustard led to a decrease in the spreading rate owing to the thickening character of the mustard (increase in viscosity). This critical mass of the mustard depends on the concentration of vinegar (Fig. 3).

The spreading dynamics of these formulations were also described by two regimes, as shown in Fig. 7.b. The use of 0.1 g of mustard led to the first regime with a spreading factor, n = 0.11, and a second, slower regime with n = 0.06. Therefore, both regimes exist in mustard-incorporated samples. As in the experiments conducted without mustard, the effects of the added mustard were elucidated by analyzing the first spreading factor corresponding to all vinegar concentrations. Fig. 8 shows plots of the spreading factor as a function of vinegar and mustard concentrations. At a fixed amount of mustard, effects similar to those obtained without mustard were observed in terms of a decrease in the spreading factor with increasing vinegar concentration. The evolution of the spreading factor as a function of the quantity of mustard appears to be linear, and decreases with the quantity of mustard. This evolution was expressed using the two equations described below based on linear fitting.

For concentrations between 10 % and 40 %, the following relationship applies:

n 1 = α 1 + β 1 × m Mustard (2)
The two coefficients, which are a function of the vinegar concentration (C v %), are expressed as follows:

α 1 (C v %) = α 11 + α 12 × C v % (3) β 1 (C v %) = β 11 + β 12 × C v % ( 4
)
This modalization is an approximation of the observed evolution, which considers the variations occurring at low concentrations of vinegar.

However, it enables the characterization and description of the emulsifying characteristics of mustard. The decrease in the spreading factor with the vinegar concentration and amount of mustard is linked to changes in texture and viscosity. Given that addition of mustard leads to a more homogeneous vinaigrette, the droplets remain well dispersed in the emulsion. These results suggest that spreading can be used to visualize the changes in the apparent viscosity of emulsions and their concentration-dependent variations. The spreading factor was selected as an indicator because the spreading rate is related to the nature of the substrate, which can provide more practical results. However, the analysis of the first spreading regime enabled mitigation of the effects of the slight difference in roughness observed on the different surfaces. In addition, phase separation during spreading can be a quick indicator of the presence or absence of certain instabilities.

IV. CONCLUSIONS

The spreading dynamics and phase separation of vinaigrette were investigated. These phenomena were described based on the outward spreading of a portion of olive oil from the main film. A formulation protocol was developed in this regard. Immediately after the preparation of the vinaigrette, films were placed on a white tile substrate inside a glove box with relative humidity and temperature control. All films had identical initial masses and were formed at 21°C and a relative humidity of 50 %. Different formulations were prepared by varying the mass concentration of vinegar from 10 % to 40 %, and the mass of mustard from 0.1 g to 0.5 g.

The spreading dynamics of the vinaigrette were analyzed based on the spreading rate and spreading factor of the first (gravitational-viscous) regime. In mustard-free formulations, the spreading rate and spreading factor decreased with increasing vinegar mass concentration because of an increase in the mixture viscosity, which was due to the dropletdroplet interactions and the friction between the dispersed and continuous phases. The addition of mustard primarily affected the emulsion stability and viscosity. At fixed mass concentrations of vinegar (less than 30 %), the spreading rate increased with the amount of mustard until a threshold was reached; the spreading rate decreased beyond this point. This threshold is a function of the vinegar concentration. However, the spreading factor appeared to decrease with the amount of mustard. This variation was attributed to the change in viscosity related to the thickening of the mustard.

Phase separation occurred because of the competition between the oil flow during the spreading of the vinaigrette and the interactions between the droplets of the dispersed phase (vinegar).

These interactions are the origin of the instabilities that separate two-phase emulsions. The addition of mustard impeded these instabilities and prevented phase separation because of its emulsifying and thickening tendencies. This phase separation did not influence the spreading dynamics.

FIG. 1 :

 1 FIG. 1: Experimental formulation protocol featuring the (a) first, (b) second, and (c) third steps.

  FIG. 2: Effects of mixing time and vinegar concentration on the spreading, phase separation, and homogeneity of vinaigrette films (4.16 g ± 2.2 %) on a white tile substrate at 21 °C and a relative humidity of 50 %. "A" represents the final spreading area. (The scale bar represent 1 cm)

FIG. 3 :

 3 FIG. 3: Effects of mustard and vinegar concentrations on the spreading and phase separation of French vinaigrette films (4.16 g ± 2.2 %) on a white tile at 21 °C and a relative humidity of 50 %. (The scale bar represent 1 cm)

FIG. 4 :

 4 FIG. 4: Time lapse of the spreading of a vinaigrette film (4.16 g ± 2.2 %, V/O = 25 %, m mustard = 0.1 g) on a white tile substrate at 21 °C and a relative humidity of 50 %, showing spreading and phase separation. (The scale bar represent 1 cm)

  FIG. 5: (a) Spreading kinetics of vinegar-oil emulsions (m = 4.16 g ± 2.2 %) on a white tile substrate at 21 °C and a relative humidity of 50 %. (b) Log-log plot featuring time evolution of the rescaled area of an equilibrated film at 21 °C and a relative humidity of 50 %. The red lines represent visual guides for two different slopes. A typical error bar is shown at a single point in each curve.

