Dr Malika Toubal

Prof Mr Bertrand Jesse Nongaillard

Mr Safouene Schiffler

Prof Ouenzerfi

Sabine

Celine Morin

Damien Meresse

Eric Delacourt

Fateh Mameri

Fethi Aloui

François Beaubert

Jean-Michel Dailliet

Marc Lippert

Maryam Parsa

Maxime Balligand

Raphaël Deltombe

Riadh Boubaker

Sabine Guilain- Houvenaghel

Sofia Korniliou

Keywords: Drop evaporation, Binary solution, Nanofluid, Marangoni effect

In recent years, increasing requirement in high efficient heat dissipation for microelectronics, spacecraft, nuclear reactors etc., encourage the development of next generation heat exchanger. Heat pipe is one of potential effective cooling equipments and most of mass and heat transfer take place at micro-region near triple phase (solid, liquid, vapor) contact line of working fluid, which is essential to thermal performance improvement of heat pipe. This study focuses on the evaporation process of sessile droplets of two novel working fluids (binary solution and nanofluid), which possess similar micro-region to that in heat pipe. Concentration gradient induced Marangoni flow and exceptional thermal conductivity are expected to significantly enhance evaporation rate of alcohol-water mixture and graphene nanofluid, respectively. A combination of acoustic and infrared techniques is developed to track alcohol concentration variation during evaporation of 1-butanol and ethanol aqueous droplets. According to observation of evaporation behavior at different substrate temperature, a series of empirical equations is suggested to predict evaporation rate of 1-butanol-water binary solution droplet considering thermal and solutal Marangoni effect. In addition, the effect of PEGylation, nanoparticle concentration and substrate temperature on drop evaporation of graphene nanofluid are investigated by microscopic, optical and infrared methods. Experimental results and thermodynamic analysis can contribute to the full understanding of involved mechanism concerning evaporation performance of graphene nanofluid.

Résumé

Résumé

Au cours des dernières années, les exigences croissantes en matière de dissipation thermique à haut rendement pour la microélectronique, les engins spatiaux, les réacteurs nucléaires, etc., encouragent le développement d'échangeurs de chaleur de nouvelle génération. Le caloduc est l'un des équipements de refroidissement efficaces et potentiels.

La plupart du transfert de masse et de chaleur se fait au niveau de la micro-région près de la ligne triple de contact (solide, liquide, vapeur), qui est essentielle à l' amélioration de la performance thermique du caloduc. Cette étude se concentre sur le processus d'évaporation de gouttes sessiles de deux nouveaux fluides de travail (solution binaire et nanofluide), qui possèdent une micro-région similaire à celle du caloduc. Le flux de Marangoni induit par le gradient de concentration et la conductivité thermique exceptionnelle devraient améliorer significativement le débit evaporé du mélange alcooleau et du nanofluide de graphène, respectivement. Une combinaison de techniques acoustiques et infrarouges est développée pour suivre la variation de la concentration d'alcool pendant l'évaporation des gouttes des mélanges 1-butanol-eau et éthanol-eau. Selon l'observation du comportement d'évaporation à différentes températures du substrat, une série d'équations empiriques est suggérée pour prédire le taux d'évaporation de la solution binaire de 1-butanol-eau en considérant l'effet Marangoni thermal et solutal. De plus, l'effet de la PEGylation, de la concentration des nanoparticules et de la température du substrat sur l'évaporation de gouttes de graphène nanofluide est étudié par des méthodes microscopiques, optiques et infrarouges. Les résultats expérimentaux et l'analyse thermodynamique peuvent contribuer à la compréhension complète du Résumé mécanisme impliqué concernant les performances d'évaporation du nanofluide de graphène.

Mots clés: Evaporation des gouttes, Solution binaire, Nanofluide, Effet Marangoni.

Chapter 1 Introduction

Chapter 1 Introduction

Background

Heat transfer enhancement

Heat transfer is a basic physical process due to temperature difference between two objects or various parts of same object that thermal energy flows from high temperature place to low temperature place. As a fundamental discipline in thermal engineering with broad applications as heat exchanger, condenser, boiler and evaporator, heat transfer becomes an important subject that attracts researchers to hunt for the enhancement methods. In 1861, Joule [START_REF] Joule | On the surface-condensation of steam[END_REF] investigated the condensation of steam by using water and air as refrigerant and found that augmented steam velocity or spiral refrigerant flow will improve heat exchange performance, which is the first attempt to enhance heat transfer efficiency. Since that, numerous studies have been reported on heat transfer enhancement with increasing need in thermal engineering. The effective enhancement techniques are generally classified in two categories: passive and active methods. The difference is that the passive methods do not require extra power input while the active methods need external power supply. Bergles [START_REF] Bergles | Techniques to enhance heat transfer[END_REF] identified several heat transfer enhancement methods whose efficiency strongly depends on the mode of heat transfer (single-phase, boiling, and condensation with natural or forced flow, respectively), the brief descriptions are following: g. Surface-tension devices involve wicking or grooved surfaces, which drive the flow of liquid to boiling area and from condensing area by capillary force. h. Additives for liquid include solid particles, gas bubbles and trace additives. The two former are used for single-phase flows while the latter for boiling systems.

i. Additives for gas include liquid droplets and solid particles, which are added in single-phase gas flows for forming dilute phase (gas-solid suspensions) or dense phase (fluidized beds). e. Injection is merely applied for single-phase flow by injecting gas, same or different liquid directly to the upstream of heat transfer section or to the convection flow through a porous heat transfer media.

Chapter 1 Introduction f. Suction is used in nucleate or film boiling to remove vapor through a porous heated surface, or in single-phase flow to withdraw fluid through a porous heated surface.

g. Jet impingement is utilized in single or multiple mode (clusters or staged axially along the flow channel) to improve the heat transfer efficiency of single-phase flow or boiling by jetting heating or cooling fluid to the heat transfer surface at vertical or inclined angle.

The compound heat transfer enhancement method is that two or more of above mentioned methods are simultaneously applied to achieve a significantly improved heat transfer, which is higher than that obtained by only one enhancement method. The heat pipe is one of compound enhancement methods, which includes several passive methods (extended surfaces, surface tension devices, additives for liquid etc.).

Heat pipe

Figure 1.1 Schema of capillary-driven heat pipe. Image is from Ref. [3] Heat pipe is a passive heat exchanger with advantages of significantly high heat transfer efficiency, flexible size, long service life, minimum maintenance and no require in external power. Fig. 1.1 represents the typical capillary-driven heat pipe with a cylindrical geometry. The heat pipe consists of a sealed pipe or tube which can be divided in three sections: evaporator section, adiabatic section and condenser section. The evaporator section is connected to the heat source while the condenser section is connected to the heat sink. The interior surface of heat pipe has wick structure. The working fluid absorbs the heat at evaporator section via thermal conduction and evaporates to become vapor phase. The generated vapor increases the vapor pressure at evaporator section which drives the vapor to arrive at condenser section through adiabatic section. The vapor concedes the latent heat of evaporation to the connected heat sink at condenser section and condenses to become liquid phase again. The wick structure drives the condensed working fluid back to the evaporator section by capillary force (thermosiphon uses gravitational force). The working fluid is in equilibrium state with its own vapor inside heat pipe and this circulation continues to conduct heat from evaporator section to condenser section until there is on sufficient vapor pressure difference or capillary force. The conventional working fluids applied in heat pipe are water, ammonia, methanol, acetone, heptane, sodium and so on. With a wide range of applications in electronic cooling, energy recovery, spacecraft thermal control, solar thermal etc., heat pipe becomes one of effective heat transfer devices. When working fluid wets smooth or wicked surface of heat pipe, a region of the meniscus interface is created near the solid-liquid-vapor triple phase contact line (Fig. 1.2). The meniscus region is usually divided into three sub regions: non-evaporating region where working fluid is absorbed by surface without evaporation, transition region where disjoining liquid pressure takes place due to long-range molecular forces, and intrinsic meniscus region where capillary force is dominant. The enhancement of heat transfer efficiency for heat pipe is limited by the thermal resistance of evaporator section which is determined by the thermal conductivity of wick material and working fluid meniscus. For convectional application, the heat flux at evaporator section is governed by the thermal resistance of wick material. However for the application of very thin (< 200 μm) high Chapter 1 Introduction thermal conductivity wick structures (k > 100 W/mK), the thermal conductivity of working fluid meniscus which is primarily determined by thickness of thin film near contact line, plays a significant role in evaporation performance [START_REF] Ranjan | Wicking and thermal characteristics of micropillared structures for use in passive heat spreaders[END_REF]. Many researchers report that most heat and mass transfer take place at the transition section of working fluid meniscus (Fig. 1.3) [START_REF] Harmand | Experimental and theoretical investigation of the evaporation and stability of a meniscus in a flat microchannel[END_REF][START_REF] Wang | Characteristics of an evaporating thin film in a microchannel[END_REF][START_REF] Potash | Evaporation from a two-dimensional extended meniscus[END_REF][START_REF] Wayner | Intermolecular forces in phase-change heat transfer: 1998 Kern award review[END_REF]. The study in nanoscale wick structure in order to increase the area of transition region or decrease the thickness of thin liquid film becomes more and more important in thermal performance improvement of heat pipe. Moreover, the capillary force of wick structure limit the sustainable working performance of heat pipe without the appearance of dry-out [START_REF] Ranjan | Assessment of nanostructured capillary wicks for passive two-phase heat transport[END_REF]. Therefore the optimization of wetting situation on wick structure is an important subject in heat transfer enhancement with increasing need in high efficiency heat exchangers.

Research Objectives and Thesis Outline

When a liquid droplet is deposited on a solid substrate, it has the same meniscus geometry near contact line as that on wick structure. Thus the study of evaporation performance and profile change in meniscus region of liquid droplet and the mechanism behind the phenomenon investigated will contribute to the optimization of wick structure as well as the heat transfer improvement of heat pipe. The main objective of this thesis is to determine the evaporation performance of droplets by using two novel solutions, binary solution and nanofluid. Binary solution can induce solutal Marangoni flow by surface tension gradient while nanofluid is supposed to possess exceptional thermal conductivity. Both will contribute to the enhancement of evaporation rate of droplets. A combination of optical, infrared and acoustic techniques is applied to investigate the Chapter 1 Introduction change in composition and profile of droplets and the temperature distribution on droplet surface, which can provide clues to full understanding of the complex evaporation behaviors and mechanisms near solid-liquid-vapor triple phase line. Another target of this thesis is focused on the effects of involved factors such as temperature, liquid composition and component concentration, on thermal performance of sessile droplets. This dissertation consists of 6 chapters. The current chapter presents the fundamental theory on heat transfer enhancement and heat pipe as well as the research goal and the thesis structure. Chapter 2 summarizes the effort of the other researchers on thermal performance improvement by using binary solution and nanofluid. Chapter 3 introduces a novel combined method of optical, infrared and acoustic techniques for tracking the alcohol centration in a sessile droplet of binary solution during evaporation, which will be very helpful to illustrate the invisible component change within droplet. Chapter 4 presents the investigations on the evaporation behavior of 1-butanol-water binary droplets and the comparison of droplet evaporation rate between binary solution and pure water. A series of empirical equations for predicting the evaporation rates of pure water or 1butanol-water binary droplets are provided. In Chapter 5, the effects of factors such as substrate temperature, PEG-functionalization, nanoparticle concentration, on evaporation performance of graphene nanofluid are investigated. The possible underlying mechanism is suggested to illustrate the evaporation rate difference between pure water and graphene nanofluid droplets. Chapter 6 concludes the accomplished experimental works and research discoveries, and proposes the perspectives in future work.

Chapter 2 Literature Review

Chapter 2 Literature Review

Binary Solutions

The evaporation of a sessile droplet is a fundamental heat and mass transfer process in the nature. When a droplet is deposited on a solid surface, its profile is determined by the equilibrium of gas, liquid and solid phases (Fig. 2.1). In 1805, Young [START_REF] Young | An essay on the cohesion of fluids[END_REF] described this equilibrium by the relationship between three interfacial tensions (solid/liquid, liquid/vapor and solid/vapor) in following equation:

SG SL LG C cos γ γ γ θ - = ⋅ (1.1)
where SG γ , SL γ , LG γ are surface tension of solid/vapor, solid/liquid, liquid/vapor interface respectively, θ C is the contact angle which is the angle between liquid/solid interface and liquid/vapor interface of droplet. In addition, the contact line is the intersection of liquid phase, solid phase and vapor phase at the periphery of droplet wetted area. The wettability of solid substrate with liquid droplet depends on the physical properties of liquid and the surface characteristics of substrate, which can classify substrate in two types by the measurement of contact angle: hydrophobic when contact angle is above 90° and hydrophilic when contact angle falls in the range of 0° ~ 90°. The evaporation of droplets of binary or multicomponent solution is a more complicated heat and mass transfer process. The more volatile liquid preferentially evaporates at the liquid/vapor interface, which is supplied by the diffusion of the same remained liquid from the bulk liquid of the droplet. The variation of composition in binary droplet leads to the change in physical and thermal properties such as surface tension, thermal conductivity, latent heat etc. Until the depletion of more volatile liquid, most of component remained in droplet is the less volatile one. After that, the evaporation behavior of droplet is similar to that for single component droplet. Sefiane et al. [START_REF] Sefiane | Experimental study of evaporating water-ethanol mixture sessile drop: influence of concentration[END_REF] divided the evaporation process of water-ethanol mixture droplet in three different stages according to the dynamic evolution of contact angle, diameter and volume of droplet (Figure 2.3): First stage with similar evaporation behavior to that for pure volatile component droplet; Transition stage with increase of contact angle, decrease of contact diameter and a moderate evaporation rate; Last stage with similar evaporation behavior to that for less volatile component droplet. In the light of particle image velocimetry investigation by Christy et al. [START_REF] Christy | Flow transition within an evaporating binary mixture sessile drop[END_REF], the internal flow filed inside water-ethanol mixture droplet can be separated into three phases corresponding to evaporation behavior: Phase I with multiple vortices driven by concentration differences; Phase II with exponential decay of vortices with the migration of the remaining vortices toward the drop periphery;

Phase III with evaporation driving outward flow to the contact line. Therefore a better understanding of heat and mass transfer mechanism behind mixture droplet evaporation, which is essential to many industrial processes such as circuit cooling, ink-jet printing, cloud formation, combustion etc., has attracted increasing interest in recent years. Two significant applicable effects produced by binary solutions are Marangoni effect and selfrewetting effect.

Marangoni effect

When concerning about the flows within a sessile single or multi component droplet on heated substrate, a surface tension difference driven effect plays an important role in evaporation kinetics. This effect is termed as Marangoni effect, named after Italian physicist Carlo Marangoni who firstly reported this surface phenomenon in 1855 [START_REF] Marangoni | Sull'espansione delle goccie d'un liquido galleggianti sulla superfice di altro liquido[END_REF]. If the substrate is heated, heat is conducted from solid/liquid interface to liquid/vapor interface. Owing to shorter heat transfer path, the temperature at vicinity of contact line is higher than that at the top of droplet. Increased temperature reduces surface tension of region near contact line and liquid is driven to the apex of droplet with higher surface tension along liquid/vapor interface (Fig. Marangoni effect demonstrates potential application in DNA mapping, film coating and micro-electronic cooling according to plentiful researches on this topic. Hu and Larson [START_REF] Hu | Marangoni effect reverses coffee-ring depositions[END_REF] experimentally and theoretically investigated the effect of thermal Marangoni flow on "coffee ring" deposition of PMMA fluorescent particles by droplet drying and found that the formation of ring-like deposit necessitates not only constant contact line evaporation process but also suppressed thermal Marangoni flow. Majumder et al. [START_REF] Majumder | Overcoming the "coffee-stain" effect by compositional Marangoni-flow-assisted drop-drying[END_REF] reported that the drying of water droplets containing nanoparticles at ethanol saturated atmosphere and ambient temperature will lead to homogenous nanoparticle deposition instead of "coffee ring" pattern. As a result of ethanol saturated pressure, water preferably evaporates and ethanol condenses from vapor phase at the vicinity region of contact line where surface tension is decreasing. The liquid flow from lower surface tension area (contact line) towards higher surface tension area (top), which is solutal Marangoni flow, recirculates nanoparticles taken by outward capillary flow near contact line and creates uniform nanoparticle deposit. In the study of Nikolov et al. [START_REF] Nikolov | Superspreading driven by Marangoni flow[END_REF], they suggested that the superspreading of aqueous trisiloxane ethoxylate surfactant solutions on hydrophobic surface is driven by solutal Marangoni flow and the spreading rate increases with larger surface tension gradient at free surface of liquid. The superspreaders can considerably improve the wetting problem on hydrophobic surface which is frequently encountered in numerous industrial processes. For heat transfer aspect, Savino

and Fico [START_REF] Savino | Transient Marangoni convection in hanging evaporating drops[END_REF] analyzed the evaporation performance of pendant drops containing silicone oil and hydrocarbon by experimental and numerical methods, and the results revealed that the Marangoni flow induced by non-uniform evaporation can improve homogeneity of temperature distribution on drop surface as well as overall evaporation rate. Buffone and Sefiane [START_REF] Buffone | Investigation of thermocapillary convective patterns and their role in the enhancement of evaporation from pores[END_REF] observed intense Marangoni convection inside the liquid meniscus formed in capillary tube. The evaporative cooling effect is considered as the driving mechanism of surface tension gradient induced convection which effectively enhances the heat and mass transfer from the pore.