FIG. 7 :

 7 FIG. 7: (a) Spreading kinetics of vinegar-oil emulsions with different amounts of mustard (m = 4.16 g ± 2.2 %, V/O = 15 %) on a white tile substrate at 21 °C and a relative humidity of 50 %. (b) Log-log plot featuring time evolution of the rescaled area of an equilibrated film at 21 °C and a relative humidity of 50 %. The red lines are visual guides that represent two different slopes. A typical error bar is shown at a single point in each curve.

FIG. 8 :

 8 FIG. 8: Spreading factor of vinaigrette (m = 4.16 g ± 2.2 %) as a function of the vinegar and mustard concentrations at 21 °C and a relative humidity of 50 % on a white tile substrate. The dashed lines represent linear fits.

ACKNOWLEDGEMENTS

The authors would like to thank Nathan & Raphael Brutin for pointing out the phenomena. Also, we would like to thank Hamza NAYA for his contribution to the experimental studies.

DATA AVAILABILITY

The data that support the findings of this study are available within the article or from the corresponding authors.

AUTHOR CONTRIBUTIONS STATEMENT

H.B. performed the experiments, analyzed the data, and prepared the manuscript. D.B. supervised the research, analyzed the data, and reviewed the manuscript.


domain: phys spi

text:
H Benabdelhalim
email: houssine.benabdelhalim@gmial.com

D Brutin
email: david.brutin@univ-amu.fr

CHAPTER 14 Drying of human blood drops

The study of blood drop drying has attracted the attention of several research groups for two main reasons:

(1) for biomedical purposes as a rapid and cheaper disease detector, and (2) for forensic applications for the interpretation of bloodstain at crime scenes. Also, it presents an interdisciplinary and challenging research subject. However, the mechanisms related to the formation of patterns at the end of the drying process are not fully understood, so this topic still represents an active branch of research that requires further efforts. When a drop of blood is deposited on a non-porous substrate in an unsaturated medium, it spreads and at the same time evaporates. The spreading is described by two regimes, a first regime controlled by the viscous-capillary balance and a second one controlled by the viscous-evaporation balance. The drop spreads until it reaches equilibrium, subsequently it keeps evaporating. The drying process is described by five distinct stages, and the final pattern is divided into three regions: the periphery, the corona, and the central region. The corona region results from the existence of a capillary flow inside the drop that transports the components to the edge of the drop (coffee ring effect). During the drying process, cracks form on the central region and the corona, this is explained in the literature by the competition between evaporation in the gel phase and adhesion to the substrate. These mechanisms (from spreading to final pattern formation) are influenced by the blood composition, the drop size, the substrate nature (wettability and contact angle), the relative humidity, and the temperature. In this chapter, we highlight the significant advances in the drying of human whole blood drops and the influence of these parameters.

Introduction

The drying of blood drops on a solid substrate leads to the formation of complex patterns, that can provide valuable information for two disciplines: forensic [START_REF] Smith | A New Forensic Tool to Date Human Blood Pools[END_REF][START_REF] Laan | Maximum Diameter of Impacting Liquid Droplets[END_REF][START_REF] Laan | Morphology of Drying Blood Pools[END_REF][START_REF] Attinger | Fluid Dynamics Topics in Bloodstain Pattern Analysis: Comparative Review and Research Opportunities[END_REF] and biomedical [START_REF] Brutin | Pattern Formation in Drying Drops of Blood[END_REF][START_REF] Chen | Blood Drop Patterns: Formation and Applications[END_REF][START_REF] Choi | Crack Density in Bloodstains[END_REF][START_REF] Bahmani | The Study of Drying and Pattern Formation of Whole Human Blood Drops and the Effect of Thalassaemia and Neonatal Jaundice on the Patterns[END_REF] . For forensic applications, bloodstains are one of the most encountered evidence at a crime scene after a bloody event [START_REF] James | Principles of Bloodstain Pattern Analysis: Theory and Practice; Practical aspects of criminal & forensic investigation[END_REF] . Crime scene investigators examine this evidence and make conclusions such as how the blood was shed [START_REF] Laan | Maximum Diameter of Impacting Liquid Droplets[END_REF][START_REF] Boos | Characterizing Drip Patterns in Bloodstain Pattern Analysis: An Investigation of the Influence of Droplet Impact Velocity and Number of Droplets on Static Pattern Features[END_REF] and the time at which stains were created [START_REF] Smith | A New Forensic Tool to Date Human Blood Pools[END_REF] . Chapter 15 provides more information for this purpose. For biomedical applications, the interpretation of dried human blood drops can be used as a clue to health status, as the morphology of the final drying pattern is highly dependent on the composition of the blood, and most diseases result in an alteration of this latter.

Several researchers have been interested in understanding the relationship between the final drying pattern of biological fluids (whole blood, plasma, and serum) and diseases to develop methods and tools that allow for fast and inexpensive diagnosis. Rapis [START_REF] Rapis | A Change in the Physical State of a Nonequilibrium Blood Plasma Protein Film in Patients with Carcinoma[END_REF] worked on the diagnosis of metastatic carcinoma by studying the drying of a human plasma film. He reported the existence of pronounced differences between the morphology of completely dried patterns of patients with the disease and those in good health. Yakhno et al. [START_REF] Yakhno | On the Existence of Regular Structures in Liquid Human Blood Serum (Plasma) and Phase Transitions in the Course of Its Drying[END_REF] investigated morphological differences in serum samples of patients with viral hepatitis B, chronic hepatitis B, and C. Buzoverya et al. [START_REF] Buzoverya | Quantitative Estimation of the Microstructural Inhomogeneity of Biological Fluid Facies[END_REF] in their quantitative study investigated the possibility of associating the final drying pattern of plasma drops with different diseases, by determining structural inhomogeneities. Also, the work of Muravlyova et al. [START_REF] Muravlyova | Structure-Forming Properties of Blood Plasma of Patients with Interstitial Lung Diseases[END_REF] on lung diseases. They used plasma samples collected from patients with interstitial lung fibrosis (ILF), patients with idiopathic interstitial pneumonia (IIP), and healthy people.

They showed the existence of modifications between the patterns of the three studied groups, which was explained by the albumin existing in the plasma and the accumulation of extracellular nucleic acids.

The use of plasma and serum requires their separation from human whole blood, thus adding an extra step in sample preparation. The serum is plasma without the components that are involved in the coagulation cascade. On the other hand, the use of human whole blood drops avoids this extra step and the probable sample modifications related to this separation. Brutin et al. [START_REF] Brutin | Pattern Formation in Drying Drops of Blood[END_REF] are the first to describe fully the five stages of drying of human whole blood drops. Moreover, they reported the existence of a morphological difference between patterns obtained from healthy persons and those with diseases. In 2016, Bahmani et al. [START_REF] Bahmani | The Study of Drying and Pattern Formation of Whole Human Blood Drops and the Effect of Thalassaemia and Neonatal Jaundice on the Patterns[END_REF] conducted a comparative study on the drying of whole blood drops for three patient groups: healthy, thalassemia, and neonatal jaundice. They showed that the morphology and more precisely the length of the cracks can be used as an indicator for these diseases.

The drying of blood drops is a complex phenomenon, which requires knowledge of biology, fluid mechanics, and heat and mass transfer. This is due to the composition of blood and its rheological behavior.

Human blood is a colloidal suspension, composed mainly of plasma (interstitial fluid) and soft components (colloids) that interact with each other and can affect the physical mechanisms inside the drops. Where the plasma consists mainly of water. Human blood has a non-Newtonian behavior 15 , and it represents thixotropic characteristics 15 , i.e. its behavior evolves. When a blood drop is deposited on a substrate, it will spread until it reaches equilibrium. At the same time, the solvent (water) evaporates outside. The nonuniformity of the evaporation flow on the drop surface leads to the formation of a capillary flow inside the drop [START_REF] Deegan | Capillary Flow as the Cause of Ring Stains from Dried Liquid Drops[END_REF] , which will transport the colloidal components towards the drop edge (coffee ring effect). The drying process is accompanied by a sol-gel phase change. In this gel phase, evaporation will take place through the pores created by the packing of the components. The competition between evaporation and adhesion to the substrate in this gel phase generates stresses, that will be released by the formation of cracks. These cracks characterize the final pattern of the dried blood drop [START_REF] Lei | Stress Development in Drying Coatings after Solidification[END_REF][START_REF] Pauchard | Stable and Unstable Surface Evolution during the Drying of a Polymer Solution Drop[END_REF][START_REF] Lazarus | From Craquelures to Spiral Crack Patterns: Influence of Layer Thickness on the Crack Patterns Induced by Desiccation[END_REF] .

The final pattern and mechanisms that lead to the formation of cracks in blood drops depend on parameters related to the health status of the person as the composition of blood. Also to external parameters: the size of the drop [START_REF] Brutin | Pattern Formation in Drying Drops of Blood[END_REF] , the substrate on which the drop is created [START_REF] Brutin | Influence of Substrate Nature on the Evaporation of a Sessile Drop of Blood[END_REF] , the relative humidity [START_REF] Bouzeid | Effect of Relative Humidity on the Spreading Dynamics of Sessile Drops of Blood[END_REF] , and the temperature [START_REF] Pal | Temperature and Concentration Dependence of Human Whole Blood and Protein Drying Droplets[END_REF] .

Understanding the influence of these parameters on the drying of blood drops allows us to isolate or control their effect from changes related to pathological effects. In this chapter, we discuss the drying of blood drops from spreading to crack formation with a literature review. In addition, we summarize all parameters that influence spreading, evaporation, and crack formation.

Biological and physical properties of human blood

Blood is a fluid tissue, permanently conveyed in the circulatory system in a unidirectional flow imposed by the cardiac pump. The whole human blood is composed of a cellular part (mainly red blood cells, white blood cells, and platelets), and a liquid part (plasma) [START_REF] Thiriet | Biology and Mechanics of Blood Flows[END_REF] . The water represents 92 % of the total volume of plasma, the other part is proteins and different substances. Red blood cells (RBCs) or erythrocytes are the most abundant, they represent 97 % of the volume of the bio-colloidal matter. They have biconcave disc shape. Their volume percentage in the blood is given by a dimensionless quantity known as the hematocrit level (hct). This latter varies between 38 % and 50 % for a healthy person. Under pathological conditions, the hematocrit may fall as low as 20% and rise to about 70%. Where the rheology and the viscosity of the blood depend strongly on the RBCs. White blood cells (WBCs) or leukocytes, are cells of the immune system. Due to their low physiological number in the blood, they contribute little to the mechanical properties of the blood. Platelets or thrombocytes play a major role in primary hemostasis; they are involved in coagulation. And they are of little rheological importance because they are very small components that do not interact with each other under normal conditions. Outside the human body, blood naturally coagulates and forms clots. During this process, fibrinogens of the plasma will be consumed, and it becomes serum.