Self-rewetting fluids

In 1973, Vochten and Petre [START_REF] Vochten | Experimental determination of the heat of reversible absorption of some alcohols[END_REF] found that the dilute aqueous solutions with high-carbon alcohol show an abnormal increase of surface tension with the rise of temperature in a specific range of temperature, which is named as self-rewetting fluids. Ono et al. [START_REF] Ono | Measurement of temperature dependence of surface tension of alcohol aqueous solutions by maximum bubble pressure method[END_REF] employed maximum bubble pressure method to measure surface tension of high-carbon alcohol aqueous solutions (butanol and pentanol) and found that pure high-carbon alcohols show a monotonically decreasing relationship of surface tension with temperature while their aqueous solutions at different alcohol concentration display selfrewetting behavior with increasing surface tension in specific temperature range (Fig.

2.6)

. Therefore with temperature gradient falling in this specific range, the part of higher temperature possesses higher surface tension in self-rewetting fluid. Due to inherent motion from lower surface tension place to higher surface tension place, self-rewetting fluid will flow towards higher temperature area, which is driven by inverse Marangoni force. On basis of this assumption, Ouenzerfi and Harmand [START_REF] Ouenzerfi | Experimental droplet study of inverted marangoni effect of a binary liquid mixture on a nonuniform heated substrate[END_REF] According to the abnormal behavior of self-wetting fluids, one important application of self-rewetting fluid is for the design of wickless heat pipe under microgravity condition.

In space environment, the gravitational force is not strong enough to bring working fluid back to evaporation section and the wickless structure can contribute to lightweight design and simplified production of heat pipe. The optimized design of heat pipe is that the Marangoni flows driving the working fluid from condenser to evaporator are induced by both temperature and alcohol concentration gradients [START_REF] Di Francescantonio | New alcohol solutions for heat pipes: Marangoni effect and heat transfer enhancement[END_REF]. Even under terrestrial condition, Hu and al. [START_REF] Hu | Heat transfer enhancement of micro oscillating heat pipes with self-rewetting fluid[END_REF] observed enhanced heat transfer and reduced capillary pressure gradient by applying self-rewetting fluid in micro oscillating heat pipes which is compared to that for the case of deionized water. The improved wetting situation at evaporation section and the effective recurrence with less capillary resistance make contributions to the ameliorated thermal performance of heat pipes. Savino et al. [START_REF] Savino | Heat pipes with selfrewetting fluids under low-gravity conditions[END_REF] conducted at terrestrial condition and at microgravity condition with wickless heat pipe containing self-rewetting fluid and pure water. Lower thermal resistance was observed during the performance of heat pipe filled with self-rewetting binary solution by comparing to that with pure water. Furthermore, the heat pipe filled with self-rewetting fluid have the similar heat transfer efficiency no matter under terrestrial or reduced gravity condition while the thermal performance of heat pipe filled with pure water is deteriorated in the parabolic flight.

Nanofluids

An innovative heat transfer medium with suspension of nanoscale particles is expected to possess extremely high thermal conductivity, which is termed as nanofluid by Choi et al. [START_REF] Choi | Enhancing thermal conductivity of fluids with nanoparticles[END_REF]. Nanometer-sized particles of metal, metallic oxide, carbon nanostructure, whose inherent thermal conductivity is quite higher than that of common liquid, are employed in preparation of nanofluid in order to enhance thermal conductivity of convention heat transfer fluids such as water, engine oil and ethylene glycol. The advantages of nanofluid are highlighted in increased heat exchange area at solid/liquid interface, improved dispersion homogeneity and stability, reduced fill quantity, reduced probability of nanoparticle obstruction and controllable physical and thermal properties by changing nanoparticle loading [START_REF] Sivashanmugam | Application of nanofluids in heat transfer[END_REF]. With above mentioned benefits, nanofluid is considered as a potential high efficiency working fluid for the design of next generation heat exchanger.

Preparation methods

Preparation methods are crucial to the application of nanofluid, which will affect suspension stability, dispersion homogeneity, physical and thermal properties of nanoparticle suspension solution. In general, nanofluid preparation methods can be classified in single-step method and two-step method. The single-step method is based on Vacuum Evaporation onto a Running Oil Substrate (VEROS) method, which was originally developed by Yatsuya et al. [START_REF] Yatsuya | A New Technique for the Preparation of Extremely Fine Metal Particles[END_REF] to produce metallic nanoparticles. The basic principle of VEROS method is that an electron beam vaporized pure metal under vacuum condition and then nanometer-sized metallic particles condense on a rotating substrate covered by radially outward moving oil. The nanoparticle suspension before drying is nanofluid. Henceforth VEROS method was modified by Wagener et al. [START_REF] Wagener | Preparation of metal nanosuspensions by high-pressure DC-sputtering on running liquids[END_REF] with employment of high pressure magnetron sputtering and improved by Eastman et al. [START_REF] Eastman | Enhanced thermal conductivity through the development of nanofluids[END_REF] with direct condensation of metallic nanoparticles on a flowing ethylene glycol.

Furthermore, the other single-step methods such as chemical reduction under microwave

Chapter 2 Literature Review irradiation [START_REF] Zhu | A novel one-step chemical method for preparation of copper nanofluids[END_REF] and vacuum submerged arc nanoparticle synthesis system (SANSS) [START_REF] Lo | Shape-controlled synthesis of Cubased nanofluid using submerged arc nanoparticle synthesis system (SANSS)[END_REF] had been developed in recent decade. The advantages of sing-step method are minimal nanoparticle agglomerations and excellent stability, but only the liquids with low vapor pressure are appropriate for base fluid. The two-step method is more extensively applied in nanofluid preparation, which consists of nanoparticle synthesis and nanoparticle dispersion in base fluid. The industrialized nanopowder production simplifies the preparation process of nanofluid and makes large scale nanofluid synthesis become possible. Nanoparticles of pure metal [START_REF] Phuoc | Synthesis of Ag-deionized water nanofluids using multi-beam laser ablation in liquids[END_REF][START_REF] Kim | Characteristic stability of bare Au-water nanofluids fabricated by pulsed laser ablation in liquids[END_REF][START_REF] Kole | Thermal performance of screen mesh wick heat pipes using water-based copper nanofluids[END_REF], metal oxide [START_REF] Li | Experimental investigations on transport properties of magnetic fluids[END_REF][START_REF] Beck | The thermal conductivity of alumina nanoparticles dispersed in ethylene glycol[END_REF][START_REF] Longo | Experimental measurement of thermophysical properties of oxide-water nano-fluids down to ice-point[END_REF][START_REF] Kannadasan | Comparison of heat transfer and pressure drop in horizontal and vertical helically coiled heat exchanger with CuO/water based nano fluids[END_REF][START_REF] Kole | Thermophysical and pool boiling characteristics of ZnO-ethylene glycol nanofluids[END_REF] and carbon nanostructure [START_REF] Kim | A study on the characteristics of carbon nanofluids at the room temperature (25° C)[END_REF][START_REF] Meng | Carbon nanotube glycol nanofluids: photo-thermal properties, thermal conductivities and rheological behavior[END_REF][START_REF] Hajjar | Enhanced thermal conductivities of graphene oxide nanofluids[END_REF][START_REF] Mehrali | Experimental investigation of thermophysical properties, entropy generation and convective heat transfer for a nitrogen-doped graphene nanofluid in a laminar flow regime[END_REF] are successfully dispersed into base fluid with durable stability.

Compared to single-step method, two-step method has a wider application range but the limit is the aggregation of nanoparticles due to high surface-activity. Thus the improvement of stability is an indispensable problem in two-step nanofluid preparation.

Stability enhancement methods

Some physical techniques are used in preparing stable nanofluid, such as ultrasonic vibration, magnetic force agitation, high-shear mixing, bead milling etc. Yu et al. [START_REF] Yu | Investigation of thermal conductivity and viscosity of ethylene glycol based ZnO nanofluid[END_REF] prepared ZnO ethylene-glycol-based nanofluid in ultrasonic bath and they observed a rapid decreasing of average nanoparticle size during first 3h of ultrasonification with the ending of approximate 210 nm. During preparation of ZnO nanofluid, Moosavi et al [START_REF] Moosavi | Fabrication, characterization, and measurement of some physicochemical properties of ZnO nanofluids[END_REF] used magnetic stirring to homogenize nanoparticle suspension which shows excellent stability for several months. dried in an oven. After 60 min physical treatment combined of magnetic stirrer and ultrasonic vibrator, MWCNTs nanofluid stays stable for more than 24 hours. However, both surfactant and functionalization can lead to an increase in thermal resistance between solid surface of nanoparticles and liquid phase, which is opposite to the aim of heat transfer enhancement. The equilibrium between stability and thermal conductivity becomes an interesting subject in the application of nanofluids.

Applications

Nanofluids prepared by different combinations of nanoparticles and base fluids exhibit various characteristics such as extraordinary thermal conductivity, intensive mass transfer, efficient heat absorption, excellent lubrication, magnetic property, antibacterial and drugdelivery activities, and tunable optical property, which bring about an wide-ranging application in energy storage [START_REF] Liu | Experimental study of thermal conductivity and phase change performance of nanofluids PCMs[END_REF][START_REF] Wu | Preparation and melting/freezing characteristics of Cu/paraffin nanofluid as phase-change material (PCM)[END_REF][START_REF] Wu | Numerical simulation on thermal energy storage behavior of Cu/paraffin nanofluids PCMs[END_REF], solar technology [START_REF] Otanicar | Nanofluid-based direct absorption solar collector[END_REF][START_REF] Shin | Enhancement of specific heat capacity of hightemperature silica-nanofluids synthesized in alkali chloride salt eutectics for solar thermal-energy storage applications[END_REF][START_REF] Taylor | Applicability of nanofluids in high flux solar collectors[END_REF][START_REF] Gnanadason | Effect of nanofluids in a modified vacuum single basin solar still[END_REF], bubble absorption [START_REF] Kim | The effect of nano-particles on the bubble absorption performance in a binary nanofluid[END_REF][START_REF] Kim | Absorption performance enhancement by nano-particles and chemical surfactants in binary nanofluids[END_REF][START_REF] Ma | Heat and mass transfer enhancement of the bubble absorption for a binary nanofluid[END_REF][START_REF] Ma | Enhancement of bubble absorption process using a CNTs-ammonia binary nanofluid[END_REF], nanolubricants [START_REF] Zhou | Tribological behavior and lubricating mechanism of Cu nanoparticles in oil[END_REF][START_REF] Shen | Application of nanofluids in minimum quantity lubrication grinding[END_REF][START_REF] Yu | Tribological properties and lubricating mechanisms of Cu nanoparticles in lubricant[END_REF][START_REF] Yu | A novel lubricant additive based on carbon nanotubes for ionic liquids[END_REF], magnetic sealing [START_REF] Kim | Application of hydrophilic magnetic fluid to oil seal[END_REF][START_REF] Kim | Application of ferro-cobalt magnetic fluid for oil sealing[END_REF][START_REF] Mitamura | Application of a magnetic fluid seal to rotary blood pumps[END_REF], biomedicine [START_REF] Zhang | Investigation into the antibacterial behaviour of suspensions of ZnO nanoparticles (ZnO nanofluids)[END_REF][START_REF] Jones | Antibacterial activity of ZnO nanoparticle suspensions on a broad spectrum of microorganisms[END_REF][START_REF] Liu | Antibacterial activities of zinc oxide nanoparticles against Escherichia coli O157: H7[END_REF][START_REF] Ghosh | Gold nanoparticles in delivery applications[END_REF][START_REF] Singh | Nanoparticle-based targeted drug delivery[END_REF][START_REF] Tripisciano | Single-wall carbon nanotubes based anticancer drug delivery system[END_REF], and optical filters [START_REF] Philip | A tunable optical filter[END_REF][START_REF] Mishra | Optical properties in nanofluids of gold nanoparticles in poly (vinylpyrrolidone)[END_REF]. The most important application base on exceptional thermal conductivity is for improving heat transfer efficiency including micro-electronic cooling [START_REF] Nguyen | Heat Transfer Enhancement by Using Al203-Water Nanofluid in a Liquid Cooling System for Microprocessors[END_REF][START_REF] Ma | Effect of nanofluid on the heat transport capability in an oscillating heat pipe[END_REF][START_REF] Shokouhmand | Performance analysis of using nanofluids in microchannel heat sink in different flow regimes and its simulation using artificial neural network[END_REF], fuel combustion [START_REF] Kao | Aqueous aluminum nanofluid combustion in diesel fuel[END_REF][START_REF] Gan | Combustion of nanofluid fuels with the addition of boron and iron particles at dilute and dense concentrations[END_REF][START_REF] Sabet Sarvestany | Effects of magnetic nanofluid fuel combustion on the performance and emission characteristics[END_REF][START_REF] Shaafi | Influence of alumina nanoparticles, ethanol and isopropanol blend as additive with diesel-soybean biodiesel blend fuel: combustion, engine performance and emissions[END_REF], industrial boiling [START_REF] Wen | Experimental investigation into the pool boiling heat transfer of aqueous based γ-alumina nanofluids[END_REF][START_REF] Liu | Boiling heat transfer characteristics of nanofluids in a flat heat pipe evaporator with micro-grooved heating surface[END_REF][START_REF] Kim | Experimental study of the characteristics and mechanism of pool boiling CHF enhancement using nanofluids[END_REF] and cooling [START_REF] Han | Synthesis and thermal characterization of phase-changeable indium/polyalphaolefin nanofluids[END_REF][START_REF] Nelson | Flow loop experiments using polyalphaolefin nanofluids[END_REF], nuclear reactor cooling [START_REF] Buongiorno | Nanofluids for enhanced economics and safety of nuclear reactors: an evaluation of the potential features, issues, and research gaps[END_REF][START_REF] Hadad | Numerical study of single and two-phase models of water/Al 2 O 3 nanofluid turbulent forced convection flow in VVER-1000 nuclear reactor[END_REF][START_REF] Sharma | Numerical investigation of heat transfer characteristics in triangular channel in light water nuclear reactor by using CuO-water based nanofluids[END_REF], and building heating system [START_REF] Park | Boiling heat transfer enhancement with carbon nanotubes for refrigerants used in building air-conditioning[END_REF][START_REF] Kulkarni | Application of nanofluids in heating buildings and reducing pollution[END_REF]. Bigerelle supported the author of this thesis for the writing of the manuscript and gave approval to the final version.

Conclusions

Abstract

Deposited on the hydrophobic silicon, the evaporation of droplets of three pure liquids (water, 1-butanol and ethanol) and four binary solutions (5 wt.% 1-butanol water-based solution and 5 wt.%, 25 wt.% and 50 wt.% ethanol water-based solutions) were investigated. A drop shape analyzer was used to measure the contact angle, diameter and volume of droplets. At the same time, an infrared camera was utilized for the infrared thermal mapping of droplet's surface. An acoustic high frequency echography technique was, for the first time, applied to track the alcohol concentration in a binary solution droplet. The evaporations of pure alcohol droplets were executed at different values of the relative humidity, among which the behavior of pure ethanol evaporation was notably influenced by the ambient humidity as a result of high hygrometry. The evaporations of droplets of water and binary solutions were performed at a temperature of 22°C and a mean humidity of approximately 50%. The times when the alcohol exhausts in the droplets estimated by the acoustic method and the visual method were similar for water-1-butanol mixture; however, the time estimated by the acoustic method is longer compared to visual method for water-ethanol mixture due to the residual ethanol at the bottom of the droplet.