The whole human blood is a complex non-Newtonian fluid that can be considered as a colloidal suspension 15 . It is characterized by a shear-thinning behavior, where its dynamic viscosity decreases with the increase of the shear rate. At shear rates higher than 100 s -1 , blood behaves like a Newtonian fluid with a dynamic viscosity equal to 4 mPa.s at a temperature of 37 °C. The blood viscosity depends on the measurement method 15 , temperature 15 , and hematocrit level 15,[START_REF] Chao | Influence of Haematocrit Level on the Kinetics of Blood Spreading on Thin Porous Medium during Dried Blood Spot Sampling[END_REF] . Harkness and Philips 15 reported a decrease of 3 % per 1 °C of the dynamic viscosity with the increase of the temperature. However, the increase in the hematocrit level causes an increase in the dynamic viscosity, which is greater at low shear rates. Although, the serum has a Newtonian behavior with a constant value of dynamic viscosity at any value of the shear rate, which is equal to 1.23 mPa.s under a temperature of 37 °C.

The surface tension of whole human blood and serum are described by a linear equation as a function of temperature in the range of 20 °C to 40 °C [START_REF] Rosina | Temperature Dependence of Blood Surface Tension[END_REF] :

For whole blood 𝜎 = (-0.473 × 𝑇 + 70.105) × 10 -3 and for serum 𝜎 = (-0.368 × 𝑇 + 66.072) × 10 -3 .

Where 𝜎, represent the surface tension on N/m, and 𝑇 , represent the temperature on °C.

Drying of whole human blood drop

From a kinetic point of view, the drying study is the characterization of the variation of the mass and the rate of evaporation as a function of time. Also, to determine the sorption curves according to the surrounding conditions. From a dynamic and morphological point of view, it is the characterization of the different forces that interact during the whole process and the description of the visual aspect. However, the understanding of the drying of blood drops requires the consideration of both approaches. The drying process of blood drops is a complex phenomenon that exhibits coupled physical mechanisms, such as spreading, evaporation, Marangoni flow, wetting, coffee ring effect, gelation, and crack formation. It was shown that under the same experimental conditions, this process is reproducible, and the final pattern depends only on the composition of the blood [START_REF] Brutin | Pattern Formation in Drying Drops of Blood[END_REF] .

When a blood drop is gently deposited on a non-porous substrate in an unsaturated medium, spreading and evaporation take place. The drop spreads to minimize its system energy and evaporates owing to the existence of a difference between the vapor concentration on the drop surface and the surrounding. Bouzeid and Brutin [START_REF] Bouzeid | Effect of Relative Humidity on the Spreading Dynamics of Sessile Drops of Blood[END_REF] studied the spreading dynamics of a drop of human blood on a clean glass substrate under a temperature of 25.5 ± 0.5 °C and relative humidity of 65 ± 2 %. Figure 14.1 shows the variation of the normalized radius of the drop as a function of time normalized by using the total evaporation time tf. This latter is defined as the time on which there is no solvent losing anymore, hence no mass variation. This time is given by:

𝑡 𝑓 = 4𝑅𝑇𝑚 0 𝜋∆𝑃𝐷 𝑓 𝐷 𝑑𝑖𝑓𝑓 (14.1)
Where 𝐷 𝑑𝑖𝑓𝑓 the coefficient of diffusion (for blood drop drying at 25 °C, this coefficient is 2.19 × 10 -5 𝑚 2 /𝑠), 𝑇 is the air temperature, 𝑅 is the gas constant, 𝑚 0 is the initial drop mass, 𝐷 𝑓 is the final wetting diameter of the wetted area, and ∆𝑃 is the difference between the saturated pressure and the air pressure.

The authors distinguished two different spreading regimes, where the first regime is faster than the second Figure 14.1. They determined the driving forces and the nature of dissipation in each regime. By using dimensionless numbers, they compared the forces involved in the spreading of a blood drop. During both regimes, the Bond number was less than 1, therefore the drop shape is spherical cap, and the gravitational forces can be neglected. Where they showed that the spreading is controlled by the balance of capillary and viscous forces in the first regime, and it is characterized by a power-law time evolution with exponent n = 0.65. While the second regime is described by the balance of driving forces generated by evaporation and viscous forces with a spreading exponent n = 0.18.

[Figure 14.1 near here]

The blood drop spreads until reaching a wetting radius and a wetting contact angle. At this time, the contact line is pinned to the substrate. In fact, for biological fluids, proteins anchor the contact line, as they will be absorbed by the substrate [START_REF] Tarasevich | Segregation in Desiccated Sessile Drops of Biological Fluids[END_REF] . The drop volume at equilibrium is given as function of the radius 𝑅 𝑓 and contact angle 𝜃 𝑓 , as follow:

𝑉(𝑅 𝑓 , 𝜃 𝑓 ) = 𝜋𝑅 𝑓 3 3 (1 -𝑐𝑜𝑠𝜃 𝑓 ) 2 (2 + 𝑐𝑜𝑠𝜃 𝑓 ) (sin 3 𝜃 𝑓 ) (14.2)
On the other hand, evaporation continues until the drop is completely dry. A blood drop evaporates with constant contact area. Brutin et al. [START_REF] Brutin | Pattern Formation in Drying Drops of Blood[END_REF] have divided the drying process of a blood drop into 5 distinct stages (1) Stage 1, the evaporation of the solvent and the surface tension gradient induces a Marangoni flow, consequently, this flow moves the biocolloid components towards the contact line [START_REF] Deegan | Capillary Flow as the Cause of Ring Stains from Dried Liquid Drops[END_REF][START_REF] Popov | Evaporative Deposition Patterns: Spatial Dimensions of the Deposit[END_REF][START_REF] Hu | Evaporation of a Sessile Droplet on a Substrate[END_REF] . The accumulation of these components creates a red deposit at the edge of the drop. Also, a drying front forms as the solvent continues to evaporate.

( (5) Stage 5, During this stage, the large, wide plates of the corona move slightly. At the end of the drying process, the final pattern has a donut shape with a typical cross-sectional deposit.

Brutin et al. [START_REF] Brutin | Pattern Formation in Drying Drops of Blood[END_REF] realized several drying blood drops experiments under the same conditions, for each dried drop they obtained a final pattern with the same characteristics Figure 14.3: The central part of the drop, the large moving plates of the corona with wide white cracks, and the fin periphery. Whereas the central part of the drop and the fin periphery adhere to the glass plate due to the absence of RBCs, the corona is where the mobile deposits form and these do not adhere to the substrate. This is due to the presence of proteins in the RBCs (glycoproteins). The role of these proteins is to avoid wetting with the veins. The final drop pattern is highly dependent on the substrate wettability, drop size, relative humidity, and temperature. The influence of all these parameters is given in detail in the following sections.

[Figure 14.

near here]

In the first stages of drying, the drop is in a liquid state. The drying is characterized by the evaporation rate. Where in hydrophilic situations, the evaporation rate of the solvent is higher near the contact line, which results in a radial internal flow [START_REF] Deegan | Capillary Flow as the Cause of Ring Stains from Dried Liquid Drops[END_REF][START_REF] Popov | Evaporative Deposition Patterns: Spatial Dimensions of the Deposit[END_REF][START_REF] Hu | Evaporation of a Sessile Droplet on a Substrate[END_REF] . This flow transports the bio-colloidal components towards the contact line, which will accumulate and reinforce the pinning of the contact line. This phenomenon is known as the "coffee stain effect". Sobac and Brutin [START_REF] Sobac | Desiccation of a Sessile Drop of Blood: Cracks, Folds Formation and Delamination[END_REF] observed an increase in concentration at the contact line, which is important since the volume of fluid is locally small and decreases during evaporation. At a critical concentration value, the particles aggregate and form a gel [START_REF] Popov | Evaporative Deposition Patterns: Spatial Dimensions of the Deposit[END_REF][START_REF] Bodiguel | Stick-Slip Patterning at Low Capillary Numbers for an Evaporating Colloidal Suspension[END_REF] . Hence the formation of a gel front at the edge of the drop, although the central part is still liquid. The gel front will propagate as th e concentration increases due to the evaporation of the solvent. The first cracks nucleate on the gelled region near the contact line. Afterward, these cracks, which are evenly spaced radially, propagate inward as they are stretched by the movement of the front. After complete gelation of the drop, some solvent is trapped inside the formed porous matrix. Drying continues by diffusion of solvent molecules through the pores, with a decrease in the rate of evaporation, so radial cracks continue to propagate. A t the end of drying, disordered cracks are formed in the central part of the drop.

During the loss of the solvent in the gel phase, important mechanical stress is formed due to the high capillary pressure in the tightly packed colloidal components. This stress leads to the appearance of two types of instabilities upon its release [START_REF] Giorgiutti-Dauphiné | Drying Drops[END_REF] , either the formation of cracking or buckling instabilities on the drop surface.

The existence or not of one of these instabilities depends on the surface wettability, the composition of the drop, and the surrounding conditions. In this chapter, we will only focus on the formation of cracks since it is the most common instability encountered in the drying of the blood drop on clean glass. The dynamics of their development were studied by several researchers, in the case of different fluids and for different applications, ranging from mud [START_REF] Goehring | Desiccation Cracks and Their Patterns: Formation and Modelling in Science and Nature[END_REF] to nano-fluid drops [START_REF] Carle | How Surface Functional Groups Influence Fracturation in Nanofluid Droplet Dry-Outs[END_REF] .

The mechanisms of crack formation in human blood drops have been well described by Sobac and Brutin [START_REF] Sobac | Desiccation of a Sessile Drop of Blood: Cracks, Folds Formation and Delamination[END_REF] .

They investigate the dynamics of rupture, average crack size, and delamination. Also, they showed that the spacing of the first crack matches perfectly with that predicted by Allain and Limat 33 .