Introduction

In recent decades, many experimental [START_REF] Deegan | Contact line deposits in an evaporating drop[END_REF][START_REF] Ristenpart | Influence of substrate conductivity on circulation reversal in evaporating drops[END_REF][START_REF] Kelly-Zion | Evaporation of sessile drops under combined diffusion and natural convection[END_REF][START_REF] Nguyen | Theoretical and experimental analysis of droplet evaporation on solid surfaces[END_REF][START_REF] Carle | Experimental evidence of the atmospheric convective transport contribution to sessile droplet evaporation[END_REF][START_REF] Gatapova | Evaporation of a sessile water drop on a heated surface with controlled wettability[END_REF] and theoretical studies [START_REF] Nguyen | Theoretical and experimental analysis of droplet evaporation on solid surfaces[END_REF][START_REF] Picknett | The evaporation of sessile or pendant drops in still air[END_REF][START_REF] Kneer | Diffusion controlled evaporation of a multicomponent droplet: theoretical studies on the importance of variable liquid properties[END_REF][START_REF] Erbil | Evaporation of sessile drops on polymer surfaces: Ellipsoidal cap geometry[END_REF][START_REF] Masoud | Analytical solution for inviscid flow inside an evaporating sessile drop[END_REF][START_REF] Sefiane | An expression for droplet evaporation incorporating thermal effects[END_REF] have investigated the process of evaporation of drops, which has a wide range of applications, e.g., ink-jet printing [START_REF] Kawase | Inkjet printed via-hole interconnections and resistors for all-polymer transistor circuits[END_REF][START_REF] De Gans | Inkjet printing of polymers: state of the art and future developments[END_REF], DNA mapping [START_REF] Wang | Scanning force microscopy of DNA molecules elongated by convective fluid flow in an evaporating droplet[END_REF][START_REF] Chopra | DNA molecular configurations in an evaporating droplet near a glass surface[END_REF], combustion engineering [START_REF] Saito | Evaporation and combustion of a single fuel droplet in acoustic fields[END_REF][START_REF] Park | Evaporation-combustion affected by incylinder, reciprocating porous regenerator[END_REF], and cooling system [START_REF] Wu | Study of self-rewetting fluid applied to loop heat pipe[END_REF][START_REF] Su | Enhancement of heat transport in oscillating heat pipe with ternary fluid[END_REF]. With optical and infrared techniques, the measurement of the parameters of a droplet (contact angle, base radius and height) can contribute to full understanding of the evaporation process. Moreover the dynamic evaporation of a binary mixture drop which can contain both of constant contact angle regime and constant contact radius regime is more complicated.

At ambient conditions, the evaporation process of the water-ethanol mixture drops was divided in three stages: the first stage conforms to the behavior of the pure volatile component evaporation; at the last stage, the drop evaporates in accordance with the less volatile component; and between the aforementioned stages, there is an intermediate (transitional) stage, where the contact angle clearly increases with nearly constant volume Chapter 3 Alcohol Concentration Tracking of Binary Sessile Droplets during Evaporation [START_REF] Sefiane | Experimental study of evaporating water-ethanol mixture sessile drop: influence of concentration[END_REF]. Christy et al. [START_REF] Christy | Flow transition within an evaporating binary mixture sessile drop[END_REF] also showed that the evaporating of water-ethanol mixture sessile drop went through three distinct stages when they studied the interior flow in droplet with PIV technology: 1. chaotic regime, dominated by multiple vortices driven by concentration differences as a result of the preferential evaporation of ethanol; 2.

transition regime, characterized by an exponential decay of vortices with the migration of the remaining vortices toward the drop periphery and a spike of the radial velocity along the drop base; 3. the third stage, characterized by the evaporation driving outward flow to the contact line, acting exactly the same as pure water drops. During the evaporation process of water-ethanol mixture, O'Hare and Spedding [START_REF] O'hare | Evaporation of a binary liquid mixture[END_REF] found that the evaporation rate of water component maintained a nearly constant value, despite the continuous decrease of the actual ethanol concentration. Furthermore, Liu et al. [START_REF] Liu | Evaporation of sessile water/ethanol drops in a controlled environment[END_REF] discovered that the evaporation behavior of water-ethanol mixture drop can be more complex: ethanol did not finish thoroughly at the end of transitional stage; rather, until the end of evaporation, a part of the residual ethanol still remained in the drop. The condensation of water vapor appeared as the mixture drop began to evaporate at high ratio of ethanol in the drop and high vapor pressure of water in the background gas.

Despite the numerous research studies performed on the evaporation of water-based binary alcohols solutions, there is still a lack of understanding of the evolution of alcohols concentration during evaporation. In this study, the dynamic evaporation of sessile drops of three pure liquids (water, 1-butanol and ethanol), as well as water-1butanol and water-ethanol mixtures, was investigated using a complementary original dual-track approach combining optical and infrared techniques on one hand and acoustics on the other hand. While the optical and infrared techniques provide macroscopic

Chapter 3 Alcohol Concentration Tracking of Binary Sessile Droplets during Evaporation information of the phenomenon at the drop surface, the use of acoustics gives access to local interface exchange mechanisms at the bottom of the drop.

An acoustical method has been developed in our laboratory for characterizing solid/ liquid interfaces at micro/nanometers scales. First, the focus was on the wetting of droplets of various surface tensions on hydrophobized textured structures [START_REF] Saad | Characterization of the state of a droplet on a micro-textured silicon wafer using ultrasound[END_REF]. The surface tension threshold of the droplet was correlated to the observation of the transition from Cassie-Baxter to Wenzel state. Another targeted application was the determination of cleaning efficiency in the nanoelectronics fabrication process. Not only did the ultrasonic technique in the tracking of Cassie -Wenzel transition on microstructures during the evaporation process of a droplet on a microstructured surface [START_REF] Dufour | Acoustic tracking of Cassie to Wenzel wetting transitions[END_REF][START_REF] Carlier | High frequency acoustic reflectometry for solid/liquid interface characterization: application to droplet evaporation[END_REF] but also in nanostructures wetting characterization on periodic surfaces [START_REF] Li | High-frequency acoustic for nanostructure wetting characterization[END_REF].

In the case of binary drop evaporation, the alcohol concentration tracking, which is the main interest of ultrasound techniques, is due to the high contrast of mechanical impedances between certain alcohols, such as 1-butanol and ethanol, trapped at the interfaces and liquids. Moreover, ultrasound techniques do not require any optical transparency. This sensitivity enables the monitoring of the evaporation kinetics of droplets of some water/alcohol mixtures at a plane of solid/liquid interface by the tracking of the concentration evolution at the interface between the droplet and the support. Depending on the binary alcohol concentration of the drop, the mechanical impedance of the liquid and the acoustic reflection coefficient will be modified. Due to a pre-established calibration curve of the reflection coefficient which depends on the alcohol concentration of droplet, it is possible to determine the concentration of alcohol on line at the interface by the acoustic reflection coefficient measurement.

Experimental Setup

Two separate devices are used, one for optical and infrared measurements, and the other for acoustic reflection coefficient measurement. In both cases, the droplets are left evaporating on the hydrophobized (100) silicon substrate treated with PFTS (PerFluorodecylTrichloroSilane). Measurements are made at a temperature of 22 °C and a mean humidity of approximately 50%. Moreover, the influence of humidity, namely 20%, 50% and 56%, on infrared and optical measurements is considered for the case of pure alcohol's evaporation.

Optical and infrared measurements

The substrates are placed in a vapor chamber (14 cm × 12.4 cm × 7.5 cm), in which the ambient temperature and the relative humidity can be controlled (Fig. 3.1 (a)). Air inside the chamber is at rest. The top of the vapor chamber has a sapphire window for the infrared camera and a hole for passing the syringe. The infrared camera (FLIR X6580SC, 640×512 pixels, 15µm detector pitch) is installed on top to be used for infrared thermal mapping and visualization of thermal instabilities on the surface of the droplets. The exploitation of dynamic infrared videos provides a good visualization of alcohol cells' motion on the droplet surface and consequently the alcohol life time during evaporation as water and alcohol have different emissivities. A Kruss® Drop Shape Analyzer is used to measure the contact angle, volume, diameter and height of sessile droplets during evaporation. A side view CCD camera (Allied Vision Technologies, 780×580 pixels) is used to record the evaporation process of the droplets for profile analysis.

Acoustic measurements

Measurements are made under controlled atmosphere thanks to an air-conditioning system. A prober system Cascade PM8 is used to control at the micro-scale the position of the S/G (Signal/Ground) probe on a piezoelectric transducer as small as 50 µm in diameter to achieve the electrical measurements (Fig. S 11 ac parameter results from the superposition of the acoustic waves generated from all the reflected waves at the interface.

An inverse Fourier Transform applied on the S 11 (f) signal makes it possible to separate the acoustic contribution from the electric one. These two signal contributions are separated by a delay corresponding to the propagation in the substrate. The signal, in the time domain, windowed on the useful echo corresponding to the first reflected echo is then processed to determine the reflection coefficient.

From a theoretical point of view, a plane of the acoustic wave propagating at normal incidence at an interface separates two media of acoustic impedances Z 1 and Z 2 ; the absolute value of the reflection coefficient R in amplitude can be calculated using the following equation:

|R| = Z 2 -Z 1 Z 1 +Z 2 (3.2)
𝑍𝑍 = 𝜌𝜌𝜌𝜌 , 𝜌𝜌 is the density of the medium and 𝜌𝜌 is the acoustic velocity of the wave propagating inside the medium. In our case, Z 1 is the acoustic impedance of the liquid, whereas Z 2 is that of the (100) silicon substrate. An online assessment of the evaporation kinetics of droplet is feasible due to the measurement of this reflection coefficient.

The width of the acoustical pulse is 5 ns. It corresponds to five times the period of the working frequency of 1GHz. Since the wavelength λ l in water is about 1.5 µm, one can consider that the wave propagates over a distance of 5 times the wavelength λ l in the Chapter 3 Alcohol Concentration Tracking of Binary Sessile Droplets during Evaporation liquid, namely 7.5 µm. Beyond this thickness, the acoustic wave undergoes a strong attenuation. Since we process droplets of 1 µL, the corresponding diameter and height are about 1.5 mm each. The information gathered is then limited to a few micrometers inside the drop at the bottom.

Experimental Results

Calibration of the acoustic measurement method

For calibrating our acoustic device, water is used as a reference liquid. The acoustic reflection coefficient is calculated from the values of the density, and the acoustic velocity of both silicon and water found in the literature. Several precautions are taken to improve the accuracy of the measurements. Temporal drifts are minimized by the use of 2 identical transducers, one for reference to air, and the other for measurement at silicon/liquid interface. Reference to air is first measured on each case. The adjustment factor |𝑅𝑅| 𝑎𝑎 is equal to the ratio of the peak amplitudes A22 and A11, which are the reflection coefficients measured with each probe on each transducer.

|R| c = � A 22 A 11 � air (3.3)
The standardized reflection coefficient, R norm at the solution (sol) / silicon interface is then deduced as:

|R| norm = � A 22 A 11 � sol � A 22 A 11 � air (3.4)
A drop of water of approximately 1 µL is deposited on the surface of the planar (100)

Chapter 3 Alcohol Concentration Tracking of Binary Sessile Droplets during Evaporation silicon substrate. According to Eq. 3.2, the reflection coefficient at silicon/water interface is deduced to be 0.8595. Reliability can be assessed according to the stability and the accuracy of the measurement compared to the theoretical value; it was determined to be 0.02%.

The physical properties of the pure liquids and their studied mixtures as well as the ( 100)

silicon substrate at a temperature of 22°C are reported on Tab. 3.1. ρ is the density, γ the surface tension, P sat the saturation vapor pressure and c the acoustic velocity. The volatility is measured through the saturation vapor pressure P sat . The higher the value of P sat , the more volatile the liquid is. Note that P sat is given for large volumes of liquid.

ρ (kg•m -3 ) γ(mN•m -1 ) P sat (kPa) c (m.s -1 ) Water 998 72.80 2.65 1488.319 [119] (100) Silicon 2330 8433.8 [120] 1-Butanol 809 24.67 0.

Evaporation of drops of pure liquids

The immediate attention was focused on pure liquids, namely pure butanol and pure ethanol. The relative humidity of 20% and 56% are the minimal and maximal value, respectively, that the vapor chamber can attain; moreover, 50% was chosen as a mean relative humidity. Acoustic measurements were made in a surrounding humidity of approximately 50%.

Pure butanol (a) Optical and infrared investigation

For each liquid, we measured the contact angle, the diameter and the volume of droplets versus time and deduced V 2/3 . All of experiments were repeated five times to guarantee a good repeatability. The plots of contact angle and V 2/3 versus time are presented in Fig.

3.2.

The evaporation of pure 1-butanol drops can be divided in two stages: initially, the stage of constant contact radius where contact angle decreased slightly, followed by the stage of constant contact angle during most time of evaporation. The different values of the relative humidity used had no obvious effect on the evaporation of pure 1-butanol drops.

For a spherical cap drop, the evaporation rate [START_REF] Erbil | Drop evaporation on solid surfaces: constant contact angle mode[END_REF] can be given by Eq. 3.5:

-� 𝑑𝑑𝑉𝑉 𝑑𝑑𝑡𝑡 � = 4𝜋𝜋𝜋𝜋 𝜌𝜌 𝐿𝐿 � 3𝑉𝑉 𝜋𝜋𝜋𝜋 � 1/3 (𝐶𝐶 𝑠𝑠 -𝐶𝐶 ∞ )𝑓𝑓(𝜃𝜃) = 𝐾𝐾𝑉𝑉 1/3 𝑓𝑓(𝜃𝜃) (3.5)
where

𝐾𝐾 = 4𝜋𝜋 2∕3 3 1∕3 𝜋𝜋(𝐶𝐶 𝑠𝑠 -𝐶𝐶 ∞ ) 𝜌𝜌 𝐿𝐿 𝜋𝜋 1∕3 𝛽𝛽 = 2 -3 cos 𝜃𝜃 + cos 3 𝜃𝜃
and 𝑉𝑉 is the volume of the spherical cap drop, 𝐷𝐷 is the diffusion coefficient of vapor in air, 𝜌𝜌 𝐿𝐿 is the liquid density of drop, 𝐶𝐶 𝑠𝑠 and 𝐶𝐶 ∞ are the vapor concentrations close to the drop surface and far from drop respectively, 𝜃𝜃 is the contact angle, 𝑓𝑓(𝜃𝜃) is the function of contact angle of the spherical cap given by the model of Picknett and Bexon

[100]: & 1 ( ) ( ) 2 Picknett Bexon s C f R θ = (3.6) For10 180 θ ≤ <   , 2 3 4
0.00008957 0.6333 0.116 0.08878 0.01033

s C R θ θ θ θ = + + - + (3.7)
Assuming that the diffusion of vapor molecules in air is steady and the contact angle remains constant during evaporation, Eq. 5 can be integrated between initial volume V 0 (t → 0) and V t (t → t):

𝑉𝑉 𝑡𝑡 2∕3 = 𝑉𝑉 0 2∕3 - 2 3 𝐾𝐾𝑓𝑓(𝜃𝜃)𝑡𝑡 (3.8)
The plots of V 2/3 versus time, as shown in According to Stefan-Boltzmann law, the radiant exitance of a grey body j is determined:

4 j T εσ = (3.9)
where σ is Stefan-Boltzmann constant, ε and T are emissivity and temperature of substance respectively. The scale in infrared thermal mapping represents the level of thermal radiation "I" received by infrared camera. The "I" level is proportional to the radiant "j". The Different colors correlate with different temperatures or different emissivities related to different substances. Water and alcohol in mixture droplet have the same temperature but the emissivity of water is higher than that of alcohol. Consequently there is a color contrast between water and alcohol that is visualized under infrared Chapter 3 Alcohol Concentration Tracking of Binary Sessile Droplets during Evaporation camera. The normal temperature profile of a single substance droplet is that the coolest at the apex of droplet and the warmest at the contact line, then temperature varies from apex to contact line gradually. According to these infrared images in Fig. 3.3, the color consistency at the surface until the end of evaporation indicates that the temperature of droplet surface was almost homogeneous and there is no second liquid present in droplet.

Moreover, the phenomenon was similar under different relative humidity conditions. These results confirm the investigation of Seaver et al. [START_REF] Seaver | Water Condensation onto an Evaporating Drop of 1-Butanol[END_REF], who showed the very low hygroscopic power of a drop of 1-butanol during evaporation.