[Figure 14.4 near here]

When gelation takes place, the trapped solvent starts to evaporate through the pores. This effect results in an intensification of the aggregation of the particles, hence consolidation of the gel. In this stage, the system is described by two interfaces Figure 14.4, a liquid-vapor interface where there is the evaporation of the solvent, and a gel-substrate interface. In the first interface, menisci form and are responsible for capillary pressure in the liquid phase 𝑃 𝑐𝑎𝑝 = -(2𝛾 𝑠,𝑎 cos 𝜃)/𝑟 𝑝 . Where 𝛾 𝑠,𝑎 is the solvent-air surface tension, 𝜃 is the liquid-solid contact angle, and 𝑟 𝑝 is the pore radius. During evaporation, the curvature of the menisci increases, which will generate a depression in the solvent. The pressure gradient leads to a migration of the solvent towards the surface and a progressive shrinking of the gel in response to the compressive force. This shrinkage is limited by the adhesion of the drop to the substrate. The competition between evaporation and adhesion leads to the development of mechanical stress, which will increase during drying and is released by the formation of cracks [START_REF] Lei | Stress Development in Drying Coatings after Solidification[END_REF][START_REF] Pauchard | Stable and Unstable Surface Evolution during the Drying of a Polymer Solution Drop[END_REF] . The ability of the gel to fracture depends on the significant existence of a pressure gradient in the pores [START_REF] Giorgiutti-Dauphiné | Drying Drops[END_REF] .

Choi et al. [START_REF] Choi | Crack Density in Bloodstains[END_REF] proposed a theoretical model to understand and predict crack density in a dry drop of blood. Their model is validated by experiments on colloidal suspensions and whole blood. Also, this model takes into account the effect of relative humidity and viscosity. The density of cracks is given by:

𝑓 = 1 𝜆 ~ 𝜇𝑟(1 -
With, 𝜆 the distance between cracks, 𝜇 the solvent viscosity, 𝑟 the characteristic size, 𝑅𝐻 the relative humidity, 𝜂 the dispersion viscosity, 𝐾 the permeability of the porous medium.

Effect of the blood drop size

Brutin et al. [START_REF] Brutin | Pattern Formation in Drying Drops of Blood[END_REF] studied the effect of drop size on crack formation in the so-called corona region, on a clean glass substrate, under a relative humidity of 47% and temperature of 22 °C, Figure 14.5. They reported that the number of cracks increases with the increase of the blood drop diameter, which is observed only from a critical diameter equal to 4.5 mm. Drops with larger diameters clearly show large, axisymmetric, and periodic cracks around the corona. However, for drops with diameters below this critical value, they did not observe axisymmetric cracks in the corona, Figure 14.5. In the previous section, we mention that the formation of the cracks is due to the developed stress. This latter results from the competition between evaporation and adhesion. This stress is lower for small drops than the one existing in drops with a diameter greater than 4.2 mm.

[Figure 14.5 near here]

Effect of substrate nature

The wettability, porosity, and thermal characteristics of a substrate have an important contribution to the formation of the final drop pattern. They mainly affect the coffee ring effect, transport of solid components, stress in the drop, and cracks formation. The wetting of a drop on a non-porous substrate is described by the apparent contact angle measured at equilibrium, i.e., when the spreading stops. This contact angle describes the geometry and drying process of the drop [START_REF] Chen | Controlling the Contact Angle of Biological Sessile Drops for Study of Their Desiccated Cracking Patterns[END_REF] . Recently, Hertaeg et al. [START_REF] Hertaeg | Predicting Coffee Ring Formation upon Drying in Droplets of Particle Suspensions[END_REF] have developed a model to predict the apparition of the coffee ring phenomenon. They showed that at a given volume fraction, there is a critical value of contact angle below which the coffee ring effect is observed. Also, at a given volume fraction, and a contact angle below a threshold value, this effect is observed. That was explained by the fact that the contact angle influences the dominance of the viscous effects on the surface tension.

Chen et al. [START_REF] Chen | Controlling the Contact Angle of Biological Sessile Drops for Study of Their Desiccated Cracking Patterns[END_REF] showed that the initial contact angle influences the final blood drop pattern. They used a glass substrate, which can control the contact angle. Three drops with different contact angles: 20 °, 35 °, and 50 ° were created. Figure 14.6 shows the morphological details obtained as a function of contact angle:

[Figure 14.6 near here]

(1) The width of the peripheral region decreases with increasing contact angle since the local thickness in this region increases with the contact angle. They explained this by using the Griffith theory [START_REF] Xu | Imaging Stress and Strain in the Fracture of Drying Colloidal Films[END_REF] , to determine the critical crack size. (Figure 14.6.a-c small red box)

(2) In the corona region Figure 14.6.a-c, they found that there is no change in crack characteristics, morphology, and spacing. They created drops of the same volume 12 um. These drops lose the same amount of solvent during the drying process; hence the same amount of energy will be released for crack formation. As a result, the same morphology for the three contact angles.

(3) The central region morphology depends on the initial contact angle, since the contact angle has a direct influence on the internal flow of the drop, hence on the transport and distribution of RBCs. They showed that the evaporation dynamics and drying time on the three substrates is almost the same despite the fact that aluminium has a high thermal diffusivity. There is a first regime of linear decrease when the drop is mainly liquid, and a second regime with a sharp decrease associated with the end of gelation. The dynamics of evaporation is the same because the limiting factor is the diffusion of the solvent vapor outside.