Pure ethanol

(a) Optical and infrared investigation Fig. 3.4 represents the evolutions of contact angle and V 2/3 of pure ethanol droplets versus time. For these three relative humidity situations, the evaporation of pure ethanol droplet went through constant contact radius regime and then constant contact angle regime at the beginning, which is similar with the evaporation of pure butanol droplet. For the case of 20% RH, the contact angle increased slightly and then decreased until the end of evaporation after first two stages. However, for the cases of higher relative humidity, the contact angle rose rapidly to a maximal value. In particular, the case of 56% RH had a transition stage before the rapid rise where the contact angle and the diameter both decreased, and the maximal value (88°) was close to the contact angle of pure water droplet (107°). According to Young's Equation:

cos 𝜃𝜃 = 𝛾𝛾 𝑆𝑆𝑆𝑆 -𝛾𝛾 𝑆𝑆𝐿𝐿 𝛾𝛾 𝐿𝐿𝑆𝑆 (3.10)
where 𝛾𝛾 𝑆𝑆𝑆𝑆 , 𝛾𝛾 𝑆𝑆𝐿𝐿 and 𝛾𝛾 𝐿𝐿𝑆𝑆 are solid/vapor, solid/liquid and liquid/vapor interfacial tension respectively. Owing to the high hygroscopic nature of pure ethanol, water vapor condenses on the surface of pure ethanol droplet during evaporation. The liquid/vapor interfacial tension increases with the increase of water/ethanol ratio of droplet at contact line which leads to the raise of contact angle (Eq. 3.10). The condensation rate of water depends on the water vapor pressure of surrounding environment. Thus, the relative humidity can notably change the behavior of pure ethanol droplets' evaporation. The evaporation time of a drop at 56% RH was nearly triple as that of a drop at 20% RH because the drop absorbed more water, which has a diffusion coefficient in the air much less than that of ethanol. In addition, the plot of V 2/3 can be obviously divided in two stages with different slope for higher relative humidity: initial steep stage when only ethanol evaporated, then gentle stage when contact angle reached the maximum, until the end and during which water mainly evaporated. We can conclude that pure ethanol droplet absorbs a non-negligible quantity of water during evaporation at 50% and 56%

relative humidity, which has a significant effect on the evaporation of pure ethanol droplet. Contrary to pure 1-butanol, the infrared thermal mapping using the infrared camera reveals heterogeneous zones during the evaporation process of a drop of pure ethanol. ethanol was present on the drop's surface, and no convection cells were found. By reducing the relative humidity to 50% and to 20%, the phenomena observed were similar and the only difference is that the convection cells were weakened and less visible. Thus, the environmental relative humidity can significantly affect the evaporation of pure ethanol droplet which absorbs water as soon as it is exposed in the air. To the best of our knowledge, there is no reference in the literature regarding the evaporation of a sessile droplet of pure ethanol. The findings presented here constitute an original result, showing that the water vapor from the ambient humidity condenses onto the droplets of pure ethanol during evaporation, and then the solution becomes a mixture of water and ethanol.

Evaporation of drops of binary solutions

In the following experiments, the droplets of pure water and binary solutions were tested at a temperature of 22°C and a hygrometry of approximately 50% with the volume of 1 μL. For the water-1-butanol mixture, the result was compared with those of pure water on the kinetics of contact angle and the plot of V 2/3 . Fig. 3.7 represents the evolutions of contact angle and V 2/3 for droplets of pure water and 5% mass concentration water-1-butanol mixture. In spite of the slight decrease at the beginning, which is due to evaporation, the contact angle of pure water drop remained constant during most of the evaporation process and decreased abruptly at the end. Different from that of pure water, the contact angle of water-1-butanol mixture initially decreased and then increased until the maximal value before decreasing abruptly at the end of drop life. The plot of V 2/3 of water droplet is linear while that of water-1-butanol mixture has a slight deviation at the beginning due to the evaporation of 1-butanol. Even though the diffusion coefficient of water vapor in air (0.282 cm 2 /s) is much higher than that of 1-butanol vapor (0.08 cm 2 /s), the ratio of evaporation rate is still lower than the water/1-butanol component ratio. Therefore the concentration of 1-butanol near the air/liquid interface decreased which created a concentration gradient between surface and bulk. For replenishing the part evaporated on the surface, the 1-butanol inside the drop flowed outward to generate the convection cells. Because the limit of solubility of 1-butanol is reached for a mass concentration of approximately 7.3%, the upper limit is fixed here at C m = 7%. Fig. 3.9 is the result of the average of a series of 3 measurements performed under the same conditions. The dispersion is in the range of 0.03%.

Comparison between acoustics and infrared observations

Acoustics provides information on the manner by which alcohol is exhausted from the bottom of the drop, whereas infrared observation is related with the disappearance of alcohol from the surface of the drop. The necessary time for alcohol to exhaust from the bottom and from the surface of the drop is reported on Tab. 3.3. The times estimated by two methods are comparable in the case of the 1-butanol with a mass concentration of 5%. However this is not the same consequence for any ethanol concentration. The possible explainable reason is the difference of volatility between ethanol and 1-butanol. At the beginning, the contact angle of water-ethanol mixture droplet decreased because of evaporation until the contact angle reached the receding angle of mixture solution. Then the contact line began to retract and the thermodynamic equilibrium of three interfaces was broken. Due to high volatility, ethanol evaporates faster than water which leads to the decrease of ethanol concentration on the air/liquid interface and the increase of surface tension of droplet from the beginning. Hence the contact angle increased since the disequilibrium of three interfaces. The ethanol concentration gradient was created between surface and interior of droplet which is the origin of convective flow. Therefore the ethanol evaporated on surface was replenished by convective flow, which generated the convection cells observed under infrared camera, and diffusion of ethanol molecules. When the total ethanol concentration became so weak as well as concentration gradient that the convective flow couldn't be engendered, the evaporation of ethanol on droplet's surface was controlled by its diffusion in droplet. It is because that the ethanol molecules need time to diffuse from the bottom to the surface of droplet and the diffusion coefficient of ethanol molecules in water (1.22 × 10 -9 m 2 /s) is much lower than in air (1.15 × 10 -5 m 2 /s). Thus, the ethanol/water ratio stayed in a very low value on the surface of droplet which couldn't be distinguished by infrared camera, and the contact angle stayed constant. The evaporation process is similar for the cases of 25 wt.% and 50 wt.% ethanol concentration, except for the case of 5 wt.% whose ethanol concentration on droplet surface is so tiny that it decreased quickly and the evaporation of ethanol was mostly controlled by diffusion in droplet. However, during the evaporation controlled by diffusion in droplet, there was still a certain quantity of ethanol in droplet which could be detected by acoustic method.

That's the reason for the large difference of exhaustion time of ethanol in droplet estimated between visual method and acoustic method. For the case of 5 wt.% water-1butanol mixture, even the same concentration as 5 wt.% water-ethanol mixture, the droplet had the same evaporation process as that of 25 wt.% and 50 wt.% water-ethanol mixture. Owing to low evaporation rate of butanol, the decrease of 1-butanol/water ratio on droplet surface was much slower than that of water-ethanol mixture which can be demonstrated by the smooth increasing curvature of contact angle during the second stage. Thence, the concentration gradient remained much longer and the convective flows were generated continuously which was distinct under infrared camera. Even though the convective flows became weak, the supply of diffusion (0.93 × 10 -9 m 2 /s) in droplet maintained the 1-butanol/water ratio on surface at a certain value, which could be detected by infrared camera, due to low evaporation rate of 1-butanol. Consequently, the exhaustion times of 1-butanol in droplet estimated by both methods are close. Because the exhaustion of 1-butanol begins from the bottom of droplet on account of diffusion, the exhaustion time estimated by acoustic method is shorter than visual method.

However, at the same concentration, the exhaustion times of alcohol estimated by acoustic method for water-ethanol and water-1-butanol mixture are very close which implies that the alcohol molecules diffusion is dominant during evaporation and with or without convection, there is no effect on the evaporation of alcohol in a mixture droplet.

Conclusions

For the first time, the acoustic method was applied for tracking the alcohol concentration in a bottom of a droplet of binary solution during evaporation. Using the pre-established acoustic reflection coefficient as a function of mass concentration, the alcohol concentration kinetics can be monitored versus time. From infrared images, the color distribution resulting from temperature and emissivity gradients is correlated to the existence of alcohol on the drop surface.

No ambient humidity influence is observed on the behavior of the contact angle and V 2/3 of a drop of pure 1-butanol during evaporation. In addition, the temperature at the surface remains constant and the acoustic reflection coefficient also remained constant during the process, i.e., no change of 1-butanol concentration occurred. These results confirm the very low hygroscopic power of a drop of 1-butanol during evaporation.

Due to the high hygroscopic nature of ethanol, the evaporation of a drop of pure ethanol is largely impacted by the relative humidity. Because of the absorption of water, the ethanol droplet became water-ethanol mixture and the convection cells appeared from the beginning. The kinetics of the acoustic reflection coefficient results in a decreasing trend of the ethanol concentration until reaching the acoustic reflection coefficient of water.

These results showed that water vapor coming from ambient humidity condensed onto the droplets of pure ethanol during evaporation and the solution becomes a mixture of water and ethanol. As a consequence of high volatility, firstly the ethanol evaporated and exhausted, and then the absorbed water continued to evaporate through the end.

The exhaustion time of ethanol in drop estimated by acoustic method is always much shorter than visual method at three different ethanol concentration. However, for the case of water-butanol mixture, both methods have the same result. This can be probably explained by the difference water/alcohol ration on drop surface due to different volatility between ethanol and butanol.

Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets

This chapter is based on the published work in The Journal of Physical Chemistry B in 2017 [START_REF] Chen | Marangoni Flow Induced Evaporation Enhancement on Binary Sessile Drops[END_REF]. The author of this thesis contributed to the designing and performing experiments, analyzing experimental results and writing manuscript. J. Schiffler codesigned this experiment and took in charge of experimental devices examination. S.

Ouenzerfi measured the surface tension of 1-butanol-water binary solution with different alcohol concentration as a function of temperature. Prof. S. Harmand supported the author of this thesis for the writing of the manuscript and gave approval to the final version.

Abstract

The evaporation processes of pure water, pure 1-butanol, and 5% 1-butanol aqueous solution drops on heated hydrophobic substrates are investigated to determine the effect of temperature on the drop evaporation behavior. The evolution of the parameters (contact angle, diameter, and volume) during evaporation measured using a drop shape analyzer and the infrared thermal mapping of the drop surface recorded by an infrared camera were used in investigating the evaporation process. The pure 1-butanol drop does not show any thermal instability at different substrate temperatures, while the convection

Introduction

As a natural phenomenon, drop evaporation has become an important topic in recent decades, attracting interest in many scientific applications such as coatings [126], ink printing [START_REF] Wang | Scanning force microscopy of DNA molecules elongated by convective fluid flow in an evaporating droplet[END_REF][START_REF] Park | Control of colloidal particle deposit patterns within picoliter droplets ejected by ink-jet printing[END_REF], and cooling systems [START_REF] O'hare | Evaporation of a binary liquid mixture[END_REF]. Numerous experimental [START_REF] Nguyen | Theoretical and experimental analysis of droplet evaporation on solid surfaces[END_REF][START_REF] Carle | Experimental evidence of the atmospheric convective transport contribution to sessile droplet evaporation[END_REF][START_REF] Vatandas | Ultrasonic velocity measurements in ethanol-water and methanol-water mixtures[END_REF][START_REF] Bennacer | Vortices, dissipation and flow transition in volatile binary drops[END_REF][START_REF] Shi | Wetting and evaporation behaviors of water-ethanol sessile drops on PTFE surfaces[END_REF], analytical [START_REF] Carle | Experimental evidence of the atmospheric convective transport contribution to sessile droplet evaporation[END_REF][START_REF] Sefiane | An expression for droplet evaporation incorporating thermal effects[END_REF][START_REF] Kawase | Inkjet printed via-hole interconnections and resistors for all-polymer transistor circuits[END_REF][START_REF] Bormashenko | Young, Boruvka-Neumann, Wenzel and Cassie-Baxter equations as the transversality conditions for the variational problem of wetting[END_REF], and numerical [START_REF] Korlie | Three-dimensional computer simulation of liquid drop evaporation[END_REF][START_REF] Widjaja | Numerical study of vapor phase-diffusion driven sessile drop evaporation[END_REF][START_REF] Barash | Evaporation and fluid dynamics of a sessile drop of capillary size[END_REF] methods have been employed to investigate the evaporation process of sessile drops at ambient conditions, the behavior of which can be classified in three regimes: constant contact angle regime, constant contact radius regime, and a combination of both regimes. (performed with parabolic flights) to validate the effect of the buoyant natural convection transport on the vapor phase in the evaporation process. Under terrestrial gravity conditions, the diffusive model value was close to the experimental value, but as the substrate was heated, the diffusive model underpredicts the evaporation rate and the deviation increased with the substrate temperature. However, under reduced gravity conditions, the diffusion-controlled evaporation model correctly predicted the experimental data. They supposed that the natural convection in the vapor phase enhanced the evaporation rate and derived an expression for the evaporation rate that took into account the diffusive and naturally convective vapor transport. By applying this model, a satisfactory estimation of the experiments was obtained when the substrate was heated: the deviation was less than 7%. However, at ambient temperature, this model overestimated the evaporation rate by 20%.

The purpose of this study is to investigate the effect of the substrate temperature on the evaporation of pure solution and binary mixture drops and also to compare the evaporation behavior between these two types of drops. When a pure solution drop is deposited on a heated substrate, the temperature at the bottom of the drop is close to that of the substrate while the temperature at the top of the drop is similar to the ambient temperature. When the temperature difference as well as the surface tension difference between the top and the periphery of the drop becomes suitably large, the liquid will flow from the low surface tension place to the high surface tension place on the drop surface. This is called the thermal Marangoni flow. The surface tension difference can be also created by non-uniformity in composition and the generated flow in this case is termed as Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets the solutal Marangoni flow. The effect of surface tension gradient-driven flow is the Marangoni effect, named after the Italian physicist Carlo Marangoni, who found this phenomenon when studying the spreading of oil on water surface [START_REF] Marangoni | Sull'espansione delle goccie d'un liquido galleggianti sulla superfice di altro liquido[END_REF]. Therefore, another objective of this study is to determine the relation between the substrate temperature and the Marangoni effect as well as their influence on the evaporation rate.

Experimental Setup

The substrates are placed in a vapor chamber (14 cm × 12.4 cm × 7.5 cm), in which the ambient temperature and relative humidity can be controlled (Fig.

Experimental Results and Discussion

In this study, the evaporation of three different drops, namely pure water, pure 1-butanol, and 5% 1-butanol aqueous solution on hydrophobic silicone substrates was investigated.

The addition of 1-butanol is for verifying the enhancement of evaporation by the solutal Marangoni flow. Water is one of the common working fluids applied in heat pipes and 1butanol aqueous solution is a novel one for wickless heat pipes. The experiments were conducted in six different substrate temperatures from T s = 22 to 80°C to investigate the influence of temperature. In addition, the ambient temperature in the vapor chamber was The substrate temperature has no obvious effect on the overall evolution of the contact angle and diameter versus time for both liquids. For the pure water drop, the contact angle stays almost constant or decreases at a slow rate during the most part of evaporation and diminishes sharply at the end. However, the drop of 1-butanol aqueous solution possesses a different behavior with respect to the contact angle and diameter in the course of evaporation. The evolution of contact angle can be divided into four stages.

First, the contact angle decreases, and then increases until the maximum value, which is very close to that of the water drop. Afterward, the contact angle decreases slowly and diminishes abruptly at the end of evaporation, which is similar to that of pure water.

Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets

Owing to its lower density, 1-butanol tends to accumulate at the liquid/air interface after deposition of the drop. Thus, the diffusion of vicinal 1-butanol molecule to liquid/air interface leads to an increase in the ratio of 1-butanol/water, which is the reason why the contact angle decreases at the beginning of evaporation of the 1-butanol aqueous solution drop. Then, the evaporation rate of the liquid depends on the difference of its vapor concentration at the liquid/air interface and in ambient environment at infinite distance.

However, in this experiment, the 1-butanol vapor concentration in the air is zero while the relative humidity of water vapor is 50%. That is why 1-butanol evaporates faster than water. Consequently, at the second stage, the ratio of 1-butanol/water at the liquid/air interface starts to decrease and the contact angle begins to increase accordingly. At the last two stages, the 1-butanol in the drop is almost depleted because of preferential evaporation and then the drops of both liquids have the same behavior in regard to the contact angle.

Regarding the temperature profile on the drop surface, the lowest temperature is found at the top and the highest temperature is situated at the contact line. The temperature difference between the top and the contact line is the source of the thermal Marangoni flow. In Fig. 4.3, no thermal instability can be detected during evaporation of the 1butanol drops at different substrate temperatures. However, at higher substrate temperatures, a ring-like thermal pattern appears near the contact line and becomes more evident with the increase of substrate temperature. first, the convection cells are irregular, chaotic, and cover the total surface of the drop;

then, these small cells disappear gradually and two big ones appear which are similar to those observed for the water drop at higher substrate temperatures. At the end of evaporation, both convection cells disappear and the temperature is almost homogenous on the drop surface. By comparing the infrared images of the evaporation process between pure water (Fig. 4.6) and 1-butanol aqueous solution drops (Fig. 4.5) at the same conditions, the small random convection cells can be deduced to be generated by the solutal Marangoni effect, while the big stable ones are formed by the thermal Marangoni effect. The disappearance of the small convection cells means that there is no large alcohol concentration difference on the drop surface. Thus, the moment when the small convection cells disappear can be determined as the moment t f when 1-butanol is nearly depleted in the drop, which is marked in Fig. 4.2. As shown in this figure, at t f , the contact angle of 1-butanol aqueous solution drop is close to the maximum value, which signifies that the ratio of 1-butanol/water at the liquid/air interface is very low and can be assumed as zero. This confirms the determination of t f . Furthermore, the accuracy of t f determination by visual observation was already confirmed in our former research by the acoustic method [START_REF] Chen | Evaporation of binary sessile drops: infrared and acoustic methods to track alcohol concentration at the interface and on the surface[END_REF]. where 50°C is the specific critical temperature for 5% 1-butanol aqueous solution.

Beyond this value, the surface tension increases with an increase of temperature as a common liquid. The duration of convection cells declines with the increase of temperature because of the reduction of total evaporation time. Beyond the specific critical temperature, the decrease of convection cells duration becomes more moderate.

a V RD V t H C π θ ρ = - - +  (4.1)
where R is the contact line radius, θ is the contact angle, D a is the diffusion coefficient in air, H is the relative humidity, C V is the saturated vapor concentration, and ρ is the density.

The result of applying Hu and Larson's equation to the ambient case is shown in Fig. 4.8.

The prediction agrees very well with the experimental data of the water drop. In the same figure, the experimental data of 1-butanol aqueous solution drop is added for comparison and the alcohol exhaustion time t f is marked. With the addition of 1-butanol, the solutal Marangoni flow created by the concentration difference clearly enhances the instantaneous evaporation rate of the drop at the beginning. At t f , the evaporation rate of the mixture drop is similar to that of the water drop when 1-butanol is depleted. Because these experiments are conducted at the same conditions, the enhancement of the evaporation rate is clearly due to the solutal Marangoni effect. However, when applying Hu and Larson's equation to the cases when the substrate is heated, the equation always underpredicts the instantaneous evaporation rate compared with the experimental data.

The convection generated by the thermal Marangoni effect, which will enhance the evaporation, is supposed to be the main reason.

Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets drop and this disparity increases with substrate temperature. To examine the influence of the initial concentration of 1-butanol on the evaporation dynamics, we compared the evaporation rate at the initial time between water and 1-butanol aqueous solution drops as shown in Fig. 4.10. The initial evaporation rate of both liquids shows an exponential growth with the increase of substrate temperature. With the solutal Marangoni effect, the mixture drop possesses much higher evaporation rate than the water drop at the initial moment when the 1-butanol concentration is maximum in mixture drop. Even at T s = 80 °C, the mixture drop evaporates faster than the water drop at the beginning, though they have similar evaporation rate until t f . The probable reason is that at the initial time, the 1butanol concentration, which has a higher evaporation rate than water, is at the peak as well as the solutal Marangoni effect. And then the solutal Marangoni effect is reduced with the decrease of the 1-butanol concentration difference in the drop. where γ is the liquid-vapor surface tension, ΔC is the alcohol concentration difference, ΔT is the temperature difference on the drop surface, L is the characteristic length (the drop radius R used in this experiment), µ is the dynamic viscosity, D l is the alcohol diffusivity in water, and α is the thermal diffusion.

The calculation results of Marangoni number for the water, 1-butanol, and 5% 1-butanol aqueous solution drops as a function of substrate temperature are shown in Fig. 4.11. The thermal Marangoni number is calculated by using the temperature difference on the drop surface at the initial time using infrared measurements. For the calculation of the solutal Marangoni number, the maximum 1-butanol concentration difference is assumed to be 5%, the same as the 1-butanol concentration in the drop. For the 1-butanol aqueous solution drop, the solutal Marangoni number increases linearly with the substrate temperature. However, the thermal Marangoni number decreases first and then increases with the increase of substrate temperature. The minimal value of the thermal Marangoni number is situated at approximately 50°C, which is the specific critical temperature for the 5% 1-butanol aqueous solution. At 80°C, both solutal and thermal Marangoni numbers reach the maximum, which means that both concentration and temperature difference probably have a comparable effect on the Marangoni flow. In addition, the duration of the solutal Marangoni flow is shorter than thermal Marangoni flow which continues to be effective after the depletion of 1-butnaol. These can explain why the increase of evaporation rate by adding 1-butanol is not noticeable at 80°C. Below 80°C, the solutal Marangoni number of the 1-butanol aqueous solution drop is much higher than the thermal Marangoni number; therefore, without the solutal Marangoni effect, the water drop evaporates more slowly than the 1-butanol aqueous solution drop. However, at ((((&((((( ((((&(((( (4.5)

The evaporation rate until t f as predicted by Eq. 4.5 is plotted in Fig. 4.9 (shown as a dashed line). Except for the case at 80°C, the calculated result is very close to the experimental one. At the highest substrate temperature, the thermal patterns or the convection cells created by the thermal Marangoni flow in Fig. 4.4, where multiple cells appear, are extremely different from the cases at lower temperatures. Therefore, there exists another mechanism for heat transfer inside the water drop at 80°C.

Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets

The 1-butanol drop evaporates faster than water, but the concentration of 1-butanol in the mixture drop is only 5%; thus, the evaporation rate enhancement of 5% 1-butanol aqueous solution due to the higher evaporation rate of 1-butanol can be neglected. The main reason for the evaporation rate enhancement is the solutal Marangoni flow generated by the 1-butanol concentration difference. Comparing the evaporation rate until t f of the 5% 1-butanol aqueous solution drop and the evaporation rate of the same duration calculated as a pure water drop by Eq. 4.5, the ratio has an approximate constant value of 1.349. Fig. 4.12 shows the surface tension measurement of different 1-butanol concentration drops at different temperatures. Obviously, the temperature has no effect on the value of ∂γ/∂C, which is why the ratio of the experimental/predicted value is independent of temperature. Thus, an equation for the evaporation rate until t f for 5% 1butanol mixture drop can be simply obtained as ((((&((((( ((((&(((( (4.6)

 2 4 concentration, & , (1 ) 1
RD H C L T V T π γ θ ρ µa - - - ∂ D = - + - × + ∂  (
Following the same steps, the initial evaporation rate prediction equations for the water and 1-butanol aqueous solution drops are deduced as follows: ((((&((((( (((((&((((( (4.7) (((&((((( (((((&(((((

2 4 & , (1 ) (0
RD H C L T V T π γ θ ρ µa - - - ∂ D = - + - × + ∂  (
 2 4 , & , (1 ) 1
RD H C L T V T π γ θ ρ µa - - - ∂ D = - + - × + ∂  ((

Conclusions

A visual method combining a CCD camera and an infrared camera is applied to investigate the dynamic evaporation process of three different solution drops (water, 1butanol, and 5% 1-butanol aqueous solution) at different substrate temperatures. The behavior of the drops with respect to the contact angle and diameter shows no dependence on the substrate temperature. The 1-butanol drop evaporates faster than that of water. Therefore, for the mixture drop, the 1-butanol is depleted at the first stage of Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets evaporation and afterward, the water mainly evaporates. Under the infrared camera, the 1-butanol drop shows no thermal instability at different substrates. However, during the earlier periods of evaporation, the convection cells appear on the water drop surface from 50°C and the mixture drop possesses an intensive flow at any substrate temperature owing to the co-existence of the thermal and solutal Marangoni effects. At higher substrate temperatures, the irregular convection cells generated by the solutal Marangoni effect in the mixture drop disappear with the exhaustion of 1-butanol. Then, the regular thermal Marangoni flow continues to act on the drop evaporation. Owing to the addition of 1-butanol and the solutal Marangoni flow created by the alcohol concentration difference, the evaporation rate of the mixture drop is always much higher than the water drop before the depletion of 1-butanol. The model of Hu and Larson is employed to calculate the evaporation rate of the water drop, and the result agrees very well the experimental data at ambient conditions. However, without considering the Marangoni effect contribution, this model underpredicts the evaporation rate when the substrate is heated. The contribution of Marangoni effect is characterized by the Marangoni number; by analyzing the relationship between the experimental data and prediction as a function of the Marangoni number, an empirical equation is developed to calculate the evaporation rate of the water drop at different substrate temperatures. Because the concentration of 1butanol in the mixture drop is small, the exceeded part of the evaporation rate can be neglected. Another empirical equation for estimating the mixture drop evaporation rate until t f is obtained based on the preceding equation. With the same steps, the empirical equations for calculating the initial evaporation rate of the water and 1-butanol aqueous solution drop are derived. The results of these equations correspond fairly well to the Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets experimental data except for the evaporation rate of the water drop at 80°C, which requires further research.

Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets

This chapter is based on the manuscript submitted for publication in 2017. The author of this thesis contributed to the designing and performing experiments, analyzing experimental results and writing manuscript. Prof. S. Szunerits and Prof. R. Boukherroub synthesized graphene oxide (GO) and PEGylated reduced graphene oxide (rGO-PEG) nanofluids, and effectuated characterizations, analysis, and manuscript writing of UV/Vis spectrum, Raman spectroscopy, and X-ray photoelectron spectroscopy for GO and rGO-PEG nanofluids. Prof. S. Harmand supported the author of this thesis for the writing of the manuscript and gave approval to the final version.

Abstract

In this study, the evaporation behavior of graphene nanofluid droplets deposited on sapphire substrate was investigated in the temperature range from ambient to 106 °C. A side-view CCD camera was utilized to record the evaporation process for the droplet profile analysis and a top-view infrared camera was used to observe the temperature distribution on the air/liquid interface of the droplets. Graphene oxide (GO, 0.25 mg/ml), PEGylated reduced graphene oxide (rGO-PEG, 0.25 and 0.8 mg/ml) nanofluids, and water were tested at ambient conditions. The PEGylation was proved to improve the nanoparticles dispersion and the evaporation performance. Preparation without PEGfunctionalization, or with an increased nanoparticle concentration, decreases the Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets evaporation rate due to the poor dispersion of graphene nanoparticles and large accumulation. On heated substrates, 0.25 mg/ml rGO-PEG nanofluid and water have similar behavior in the variation of droplet profile during evaporation, but the evaporation rate of water is dramatically higher than 0.25 mg/ml rGO-PEG nanofluid at high substrate temperature despite the exceptional thermal conductivity of graphene nanofluid. The convective flows induced by thermal Marangoni effect are responsible for the increased evaporation rate of water at high substrate temperature and the application of graphene nanofluid to enhance the heat transfer efficiency is more effective at low substrate temperature.

Introduction

The prediction of Moore [START_REF] Moore | Cramming more components onto integrated circuits[END_REF] proves that for nearly every two years, the number of transistors contained in an integrated circuit will be double and the miniaturization of electrical elements results in an increased demand of high efficiency heat dissipation.

Since the first time used by Choi et al. [START_REF] Choi | Enhancing thermal conductivity of fluids with nanoparticles[END_REF] as a term to refer to the fluids with suspended nanoparticles, nanofluid is considered as an excellent coolant with anomalous high thermal conductivity. Owing to intrinsic high thermal conductivity, pure metals, metal oxides and different nanostructures of carbon are dispersed as nanoparticles in conventional low efficiency heat transfer fluid, as water, ethylene glycol and engine oil etc., to improve thermal performance. Eastman et al. [START_REF] Eastman | Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles[END_REF] reported an enhancement of 40% of the thermal conductivity of copper ethylene-glycol-based nanofluids with very low volume fraction of 0.3%. In the study of Hong and Yang [START_REF] Hong | Study of the enhanced thermal conductivity of Fe nanofluids[END_REF], Fe nanoparticles were found to create a larger increase of thermal conductivity than Cu nanoparticles in Droplets ethylene glycol, which indicated that the enhancement of thermal conductivity is independent of inherent thermal properties of nanoparticles. Patel et al. [START_REF] Patel | Thermal conductivities of naked and monolayer protected metal nanoparticle based nanofluids: Manifestation of anomalous enhancement and chemical effects[END_REF] prepared Ag and Au aqueous nanofluids with citrate stabilization and recorded 5-21% and 7-14% thermal conductivity enhancement for 0.026 vol.% Ag and 0.011 vol.% Au nanofluids, respectively at the same temperature range of 30-60°C. Wang et al. [START_REF] Wang | Thermal conductivity of nanoparticlefluid mixture[END_REF] dispersed Al 2 O 3 and CuO nanoparticles in different base fluids (water, vacuum pump fluid, engine oil and ethylene glycol) and the experimental results revealed thermal conductivity improvement in base fluids which were higher than predictions from existing models. They proposed that microscopic motion, nanoscale structure, surface properties of nanoparticles should be taken into account for the effective thermal conductivity calculation of nanofluid.

Murshed et al. [START_REF] Murshed | Enhanced thermal conductivity of TiO2-water based nanofluids[END_REF] used two different shapes (rod-shape of ∅10nm×40nm and spherical shape of ∅15nm) TiO 2 nanoparticles to prepare aqueous nanofluids and they observed a thermal conductivity increase of approximately 33% for rod-shape and around 30% for spherical shape TiO 2 nanofluids, respectively with 5 vol.% nanoparticle concentration, which unveiled the effect of nanoparticle shape and size. Park and Kim [START_REF] Park | A study on the characteristics of carbon nanofluid for heat transfer enhancement of heat pipe[END_REF] improved the stability of multi-walled carbon nanotubes dispersion by applying a chemical reformation process to adhere the hydroxyl radicals to the oxidized multi-walled carbon MWCNTs' surfaces. At 90°C, the thermal conductivity of MWCNTs nanofluid is 12.6% higher than that for base fluid. Phuoc et al. [START_REF] Phuoc | Viscosity and thermal conductivity of nanofluids containing multi-walled carbon nanotubes stabilized by chitosan[END_REF] measured the thermal conductivity and the viscosity of multi-walled carbon nanotubes (MWCNTs) nanofluids with chitosan and the experimental results disclosed a significant enhancement of thermal conductivity that is much higher than the predictions of Maxwell's theory. Tested with difference chitosan Droplets Al 2 O 3 nanoparticles. However, the boiling heat transfer coefficients of all nanoparticles loading were the same as pure water for which the authors cannot make any explanation.

On the other hand, inconsistent results are reported. Putnam et al. [START_REF] Putnam | Thermal conductivity of nanoparticle suspensions[END_REF] developed an optical beam deflection method to measure the thermal conductivity of nanofluids of C60-C70 fullerenes in toluene and alkanethiolate-functionalized Au in ethanol and toluene. They did not observe abnormal thermal conductivity improvement with low nanoparticle loading (maximum 0.6 vol.%) and the thermal conductivity of nanofluids investigated is independent of nanoparticle concentration. Moghiman and Aslani [START_REF] Moghiman | Influence of nanoparticles on reducing and enhancing evaporation mass transfer and its efficiency[END_REF] designed an experimental system to measure the evaporation performance of different aqueous nanofluids (clay, TiO 2 , ZrO 2 , Fe 2 O 3 and Ni/Fe) at different air velocities and compared the results with base fluid. They found that the evaporation performance of base fluid is ameliorated or degraded, depending on the type of nanoparticle and the nanoparticle concentration also has an important influence on the evaporation rate of base fluid. When Putra et al. [START_REF] Putra | Natural convection of nano-fluids[END_REF] applied Al 2 O 3 and CuO nanofluids in a horizontal cylinder with one end heated, they observed the deterioration of natural convection in the presence of both nanoparticles. Moreover, the deterioration was strengthened with the increase of nanoparticle concentration and the aspect ratio of container. Wen and Ding [START_REF] Wen | Formulation of nanofluids for natural convective heat transfer applications[END_REF] applied aqueous TiO 2 nanofluid in a horizontal PTFE cylinder with bottom heated to compare the natural convection with pure water. The deterioration of heat transfer coefficient with the presence of nanoparticles was observed, which is intensified with the increase of nanoparticle concentration. The increased viscosity, the concentration gradient driven convection, the interparticle interaction and the deposition of nanoparticle aggregated on the heating surface were supposed to be the reasons of deterioration. Chopkar et al. [START_REF] Chopkar | Pool boiling heat transfer characteristics of ZrO2-water nanofluids from a flat surface in a pool[END_REF] Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets investigated ZrO 2 nanofluid dispersed in deionized water to the pool boiling experiment.