The drying of a drop on a glass substrate is already considered in the previous sections. For the other two substrates with a contact angle of about 90 °, the morphology is completely different. During the drying process, a glassy skin is formed in the drop/liquid interface, afterwards this plastic shell will deform and leads to the final pattern as shown in Figure 14.7.b-c. They associated this phenomenon with the evaporation dynamics. In the case of a wetting drop with a contact angle less than 40°, the evaporation rate high along the periphery and decreases across the interface [START_REF] Hu | Evaporation of a Sessile Droplet on a Substrate[END_REF] . Although in the case of a non-wetting drop, about 90 °, the evaporation rate is mostly constant across the interface [START_REF] Hu | Evaporation of a Sessile Droplet on a Substrate[END_REF] . In the latter case, RBCs

will not be transported to the edge of the drop, hence no coffee ring effect. Also, the drops at the end of the drying dewet and retract from the metal substrate and develop a hole in the center of the drop Figure 14.7.b-c. Pauchard et allain [START_REF] Pauchard | Stable and Unstable Surface Evolution during the Drying of a Polymer Solution Drop[END_REF] observed the same pattern for polymer drops, which was explained by the "buckling" phenomenon.

Effect of the relative humidity

The evaporation rate is a function of the relative humidity, it can be almost zero in saturated environments (𝑅𝐻 = 100%), as it can be maximum at low relative humidities. Therefore, its value decreases with increasing humidity. The evaporation rate describes the speed at which a drop of a volatile fluid evaporates.

Bouzeid and Brutin 21 investigated the effect of relative humidity (RH) on the spreading of blood drops, under a temperature of 25.5 ± 0.5 °C and a relative humidity rank ranging from 8% to 90%. They showed that at low evaporation rates (high RH), the spreading is quick in contrast to high evaporation rates (low RH) Figure 14.8. Hence the equilibrium drop area increases with increasing RH. This is because solvent loss is lower at high RH, then more solvent will spread out. Also, the rate of contact line advancement decreases with increasing RH. Bouzeid and Brutin [START_REF] Bouzeid | Influence of Relative Humidity on Spreading, Pattern Formation and Adhesion of a Drying Drop of Whole Blood[END_REF] constate a linear variation of the contact angle as function of humidity, which is given by the following equation:

𝜃 𝑅𝐻 = 21(1 -𝑅𝐻) (14.4)
That was obtained by fitting the experimental results. The substitution of the equation (14.4) into equation ( 14.2) provides the radius variation with RH:

𝑅 𝑅𝐻 = ( 3𝑉 𝜋 sin 3 𝜃 𝑅𝐻 (2 + cos 𝜃 𝑅𝐻 )(1 -cos 𝜃 𝑅𝐻 ) 2 ) 1 3 (14.5)
Hu and Larson 37 derived a simple analytical expression to describe the evaporation rate of droplet, which is valid for the case with a constant area drying mode and contact angle less then 90 °. This latter was described by Bouzeid and Brutin [START_REF] Bouzeid | Influence of Relative Humidity on Spreading, Pattern Formation and Adhesion of a Drying Drop of Whole Blood[END_REF] for blood droplet and as function of RH as flow:

𝐽 𝑏𝑙𝑜𝑜𝑑 = 𝜋𝑅 𝑅𝐻 𝐷 𝑑𝑖𝑓𝑓 𝐶 𝑣 (1 -𝑅𝐻)𝑓 𝑅𝐻 (14.6) where 𝐶 𝑣 (1 -𝑅𝐻) is the vapor concentration difference between the saturated vapor at the apex and the vapor concentration in the far-field from the drop and 𝑓 𝑅𝐻 is a function that depends on the contact angle and the relative humidity given by: 𝑓 𝑅𝐻 = (3.59 × 10 -2 )𝑅𝐻 2 -(7.18 × 10 -2 )𝑅𝐻 + 1,33 (14.7)

[Figure 14.8 near here]

In another study, Bouzeid and Brutin 38 investigated the effect of relative humidity on the final dried drop pattern. In a range of relative humidity from 13.5 % to 78.0 %, on a clean glass substrate. They showed that the relative humidity has a strong influence on the contact angle, the final pattern, and the end of the drying process. The contact angle decreases with RH, which will influence the final pattern. Figure 14.9 shows the different final patterns obtained at the end of the drying process as a function of RH. The surface of the mobile plates in the corona depends on the relative humidity. By the change in evaporation rate, the mechanical properties of the gel are changed such as the adhesion to the substrate. They found a decrease in adhesion energy at RH ranging from 13.5% to 50.0%, from which the surface area of the plates becomes progressively large. For patterns obtained at RHs above 50%, the mobile plates are smaller with significant adhesion energy. In contrast, the width of the drop edge increases continuously as a function of RH, the yellow lines in Figure 14.9. This thin edge is due to the absence of RBCs caused by the propagation of the gel front.

[Figure 14.9 near here]

Using model (14.3), Choi et al. [START_REF] Choi | Crack Density in Bloodstains[END_REF] predicted crack density as a function of relative humidity in whole blood drops and colloidal suspensions. They reported a decrease in crack density as a function of relative humidity. Also, their model is in agreement with the experimental results, presented by the solid line [Figure 14.10 near here]

Effect of the temperature and the concentration

In this section, we will highlight the recent work of Pal et al. [START_REF] Pal | Temperature and Concentration Dependence of Human Whole Blood and Protein Drying Droplets[END_REF] on the effect of temperature and concentration on the drying morphology of blood drops. In this regard, they created drops of 1 ul volume with different concentrations ranging from 12.5 % up to 100 %, on a substrate with a controlled temperature of 25 °C to 45 °C, under 50 % relative humidity. Figure 14.11 shows the final patterns obtained after the total drying.