Surprisingly they found that the highest boiling heat transfer coefficient was obtained at the lowest nanoparticle concentration (0.005 vol.%) and with the increase of nanoparticles loading, the heat transfer was deteriorated even inferior to the application of pure water at the highest nanoparticle concentration (0.15 vol.%). In summary, the application of nanofluid for enhanced heat transfer performance needs more future researches.

Graphene is a single-atom-thick layer of carbon arranged in a 2D honeycomb lattice.

Since its discovery by Novoselov et al. [START_REF] Novoselov | Electric field effect in atomically thin carbon films[END_REF] in 2004, graphene has attracted numerous interests and one of its exceptional properties is the dramatically high thermal conductivity [START_REF] Balandin | Superior thermal conductivity of single-layer graphene[END_REF][START_REF] Ghosh | Extremely high thermal conductivity of graphene: Prospects for thermal management applications in nanoelectronic circuits[END_REF]. Thus, the graphene nanofluid is believed to be a good candidate for heat transfer enhancement. Graphene oxide (GO), synthesized via thermal exfoliation method and acid treatment, used as aqueous nanofluid exhibited an enhancement of 64%

in thermal conductivity at 50 °C with only 0.056 vol.% GO concentration [START_REF] Baby | Investigation of thermal and electrical conductivity of graphene based nanofluids[END_REF]. After that the same group investigated hydrogen exfoliated graphene (HEG) deionized (DI)

water and ethylene glycol (EG) based nanofluids without surfactant [START_REF] Baby | Enhanced convective heat transfer using graphene dispersed nanofluids[END_REF]. The After subtraction of the Shirley-type background, the core-level spectra were decomposed into their components with mixed Gaussian-Lorentzian (30:70) shape lines using the CasaXPS software. Quantification calculations were performed using sensitivity factors supplied by PHI. The sample was prepared by casting a concentrated aqueous solution of the material onto silicon substrate followed by drying at 100 °C for 1 h.

The GO investigated in this work was synthesized according to a modified Hummer's method, while the PEGylation of GO involved a two-step reaction. GO was first enriched with carboxylic acid groups through chemical reaction with chloroacetic acid under strong basic conditions (0.7 M) at 80°C. Under these experimental conditions, the epoxy and ester groups, on GO surface, were converted into hydroxyl groups, which were in turn transformed into carboxylic acid (-COOH) moieties via reaction with chloroacetic acid. At the same time GO was partially reduced to yield rGO-COOH. To improve the solubility and stability of the rGO-COOH nanosheets in aqueous media, PEGylation was performed with a polyethylene glycol diamine (PEG-NH 2 ; MW=1.5 kDa) via EDC activation reaction at 40°C through amide bond formation.

The UV/Vis spectrum (Fig. 5.1(a)) of GO shows a main absorption peak at around 229 nm due to π-π* transition from the C=C bonds, while rGO-PEG shows a higher absorption in the NIR and a red shift of the main absorption band to 269 nm. The result suggests that the GO nanosheets have been partially reduced to reduced graphene oxide Droplets (rGO) and the electronic conjugation within the rGO nanosheets was partially restored.

The zeta potential of GO in water was determined as -40±2 mV.

Raman spectroscopy was used in addition to investigate GO and rGO-PEG sheets. Fig.

5.1(b)

shows the expected D (≈1350 cm -1 ) and G (≈1580 cm -1 ) bands for carbon based materials, which are assigned to the local defects/disorder and the sp 2 graphitized structure of GO. The ID/IG intensity ratio was determined to be 1.19 for GO and 0.72 for rGO-PEG; the smaller ID/IG peak intensity of rGO-PEG, corresponding to lower defect/disorders, is due to the improvement in the sp 2 graphitized rGO-PEG structure of the sheets during the reduction process. The 2D band at 2712 cm -1 is highly sensitive to stacking degree of the sheets. While a single-layer graphene sheet exhibits a 2D band at 2679 cm -1 , for multi-layered graphene sheets the 2D band appears as a broadened peak with 19 cm -1 shift into higher wavenumbers. In the case of GO the 2D band is positioned at 2714 cm -1 , while rGO-PEG shows a broad band centered at 2919 cm -1 , indicating that monolayer to bilayer structures are predominant in GO while rGO-PEG has a multilayered structure.

X-ray photoelectron spectroscopy (XPS) was in addition used to follow the chemical changes that occurred upon carboxylation and PEGylation of GO. Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets

Experimental setup

The optical and infrared techniques were applied to investigate the dynamic evaporation of droplets of graphene nanofluid and base fluid. The droplet is formed by an automatic dosing system, which can control the volume of droplet as well as dosing speed, and then is deposited on a sapphire substrate below which there is a black-painted heater connected to an electrical controller (see Fig. The droplets of all the graphene nanofluid samples have similar evaporation behavior as that of pure water, i.e., the typical constant contact line regime. The contact angle of each droplet decreases continuously during evaporation, while the diameter remains constant until it shrinks rapidly at the end. It seems that PEG-functionalization and the difference in rGO-PEG concentration have no influence on the evolution of the droplet profile, as seen by comparing the 0.25 mg/ml GO and rGO-PEG nanofluids results, and also from the 0.8 mg/ml rGO-PEG nanofluid results. The only significant difference is in the instantaneous evaporation rate. The droplets of 0.25 mg/ml rGO-PEG nanofluid have the highest evaporation rate, while the same concentration of GO nanofluid has the lowest.

For the pure water and 0.8 mg/ml rGO-PEG nanofluid, the instantaneous evaporation rates are very close but the rate for pure water is somewhat higher. At ambient temperature, the dominant heat transfer inside the droplet is thermal conduction. With its extraordinarily high thermal conductivity, the rGO-PEG nanofluid is expected to evaporate much faster than water base-fluid alone; the result obtained for 0.25 mg/ml rGO-PEG nanofluid confirms this assumption. However, the 0.25 mg/ml GO, and the 0.8 mg/ml rGO-PEG, exhibit contradictory results. The former case can be explained by degraded thermal conduction, and hence reduced evaporation, resulting from poor dispersion of GO in water. For the latter case, with a higher concentration of rGO-PEG, it is suggested that agglomeration inside the droplet can easily take place, resulting in reduced thermal conduction and evaporation. The ideal graphene nanofluid should have good stability with appropriate nanoparticle concentration. Fig. 5.5 shows microscopic images of graphene nanoparticle deposition after evaporation.

In this experiment, all droplets are in the constant contact line regime because of the hydrophilic substrate. Most of the evaporation takes place at the contact line, leading to outward capillary flow from the droplet center to the periphery. The outward flow transports the nanoparticles to the contact line where they deposit at the edge of the meniscus region. As evaporation progresses, more and more nanoparticles accumulate and the "coffee ring" left after evaporation is obvious in all the microscopic photographs.

As seen in the image for 0.25 mg/ml GO nanofluid (Fig. 5.5(a)), the non-uniform dispersion of nanoparticles results in a heterogeneous deposition of GO inside the "coffee ring," with some locations free of nanoparticles. Nevertheless, large clusters of GO nanosheets are found. For the 0.25 mg/ml rGO-PEG nanofluid (Fig. In order to understand the mechanism of nanoparticle deposition, the evaporation of graphene nanofluid droplets was investigated under a microscope. In stages of evaporation, the contact angle becomes so small that the nanoparticles in the stream do not approach the contact line and deposit at a distance away or join the dispersed nanoparticles at the air/liquid interface. The strong surface tension separates the nanoparticle dispersion from the accumulation at the contact line, creating a vacancy of nanoparticles in the gap; the concentration of dispersed nanoparticles at the air/liquid interface forms the second ring. In the case of the 0.25 mg/ml rGO-PEG nanofluid, the nanoparticle dispersion at air/liquid interface is thinner and a thin layer of nanoparticles remains inside the "coffee ring"; the region with a vacancy of nanoparticles is much narrower. In contrast, for the GO nanofluid, the poor dispersion of nanoparticles results in a heterogeneous deposition inside the "coffee ring". The supposition about the heat transport mechanism inside the droplets is confirmed by analysis of the microscopic videos.

Experimental results on heated substrates

In the previous part, the evaporation properties of different graphene nanofluids and water were studied under ambient conditions. The temperature has a central influence on the dynamic viscosity, the thermal conductivity, and the specific heat capacity of fluids so two graphene nanofluids (0.25 mg/ml GO and rGO-PEG) and water were tested on heated sapphire substrates to investigate the effect of substrate temperature (The ambient Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets temperature and relative humidity were 22 °C and 50%, respectively). From the previous results, it was found that an increase of rGO-PEG nanoparticle concentration had no influence on the enhancement of droplet evaporation rate; the 0.8 mg/ml rGO-PEG nanofluid is therefore not included in the heated substrate tests.

The sapphire substrates were heated at different temperatures (50, 66, 84, 106 °C) and the profile analysis shows no evident influence of substrate temperature on the evolution mode of the contact angle, volume, and diameter. However, the substrate temperature plays an important role in determining the time for complete evaporation of the droplets.

The results of evaporation rate are displayed in Fig. 5.7; the inset is an enlarged view at lower temperatures. Each test was repeated 6 times to ensure the reproducibility of the experiments and the average values are presented in the figure. The evaporation rates of all liquids increase significantly with the rise of substrate temperature. As previously observed for ambient temperature, the evaporation rate for GO nanofluid is lower than that of the other two liquids (water, rGO-PEG nanofluid) at all substrate temperatures investigated. The probable reason is that instabilities in the GO nanofluid lead to agglomeration of nanoparticles, which reduces the heat transfer efficiency. Having large nanoparticle clusters and subsequently a low evaporation rate, the GO nanofluid is not a suitable material for evaporation performance improvement, and is not included in the following analysis. Droplets For the rGO-PEG nanofluid, the addition of graphene nanoparticles enhances the thermal performance of the base fluid at low substrate temperatures (22 and 50 °C). However, the situation is reversed at high substrate temperatures (84 and 106 °C) that the evaporation rate of the rGO-PEG nanofluid is significantly much lower than that of water. Tab. 6; water and 0.25 mg/ml rGO-PEG nanofluid).

In order to explain this evaporation rate behavior, the temperature distribution on the surface of droplets for different substrate temperatures are observed from infrared images (Fig. 5.8). For the rGO-PEG nanofluid, thermal instability is not detected at any substrate temperature. However, for a substrate temperature T s = 66 °C, convection cells are apparent on the surface of water droplets; these become more distinct and intense at higher substrate temperatures. The observation is in accordance with the previous study on hydrophobic silicon substrates [START_REF] Chen | Marangoni Flow Induced Evaporation Enhancement on Binary Sessile Drops[END_REF]. Coincidentally, the water droplet evaporates faster than the rGO-PEG nanofluid when the substrate temperature exceeds 66 °C. The heat transfer mode for both liquids at low substrate temperature is thermal conduction;

other reports [START_REF] Baby | Investigation of thermal and electrical conductivity of graphene based nanofluids[END_REF][START_REF] Baby | Enhanced convective heat transfer using graphene dispersed nanofluids[END_REF][START_REF] Yu | Enhanced thermal conductivities of nanofluids containing graphene oxide nanosheets[END_REF][START_REF] Yu | Experimental investigation on thermal conductivity of nanofluids containing graphene oxide nanosheets[END_REF] have shown that addition of graphene nanoparticles can significantly augment the thermal conductivity of a base fluid, so it is consistent that the graphene nanofluid shows better thermal performance than water at low temperature.

However, with increased substrate temperature, thermal convection appears inside the water droplet, while the graphene nanofluid droplet continues to transfer heat from the Droplets substrate by conduction only. The addition of convection improves the heat transfer efficiency of the water droplet, and its evaporation rate becomes considerably higher than that of the rGO-PEG nanofluid. From the infrared videos, the highest temperature is found at the contact line and the lowest temperature is normally situated at the top of the droplet. The temperature difference between the contact line and the top of the droplet surface drives a thermal Marangoni effect. Nevertheless, for water droplets on the higher temperature substrates, the lowest temperature is located near the top because of convection. From infrared camera thermal mapping data, the initial temperature differences across the droplet surface of water and rGO-PEG nanofluid were measured when the droplets were placed on the substrates as a function of substrate temperature (Fig. 5.9). The initial temperature difference increases with the rise of substrate temperature for both liquids, and (with the exception of the unheated substrate) is always higher for the graphene nanofluid droplet than for water. The graphene nanofluid is assumed by many researchers to possess a significantly higher thermal conductivity than water, implying that the temperature at the top of the droplet is closer to that at the contact line than for water. However, the experiments indicate the converse, with convection in the water droplet making the temperature distribution on the surface more homogeneous than for the graphene nanofluid. Droplets Thermal convection in a single-component droplet can be driven by either gravity or surface tension. In this study, the droplets are so small that their radii are less than the capillary length. As a result, the effect of gravity as a buoyancy force can be excluded.

Moreover, in our previous study using hydrophobic silicon substrates at high temperatures, convection cells appeared in pure water droplets but not in pure butanol droplets [START_REF] Chen | Marangoni Flow Induced Evaporation Enhancement on Binary Sessile Drops[END_REF]. If the convection cells are generated by buoyancy, they will exist in the droplets of both liquids. Therefore, the convection cells in the present study are surface tension driven, with a gradient in surface tension caused by the temperature difference Droplets across the water droplet surface. This is the so-called thermal Marangoni effect, which is characterized by the thermal Marangoni number:

T L T Ma T γ µa ∂ D = - ∂ (5.1)
where γ is the liquid-vapor surface tension, ΔT is the temperature difference across the droplet surface, L is the characteristic length (the drop radius R used in this experiment), µ is the dynamic viscosity, and α is the thermal diffusivity. The thermal diffusivity can be expressed by

, p v k C a =
where k is the thermal conductivity and C p,v is the volumetric heat capacity. Consequently, the thermal Marangoni number can be written as:

, p v T RC T Ma T k γ µ D ∂ = - ∂ (5.2)
Some of the properties required to calculate the thermal Marangoni number are presented in Tab. 5.2. The dynamic viscosities of 0.25 mg/ ml rGO-PEG nanofluid were measured using a Stabinger Viscometer (incertitude ± 5 %) at five different temperatures. Fig. 5.11

shows that the dynamic viscosity of water and rGO-PEG nanofluid both decrease with increasing temperature, but the graphene nanofluid has a higher viscosity at each temperature. Moreover, this percentage enhancement of dynamic viscosity with the

k k k k k k f β β = - - + + + 3 3 3 3 3 1 [ ( ) ])( ( 2 ) ( ) [ 1]) l p lr f f l p lr p lr p l k k k k k k k β f β β f β β - × - + + - - + - (5.3)
In this expression, 1 + h/a = β and 1 + h/2a = β l , where h is the interfacial layer thickness and a is the particle radius. The particle volume fraction is ϕ p ; k p , k f , and k lr are the thermal conductivities of the particles and the liquid and interfacial layers, respectively.

The calculated thermal conductivities using Eq. 5.3 are given in Tab. 5.2; the thermal conductivity of graphene nanofluid is significantly enhanced in comparison to the base fluid. These calculated results are consistent with other reports [START_REF] Baby | Investigation of thermal and electrical conductivity of graphene based nanofluids[END_REF][START_REF] Baby | Enhanced convective heat transfer using graphene dispersed nanofluids[END_REF][START_REF] Yu | Enhanced thermal conductivities of nanofluids containing graphene oxide nanosheets[END_REF][START_REF] Yu | Experimental investigation on thermal conductivity of nanofluids containing graphene oxide nanosheets[END_REF], claiming that a The surface tension of rGO-PEG nanofluid was measured at different temperatures by the pendant drop method with Kruss ® DSA. The pendant drop method is based on the Young-Laplace equation which describes the relationship between the drop shape and the interfacial tension. The surface tension is calculated from the shadow image of a drop suspended from a needle by drop shape analysis. Fig. 5.12 shows the measurement results for water and rGO-PEG nanofluid. As common liquids, the surface tensions of both liquids decrease almost linearly with the increase of temperature. However, the addition of rGO-PEG nanoparticles reduces the surface tension and the evolution for rGO-PEG nanofluid has a steeper slope than for water which is also observed in the study of 125 Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets Ahammed et al. [START_REF] Ahammed | Effect of volume concentration and temperature on viscosity and surface tension of graphene-water nanofluid for heat transfer applications[END_REF]. Owing to the hydrophilic nature of rGO-PEG nanoparticle, the strong attraction force adsorbs water molecules to create an interlayer on solid surface and the intermolecular space of water molecules between each interlayer increases. Therefore, on the free surface of droplet, the attraction force from water molecules in bulk is weakened which is perceived as a decline in surface tension. The surface tension of water from the international tables [START_REF] Vargaftik | International tables of the surface tension of water[END_REF] is added to examine the measurement accuracy. From Fig. 5.12, it is clearly observed that the measured surface tension of water agrees well with the theoretical data with a maximum deviation of ± 2.8%. Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets

The temperature difference across the droplet surface was applied to calculate (using Eq. 5.

2) the thermal Marangoni numbers of water and rGO-PEG nanofluid throughout evaporation. The case at substrate temperature of 84 °C is presented in Fig. 5.13. The evolutions of thermal Marangoni number for both liquids have the same trend as temperature difference: for rGO-PEG nanofluid, a sharp reduction is observed which lasts only a few seconds at the beginning and then the thermal Marangoni number decreases almost linearly since the evaporation of droplet reaches the steady state (when the temperature difference begins to decrease with a constant rate); for pure water, the thermal Marangoni number stays constant when the evaporation process starts and then undergoes a rapid decrease after 10 s which is more intense than for rGO-PEG nanofluid.

The initial Marangoni number for rGO-PEG nanofluid droplet is considerably high, but its duration is too short that the Marangoni effect cannot generate visible convection cells.

On the other side, the thermal Marangoni number for water droplet keeps a relative long period of high value at which the Marangoni effect induces thermal convection and improves the evaporation performance. Droplets droplet at 66 °C (around 20000) is considered as the threshold beyond which the evaporation rate will be significantly improved by the appearance of convection cells.

Conclusions

The evaporation behavior of droplets of pure water and three different water-based graphene nanofluids was investigated; it is confirmed that graphene oxide functionalization with polyethylene glycol (PEG) promotes the dispersion of graphene Droplets nanoparticles and increases the evaporation rate. Preparation without PEGfunctionalization, or with an increased nanoparticle concentration, decreases the evaporation rate; the poor dispersion of graphene nanoparticles and their agglomeration are the main causes, indicated by analysis of the nanoparticle depositions and the microscopic videos, respectively.

Heating of the substrate can greatly enhance the droplet evaporation rate of water and graphene nanofluids (GO and rGO-PEG). The poor dispersion of GO nanoparticles leads to reduced heat transfer efficiency and a lower evaporation rate, in comparison to water and rGO-PEG nanofluid. Because of better heat transfer efficiency, the droplet of rGO-PEG nanofluid exhibits a higher evaporation rate than water at ambient temperature. The enhancement of evaporation rate in our study is at maximum at ambient temperature and then decreases with further increase of substrate temperature, to the extent that at a substrate temperature of 106 °C, the water droplet evaporates much faster than the rGO-PEG nanofluid. From infrared videos, convection cells appear on the surface of water droplets at the higher substrate temperatures, while thermal instability is not detected on the droplet surface of rGO-PEG nanofluid. Convective flows increase the evaporation of water droplets, and only results from the thermal Marangoni effect in small droplets of single-component. The thermal Marangoni number, which characterizes the thermal Marangoni effect, is always under the threshold of convective flow for droplets of rGO-PEG nanofluid. The increase in the dynamic viscosity from the addition of rGO-PEG nanoparticles to the base fluid is believed to be the main reason that the heat convection is inhibited. The application of graphene nanofluid to enhance the evaporation rate is more effective at low substrate temperature. The correlation seen between evaporation Raman spectroscopy, and X-ray photoelectron spectroscopy were devoted to the characterizations of nanofluid.

For binary solutions, different diffusion coefficient in the air leads to different alcohol/water ratio at droplet free surface between 1-butanol and ethanol aqueous solutions during evaporation under ambient condition. The infrared camera detects the existence of alcohol by visible convection cells at liquid/vapor interface while the acoustic echography measures reflection coefficient at solid/liquid interface. Due to high volatility, the ratio of ethanol/water stays at very low level on droplet surface and most of ethanol molecules are situated in the bulk of droplet, which results in a large disparity of alcohol exhaustion time estimation between infrared and acoustic methods. Nevertheless, the coincidence of 1-butanol depletion time estimations confirms the feasibility of acoustic method to monitor 1-butanol concentration kinetics as a function of time.

Furthermore, hygroscopic power difference between pure 1-butanol and ethanol was also The results of these equations correspond fairly well to the experimental data at different substrate temperature.

For nanofluid, the effects of PEG-functionalization and nanoparticle concentration on suspension stability and evaporation behavior were investigated at ambient condition.

The PEGylation treatment was proved to not only improve graphene nanoparticle dispersion but also enhance evaporation performance by the comparison of deposition pattern and overall evaporation rate between 0.25 mg/ml graphene oxide (GO), 0.25 mg/ml and 0.8 mg/ml PEGylated reduced graphene oxide (rGO-PEG) nanofluids. Non-PEGylating or inappropriate concentration will deteriorate nanoparticle dispersion homogeneity and then evaporation performance due to large nanoparticle agglomerations.

The effect of substrate temperature was investigated during evaporation process of pure water and 0.25 mg/ml rGO-PEG nanofluid droplets at five substrate temperatures (22, 50, 66, 84, 106 °C). Evaporation rates of both liquids increase with the rise of substrate temperature. Owing to reported exceptional thermal conductivity, rGO-PEG nanofluid evaporates faster than pure water at ambient temperature. However, this heat transfer enhancement by adding graphene nanoparticles decreases with further substrate heating.

When temperature goes above 66 °C, water droplet reveals dramatically higher evaporation rate than that for rGO-PEG nanofluid. This theatrical transformation is attributable to thermal Marangoni effect on water droplet evaporation, which is presented in the form of convection cells under infrared camera. The addition of rGO-PEG nanoparticles increases dynamic viscosity, which is considered to be responsible for the suppression of heat convection within nanofluid droplet.

Despite findings from this study, the mass and heat transfer mechanisms of binary solution and the controversial thermal performance of nanofluid necessitate a large scope of future researches. The acoustic high frequency echography is demonstrated to precisely monitor alcohol concentration at solid/liquid interface and thus the application can be extended to track overall not local alcohol concentration variation or to reveal nanoparticle deposition rate on substrate within evaporating nanofluid droplet which is beneficial to DNA mapping and inkjet printing. More factors such as alcohol concentration, surface properties of substrate, drop profile etc. need to be added in the equation for predicting evaporation rate of low volatile alcohol aqueous droplet, which lacks experimental data. Besides, the study on dynamic equilibrium of ethanol condensation and evaporation at liquid/vapor interface can contribute to the evaporation rate prediction for ethanol-water mixture droplet. The application of rGO-PEG nanofluid to improve heat transfer is more effective at low substrate temperature. Thus, the method for reducing dynamic viscosity is expected to considerably enhancement thermal performance of rGO-PEG nanofluid and to widely extend application range.

  Treated surfaces with continuous or discontinuous fine-scale on surface finish or coating are applied principally in boiling and condensation. The roughness height of surface is inferior to that for single-phase heat transfer. b. Rough surfaces with modified configurations varying from random sand-grain roughness to discrete protuberances are generally assigned to enhance heat transfer of single-phase flow. The aim of surface configuration is for turbulence promotion instead of heat transfer surface area extension. c. Extended surfaces with increased effective heat transfer surface are customarily used for heat exchangers. The new development trend of extended surfaces is to combine surface area enlargement with improved heat transfer coefficient by modifying finned surfaces. d. Displaced enhancement devices installed at interior surface of flow channel are employed for forced convection by indirect energy transport improvement at the heat exchange surface. e. Swirl-flow devices including helical wire coils, twisted tapes, inlet vortex vanes, axial cores with screw-type windings, periodic spaced propellers etc., are engaged to induce swirl or secondary flows for single-phase or two-phase forced convection in channel. f. Coiled tubes are employed in single-phase flow or most region of boiling, which induce secondary flows or Dean vortices to enhance heat transfer coefficient by coiled inner surface.

  Active methods a. Mechanical aids include stirring, surface scraping, rotating surfaces and resonating pulse reactor, which agitate the fluid by mechanical means or by rotating the surface. b. Surface vibration with either low or high frequency is primarily utilized to enhance the heat transfer efficiency of single-phase flows. c. Fluid vibration as well as fluid pulsation, is the most practical vibration technique principally for heat transfer enhancement of single-phase fluids with vibration frequency ranging from 1 Hz to ultrasound. d. Electrostatic fields (dc or ac sources) are used to create electric or magnetic fields, or combined field of both, which can intensify bulk fluid mixing and generate forced convection in dielectric fluids in order to improve heat transfer.

Figure 1 . 2

 12 Figure 1.2 Schema of meniscus region near contact lines for thin liquid films. Image

Figure 1 . 3

 13 Figure 1.3 Distribution of evaporation flux along liquid meniscus. Image taken from Ref.

Figure 2 . 1

 21 Figure 2.1 Contact angle of a liquid droplet wetted to a rigid solid surface. Image taken

Figure 2 . 2

 22 Figure 2.2 Different modes of droplet profile evolution: (1) constant contact line regime

Figure 2 . 3 Figure 2 . 4

 2324 Figure 2.3 The evolution of parameters ((i) contact angle (ii) drop diameter (iii) drop

Figure 2 . 5

 25 Figure 2.5 Flow structure within a single-component sessile droplet on (a) heated

  2.5 (b)). The induced flow is called thermal Marangoni flow or thermocapillary flow. For the case of multi-component, the more volatile constituent preferably evaporates and most of mass transfer takes place at micro Chapter 2 Literature Review region, which results in a sharp decreasing of concentration at vicinal region of contact line. As a consequence, a non-homogeneous distribution of component concentration as well as surface tension is created along the free surface of the droplet which generates the so-called solutal Marangoni flow.

Figure 2 . 6

 26 Figure 2.6 Measurement results of surface tension for (a) butanol and butanol aqueous

Figure 2 . 7

 27 Figure 2.7 Snapshots from optical and infrared cameras of self-rewetting fluid droplets in

Figure 3 . 1

 31 Figure 3.1 Schema of the experimental setup: (a) workbench of modified Kruss® Drop

Fig. 3. 2 ,

 2 are linear regardless of the conditions of relative humidity. In the case of 56% relative humidity, according to the slopes of ours plots, Kf(θ) varies in the 1.42 × 10 -5 to 1.69 × 10 -5 cm 2 /s range. These values are Chapter 3 Alcohol Concentration Tracking of Binary Sessile Droplets during Evaporation comparable to the theoretical ones calculated from Eq. 3.5 to 3.7, which fall in the 1.22 × 10 -5 to 1.33 × 10 -5 cm 2 /s range.

Figure 3 . 2

 32 Figure 3.2 Evolutions of the contact angle and V 2/3 for pure 1-butanol droplets under

Fig. 3 .

 3 Fig. 3.3 shows the evaporation process of the pure 1-butanol droplets at 56% relative

Figure 3 . 3 .

 33 Figure 3.3. Snapshots from an infrared video of the evaporation process of a pure 1-

Figure 3 . 4

 34 Figure 3.4 Evolutions of the contact angle and V 2/3 for pure ethanol droplets under

Fig. 3. 5 (

 5 Fig. 3.5 (see also the movies on line at Ref. [122]) represents the infrared images of the

Figure 3 . 5

 35 Figure 3.5 Snapshots from an infrared video of the evaporation process of a pure ethanol

Figure 3 . 6

 36 Figure 3.6 Kinetics of the acoustic reflection coefficient for a drop of pure ethanol

  Concentration Tracking of Binary Sessile Droplets during Evaporation Water/butanol mixture (a) Optical and infrared investigation

Figure 3 . 7

 37 Figure 3.7 Evolutions of contact angle and V 2/3 for droplets of pure water and 5% mass

  Fig.3.8 shows the evaporation process of the water-1-butanol mixture droplets with 5% butanol mass concentration under the infrared camera (see also the movies on line at Ref.[122]). At the beginning, the motion of convection cells is fierce and random without any thermal pattern. Since the drop evaporated at ambient temperature, there is no large temperature gradient in the droplet.Therefore, the color difference of convection cells is due to emissivity difference, which indicates different substances, instead of temperature difference. As evaporation progressed, convection cells became smaller and slowed down towards the contact line until disappeared. With these infrared videos, we can visually identify the time when the thermal instabilities disappeared and the color distribution on droplet surface became stable as the moment when the 1-butanol in the droplet exhausted. The duration of 1butanol is marked on Fig.3.7, where the 1-butanol disappeared at 264 seconds. The finish point determined by infrared video is also the moment when contact angle reached maximal value close to that of water and the constant contact angle stage began.

Figure 3 . 8

 38 Figure 3.8 Snapshots from an infrared video of the evaporation process of a water-1-

Figure 3 . 9 Figure 3 . 10 2 3

 393102 Figure 3.9 Calibration curve for 1-butanol at a temperature of 22°C and a hygrometry of

Figure 3 .

 3 Figure 3.11 Evolution of contact angle and V 2/3 for droplets of pure water and droplets of

Figure 3 . 12

 312 Figure 3.12 Snapshots from an infrared video of the evaporation process of a water-

Figure 3 . 13

 313 Figure 3.13 Snapshots from an infrared video of the evaporation process of a water-

Figure 3 . 14

 314 Figure 3.14 Calibration curve for ethanol at a temperature of 22°C and a hygrometry of

Figure 3 . 15

 315 Figure 3.15 Mass concentration kinetics during evaporation of droplets of 5%, 25%, 50%

Chapter 4

 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets cells created by the thermal Marangoni effect appear on the surface of the pure water drop from 50°C. Because 1-butanol and water have different surface tensions, the infrared video of the 5% 1-butanol aqueous solution drop shows that the convection cells are generated by the solutal Marangoni effect at any substrate temperature. Furthermore, when the substrate temperature exceeds 50°C, co-existence of the thermal and solutal Marangoni flows is observed. By analyzing the relation between the ratio of the evaporation rate of pure water and 1-butanol aqueous solution drops and the Marangoni number, a series of empirical equations for predicting the evaporation rates of pure water and 1-butanol aqueous solution drops at the initial time as well as the equations for the evaporation rate of 1-butanol aqueous solution drop before the depletion of alcohol are derived. The results of these equations correspond fairly well to the experimental data.