[Figure 14.11 near here] At 25 °C, there are all the regions seen previously in the work of Brutin et al. [START_REF] Brutin | Pattern Formation in Drying Drops of Blood[END_REF] , the central region, and the socalled corona region. At 45 °C, the central region is absent at concentrations higher than 62 %. They reported that cracks morphology does not represent a significant difference depending on the three temperatures studied. The temperature of the substrate will reduce drying time, and it will intensify the Marangoni flow inside the drop, hence increasing the internal flow velocity. However, the width of the corona increases with the concentration and the width of the central region decrease. Recently, Parthasarathy et al. [START_REF] Parthasarathy | Further Insights into Patterns from Drying Particle Laden Sessile Drops[END_REF] observed the same behavior as a function of concentration and particle size. They attribute this suppression of the corona "coffee ring effect" to components aggregation. Pal et al. [START_REF] Pal | Temperature and Concentration Dependence of Human Whole Blood and Protein Drying Droplets[END_REF] showed the existence of a difference in the drying process as a function of concentration, at a concentration of 100 %, the cracks propagate radially from the center to the edge, in contrast to a concentration of 12.5 %, in which the cracks propagate from the edge to the center. The central region and corona have different thicknesses for concentrations of 50 to 12.5 %, in contrast to concentrations of 100 % to 62 %, in the latter the difference is not too visible. Also, the number of cracks increases, and the spacing between cracks becomes thin with decreasing concentration.

Conclusion

The final pattern of a completely dried blood drop can be used as a biological marker for certain diseases, since it represents a fast procedure and does not require large quantities of human blood. For this purpose, it is necessary to clearly distinguish between the effect of blood composition and other external parameters on the dried pattern. The mechanisms that lead to the formation of the final pattern are complex. In order to understand them, several important works have been done so far, in which the influence of external parameters is taken into account. However, our knowledge about the link between the morphology of the final patterns and a given disease is not yet clear. Therefore, further studies on cellular and molecular biophysical interactions are needed before moving on to medical applications. 𝐿 represent the length of large plaques [START_REF] Chen | Controlling the Contact Angle of Biological Sessile Drops for Study of Their Desiccated Cracking Patterns[END_REF] . Copyright 2018 Royal society of chemistry.

Figure 14 . 2 .

 142 Figure 14.2. Where each stage is driven by specific mechanisms:

  ) Stage 2, the drying process continues by the propagation of the drying line towards the center of the drop. The inner flow creates a difference in fluid composition, which results in the formation of a dark red torus. (3) Stage 3, the Marangoni flow is no longer possible since the volume fraction of the solid components has increased, and now the drop has a flat central area. The torus dries quickly, and the central part becomes lighter red. At the end of this stage, most of the cell components are in the so-called corona zone Figure 14.3 and some RBCs are trapped in the central zone. A first crack appears around the drop between the corona and the central part of the drop. (4) Stage 4, The drying of the corona area is completed, and circular drying patterns are observed around the corona. The central area starts to dry completely and shows the formation of small cracks.

Figure 14 .

 14 Figure 14.6.d-f clearly shows the effect of the contact angle on this region. The latter increases

Figure 14

 14 Figure 14.10.

Figure 14 . 1

 141 Figure 14.1 Evolution of the dimensionless radius, (𝑟(𝑡) -𝑅0)/(𝑅𝑓 -𝑅0), as a function of dimensionless

Figure 14 . 2

 142 Figure 14.2 Time-lapse of a drying blood drop with 5.9 mm of diameter on microscope glass substrate at

Figure 14 . 3

 143 Figure 14.3 Closer view of pattern of a dried blood drop with 5.9 mm of diameter on microscope glass

Figure 14 . 4

 144 Figure 14.4 Schematic representation of the formation of a porous matrix during the drying process. A close

Figure 14 . 5

 145 Figure 14.5 Cracks number in the corona as a function of drop diameter. All drops are created with the same

Figure 14 . 6

 146 Figure 14.6 Corona (left) and centrale region (right) morphology as a function of initial contact angles: (a,d)

Figure 14 . 7

 147 Figure 14.7 Morphologies of dried blood drops formed on different substrates: (a) glass; (b) gold; (c)

Figure 14 . 8

 148 Figure 14.8 Schematic representation of spreading drops for the case of: (a) RH = 10 % and (b) RH = 80 %.

Figure 14 . 9

 149 Figure 14.9 Dried pattern morphology as a function of relative humidity (RH varying between 13.5 % and

Figure 14 . 10

 1410 Figure 14.10 Crack density measurement and visualization as a function of relative humidity. Measurement

Figure 14 . 11 FiguresFigure 14 .

 141114 Figure 14.11 Final pattern of whole human blood drops at different initial concentrations (∅ 𝑏 ) ranging from 100 to 12.5% (𝑣/𝑣), dried under three different substrate temperature of 45 °C, 35 °C, and 25 •C. The scale

1

 1 Figure 14.1

Figure 14 . 2 Figure 14 . 3

 142143 Figure 14.2

Figure 14 Figure 14 . 5 Figure 14 Figure 14 . 7 Figure 14 . 8

 1414514147148 Figure 14.4

Figure 14 . 9 Figure 14 . 10

 1491410 Figure 14.9

Figure 14

 14 Figure 14.11