Picknett and Bexon [ 101 ]

 101 studied an evaporating drop of methyl acetoacetate on a nearly flat surface covered by a layer of PTFE (polytetrafluoroethylene). The droplet evaporation was conducted at ambient temperature and its change of mass was recorded Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets by a microbalance. Based on Maxwell's analogy between diffusive flux and electrostatic potential, they obtained the evaporation rate equation for constant contact angle regime and constant contact radius regime. The comparison of droplet half-life by theoretical prediction with the experimental data showed a satisfactory agreement in both modes of evaporation at a particular range of contact angle, drop size, and vapor pressure. Rowan et al. [134] measured the change of contact angle and height of small water drops on poly-(methyl methacrylate) (PMMA) in constant contact radius regime. Based on a spherical cap geometry model, they derived a drop mass loss equation that included the liquid-vapor interface diffusion effect. The prediction result of their equation was validated by experimental data for a contact angle below 90°. Shanahan and Bourges-Monnier [135,136] conducted a series of experiments with sessile water and n-decane drops deposited on three different polymer substrates (polyethylene, epoxy resin, and Teflon) with and without saturated vapor pressure condition. The measurements of contact angle, contact diameter, and height of drops versus time revealed that the evaporation process could be divided in three or four distinct stages in open air, which depends on the roughness of the substrate. By analyzing the second stage, which is in constant contact radius regime, they proposed a model to evaluate the diffusion coefficient of liquid vapor into the air with the radial diffusion assumption. Hu and Larson [137] used experimental, analytical, and computational techniques to investigate the evaporation process of a sessile water drop in constant contact radius regime at ambient atmosphere. The quasi-steady water vapor concentration distribution and evaporation flux above the drop were calculated by a finite element method (FEM). Both experimental and computational results disclosed a time-independent constant Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets evaporation rate when the initial contact angle was less than 40°, despite an extraordinarily high evaporation flux at the periphery of the drop. An approximate model for evaporation rate at ambient condition was developed by comparing the FEM and analytical solution results, which agreed fairly well with the experimental data in the literature.When the environmental condition is not ambient, the evaporation process of sessile drops will become more complicated with additional interfering factors such as temperature, humidity, vapor pressure, and convection in the drop or in the air. Girard et al.[START_REF] Girard | Infrared thermography investigation of an evaporating sessile water droplet on heated substrates[END_REF] used an infrared camera to investigate the water deposited on heated copper substrates at different temperatures and determined the contact line using the maximum value in the temperature profile. The infrared method result showed a satisfactory quantitative and qualitative agreement with the measurements using the optical technique. Furthermore, they used local energy conservation laws associated with the local measurements of the interface temperature to deduce the equation of local evaporative mass flux. The calculated evaporative flux was represented in a 3D plot with time. The mass flux increased as time proceeded and when approaching the contact line, the evaporation rate increased abruptly and tended to approach infinity. Their result was in agreement with the theories proposed for the evaporation of menisci; however, they did not present any experimental result on the evaporation rate. P.L. Kelly-Zion et al.[START_REF] Nguyen | Theoretical and experimental analysis of droplet evaporation on solid surfaces[END_REF] investigated the evaporation of droplets of four hydrocarbon components (3methylpentane, hexane, cyclohexane, and heptane) with different base areas at atmospheric condition on aluminum and used an analytical balance to measure the reduction of the droplet mass. They first calculated the evaporation rate by Stefan's Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets equation, which is based on diffusion-controlled mode. They found that the diffusioncontrolled mode underestimates the evaporation rate and even the measured rate is 475% greater than the value from the diffusion-controlled mode with a large drop radius. They developed an empirical model combined with convective transport, which is estimated by correlation with the Grashof number. This combined transport model agrees well with the measured evaporation rates and the error is less than 8%. Tuan A.H. Nguyen et al.[START_REF] Carle | Experimental evidence of the atmospheric convective transport contribution to sessile droplet evaporation[END_REF] performed a theoretical analysis in order to determine the volume change of a sessile droplet due to natural evaporation and validate the volume change with the change in the transient contact angle and base radius as measured by tensiometry. In that study, they investigated two-stage evaporation: first at constant contact radius regime, then at constant contact angle regime. Based on Fick's second law, which describes the mass conservation for the vapor evaporation by diffusion, the Laplace partial differential equation of second order can be conveniently solved for the vapor concentration in the toroidal coordinate. By applying the separation-of-variables method and the Mehler-Fock integral transform, they obtained the solution for the vapor concentration around the droplet and then the net of the surface diffusive flux. Finally, they obtained the total evaporation rate by integrating the diffusive flux for the constant contact angle regime.They found that the total evaporation rate was a negative and monotonically decreasing function of the contact angle, only if the contact angle and wetted base radius were sufficiently small, and the residual droplet volume linearly decreased during the first stage. Carle et al.[START_REF] Gatapova | Evaporation of a sessile water drop on a heated surface with controlled wettability[END_REF] investigated ethanol droplets that evaporated in air at a temperature of 25 °C on a cylindrical heated aluminum substrate. A heat flux meter was attached to the substrate in order to determine the evaporation rate. Two sets of experiments were Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets conducted with similar setups under terrestrial (1𝑔𝑔) and reduced gravity (μ𝑔𝑔) conditions

  4.1) without air current. At the top of the vapor chamber, there are a sapphire window for the infrared camera and a hole for passing the syringe. The drops are deposited on the hydrophobic silicon substrate, below which a heater connected to an electrical controller is attached.The infrared camera (FLIR X6580SC, 640 × 512 pixels, 200Hz, 15 µm detector pitch) is installed on top for infrared thermal mapping and visualization of thermal instabilities on the surface of the droplets. The use of dynamic infrared videos provides a good visualization of the convection cell motion on the droplet surface and consequently the alcohol life time during evaporation, as water and alcohol have different emissivities. A side view CCD (charge-coupled device) camera (Allied Vision Technologies, 15 fps, 780 × 580 pixels) is used to record the evaporation process of the droplets for profile analysis by using a Kruss® drop shape analyzer (DSA) to measure the contact angle, volume, diameter, and height of the sessile droplets during evaporation.

Figure 4 . 1

 41 Figure 4.1 Schematic of the experimental setup of modified Kruss® drop shape analyzer

Chapter 4 Figure 4 . 2

 442 Figure 4.2 Evolution of contact angle and diameter for pure water and 5% 1-butanol

Fig. 4 .

 4 [START_REF] Ranjan | Wicking and thermal characteristics of micropillared structures for use in passive heat spreaders[END_REF] shows the snapshots of infrared videos of water drop when they are deposited on the substrate. From the substrate temperature T s = 50°C, the convection cells created by the thermal Marangoni flow are obvious under the infrared camera and become clearer and more intense with the Droplets increase of substrate temperature. However, for the drop of 1-butanol aqueous solution, both thermal and solutal Marangoni effects work together. The former is caused by the temperature difference, while the latter is by the 1-butanol concentration difference.Based on the infrared videos (Fig.4.5), the convection cells have two different patterns:

Figure 4 . 3

 43 Figure 4.3 Snapshots from infrared videos of the evaporation process of 1-butanol drops

Figure 4 . 4

 44 Figure 4.4 Snapshots from infrared videos of the evaporation process of water drops at

Figure 4 . 5

 45 Figure 4.5 Snapshots of different moments from infrared videos of the evaporation

Figure 4 . 6

 46 Figure 4.6 Snapshots of different moments from infrared videos of the evaporation

Fig. 4 .

 4 Fig. 4.7(b) represents the relation between the ratio of 1-butanol duration on total

Figure 4 . 7

 47 Figure 4.7 (a) Surface tension and convection cells duration of 5% 1-butanol aqueous

Figure 4 . 9

 49 Figure 4.9 Evaporation rate until alcohol exhaustion time t f of water and 5% 1-butanol

Figure 4 . 10 Chapter 4

 4104 Figure 4.10 Initial evaporation rate of water and 5% 1-butanol aqueous solution drops

Chapter 4

 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile Droplets80°C, the thermal Marangoni number of the water drop is also at peak. The effect of the concentration difference on the Marangoni flow is no longer significant as mentioned above and the water drop also has an intense convective flow owing to the thermal Marangoni effect. For the pure solution drops, namely water and 1-butanol, only the thermal Marangoni effect occurs. The thermal Marangoni number of the water drop increases with temperature. The value at the substrate temperature of 50°C (approximately 2000) is the critical thermal Marangoni number for the water drop, beyond which convection cells appear. As for the 1-butanol drop, the thermal Marangoni number is always lower than that of the water drop at same substrate temperature.

Figure 4 .

 4 Figure 4.11 Marangoni number of water, 1-butanol, and 5% 1-butanol aqueous solution

 ( 4 . 8 )

 48 Chapter 4 Effect of Marangoni Flow on Evaporation Performance of Binary Sessile DropletsThe calculated results, which fairly agree with the experimental values, are plotted in Fig.4.9 and 4.10.

Figure 4 . 12

 412 Figure 4.12 Surface tension of different 1-butanol concentration aqueous solution drops

  investigation of thermal performance in straight stainless steel tube showed that the addition of HEG induces considerable enhancement in thermal conductivity and heat transfer compared to the base fluid, which increases with temperature and volume fraction. Yu et al.[START_REF] Yu | Enhanced thermal conductivities of nanofluids containing graphene oxide nanosheets[END_REF] noticed a significant thermal conductivity enhancement (61.0% with 5.0 vol.% nanoparticles) of ethylene-glycol-based GO nanosheets nanofluid independently of the test temperature. Then they prepared GO nanosheets nanofluids with different base fluids (distilled water, propyl glycol and liquid paraffin) and found that the Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets 0.1 eV energy step. All spectra were acquired at 90° between X-ray source and analyzer with the use of low energy electrons and low energy argon ions for charge neutralization.

Fig. 5 .Figure 5 . 1

 551 Figure 5.1 Characterization results of GO and rGO-PEG nanofluid: (a) UV-vis

Chapter 5 Figure 5 . 3 Figure 5 . 4

 55354 Figure 5.3 Sedimentation of graphene nanofluids: (a) 0.25 mg/ml GO, and (b) 1 mg/ml

Figure 5 . 5

 55 Figure 5.5 Microscopic photographs of nanoparticle deposition from graphene

Fig. 5 .

 5 6, the contact line of a 0.8 mg/ml rGO-PEG nanofluid droplet is shown (22 °C environmental temperature, 50% relative humidity). As evaporation progresses, the nanoparticles separate into three layers: (1) sediment at the solid/liquid interface, (2) a stream towards the contact line by capillary flow, and (3) dispersion at the air/liquid interface. Some larger particles deposit at the bottom of the droplet in the first stage of sedimentation; they remain in their initial location throughout evaporation. The stream of graphene nanoparticles is transported by an outward capillary flow, and during the early stage of evaporation, the nanoparticles move slowly toward the droplet periphery with fluctuations, indicating Brownian motion. Because of the high contact angle, these nanoparticles can reach a location very close to the contact line and accumulate there, forming the first ring. At the same time, the remaining nanoparticles, which are out of the outward flow, disperse homogeneously at the air/liquid interface. As a result of Droplets evaporation, the contact angle decreases slowly and the nanoparticle dispersion is also slowly driven to the summit of the droplet by the surface tension of water. As the evaporation progresses, the velocity of the outward nanoparticle stream increases and the nanoparticle dispersion at the air/liquid interface shrinks more rapidly. During the last

Figure 5 . 6

 56 Figure 5.6 Evaporation along the contact line. Photographs from the microscopic video

Figure 5 . 7

 57 Figure 5.7 Evaporation rates for pure water and 0.25 mg/ml graphene nanofluid (GO and

Figure 5 . 8

 58 Figure 5.8 Evaporation of droplets of (a) rGO-PEG nanofluid and (b) water, for different

Figure 5 . 9 Figure 5 .

 595 Figure 5.9 Initial temperature difference across the droplet surface as a function of

  considerable thermal conductivity enhancement can be achieved in water-based graphene nanofluid with a very low volume fraction. Temperature T s (°C) Dynamic viscosity µ (mPa•s) Volumetric heat capacity C p,v (J•cm -3 •K -1 ) Thermal conductivity k (W•m -1

Figure 5 .

 5 Figure 5.11 Dynamic viscosity as a function of temperature, for pure water and 0.25

Figure 5 . 12

 512 Figure 5.12 Relation of surface tension and temperature for pure water and 0.25 mg/ml

Figure 5 . 14

 514 Figure 5.14 Dependence of the thermal Marangoni number on substrate temperature, for

Figure 5 . 15

 515 Figure 5.15 Relation between evaporation rate and thermal Marangoni number, for pure

  confirmed with the aid of infrared thermography and acoustic echography. When deposited on heated substrate, the pure 1-butanol droplet does not show any thermal instability at different substrate temperatures while the co-existence of thermal and solutal Marangoni flows was observed for 1-butanol-water mixture droplet at substrate temperature of above 50 °C. Thermal Marangoni flows appear on the surface of pure water droplet when substrate temperature exceeds 50 °C. By comparing with pure 1butanol and water droplets, the evaporation rate of 1-butanol aqueous solution droplet is enhanced by the contribution of solutal Marangoni effect which is induced by inhomogeneous distribution of 1-butanol concentration at liquid/vapor interface. By analyzing the relationship between the experimental data and prediction of Hu and Larson model as a function of thermal Marangoni number, a series of empirical equations was developed to calculate overall and initial time evaporation rate of pure water droplet at different substrate temperature. And then by including solutal Marangoni effect, the empirical equations were derived to calculate evaporation rate before depletion time and at initial time for 1-butanol-water binary droplet which are based on precedent equations.

Table 3 .

 3 [START_REF] Gan | Combustion of nanofluid fuels with the addition of boron and iron particles at dilute and dense concentrations[END_REF]

	Water+5%1-Butanol	989	33.60	2.56
	Ethanol	789	22.31	5.80
	Water+5%ethanol	988	56.41	2.81
	Water+25%ethanol	946	36.09	3.44
	Water+50%ethanol	894	28.51	4.23

1 Physical properties of fluids and (100) silicon at 22 °C and 1 atm.

Table 3 .

 3 [START_REF] Hendarto | Size sorting of floating spheres based on Marangoni forces in evaporating droplets[END_REF], one can extract relevant parameters, such as the necessary time t C0 for the concentration to decrease to zero. The precision on t C0 is approximately 15 s. Tab. 3.2 summarizes the t C0 times for the different concentrations of ethanol and 1-butanol.

	C m (%)	t C0 (s) ethanol	t C0 1-butanol
	5	230 ± 15 s	220 ± 15 s
	25	330 ± 15 s
	50	405 ± 15 s
	100	420 ± 15 s

2 t C0 for the different concentrations of ethanol and 1-butanol

Table 5 . 1

 51 Enhancement of evaporation rate by addition of graphene nanoparticles. (Data from Fig.

	5.1

  Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets low nanoparticle concentration. The thermal conductivities of rGO-PEG nanofluid were calculated by applying the model of Leong et al.[START_REF] Leong | A model for the thermal conductivity of nanofluids-the effect of interfacial layer[END_REF] (which includes the effect of the

	interfacial layer):
	eff	((	p	lr	)	p lr	[2	3 l	3	1] (	p	2 ) lr
	addition of rGO-PEG nanoparticles increases with temperature. The heat capacity for
	graphene nanofluid with PEG was measured by differential scanning calorimetry
	(incertitude ± 1 %) under 10 bar of nitrogen. In Tab. 5.2, the heat capacities of rGO-PEG

nanofluid at different temperatures are very similar to those of water because of the very 123 Chapter 5

Table 5 . 2

 52 •K -1 ) Physical and thermal properties of (i) water and (ii) rGO-PEG nanofluid (0.25 mg/ml), at specified temperatures. Droplets

		Water	rGO-PEG Water	rGO-PEG Water	rGO-PEG
	22	1.002	1.08	4.174	4.19	0.5984	1.7961
	50	0.547	0.65	4.131	4.13	0.6435	1.9314
	66	0.429	0.52	4.103	4.10	0.6596	1.9797
	84	0.339	0.39	4.071	4.07	0.6721	2.0173
	106	0.270	0.34	4.032	4.03	0.6801	2.0414

(a) Contact angle (b) Volume

Scientific and Engineering Research, 3, 2229-5518.

Acknowlegements

Acknowledgements

I would like to express the deepest appreciation to all people who helped, encouraged and supported the accomplishment of my PhD dissertation. First of all, a thank you to my supervisors Prof. Souad Harmand and Prof. Maxence Bigerelle, who gave me this opportunity and continuously offered insights and guidance throughout my PhD study. I would also like to express my gratitude to Prof. Rachid Bennacer and Dr. Cherifa Abid for spending valuable time to provide very helpful feedbacks and advices to improve my research. I would like to acknowledge the rest of my committee members Dr. Valérie Sartre, Dr. Julien Carlier for sharing their ideas and advising me throughout this process.

Based on the analysis mentioned previously, after the exhaustion time t f , the 1-butanol is practically depleted in the mixture drop and a similar behavior as the water drop can be observed. Hence, the evaporation enhancement by addition of 1-butanol is only effective before t f . Fig. 4.9 shows the comparison of the evaporation rate until exhaustion time between the water and 1-butanol aqueous solution drops. With the solutal Marangoni effect, the mixture drop possesses a higher evaporation rate than the water drop from ambient temperature and this enhancement increases with increasing substrate temperature. However, at T s = 80°C, the gap becomes unexpectedly very slight and both drops have similar evaporation performance. The blue dashed line represents the prediction of evaporation rate by Hu and Larson's model. Except for the ambient case, the Hu and Larson's model always underpredicts the evaporation rate until t f of the water Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets concentration, they found that the thermal conductivity enhancement is independent of the base fluid viscosity, which is contrary to the micro convection theory.

Four possible mechanisms of heat flow in nanofluids are proposed by Keblinski et al. [START_REF] Keblinski | Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids)[END_REF] to explain the anomalous enhancement in thermal conductivity: Brownian motion of the particles, molecular-level layering of the liquid at the liquid/particle interface, the nature of heat transport in the nanoparticles, and the effects of nanoparticle clustering.

The other theories such as micro convection [START_REF] Kumar | Model for heat conduction in nanofluids[END_REF], nanoparticles interaction [START_REF] Xuan | Heat transfer enhancement of nanofluids[END_REF], thermo-phoretic motion [START_REF] Koo | Impact analysis of nanoparticle motion mechanisms on the thermal conductivity of nanofluids[END_REF] etc. are proposed as responsible for the significantly improved thermal conductivity of nanofluids. However, thermal conductivity is only one aspect of thermal characteristics and the practical application of nanofluid in heat transfer improvement is still controversial. Chen et al. [START_REF] Chen | Effects of nanoparticles on nanofluid droplet evaporation[END_REF] applied the pendant drop method to examine the effect of evaporation rate of different nanofluids (Laponite, Fe 2 O 3 and Ag) and the experimental results revealed that the additive PVP can not only stabilize the nanofluid solution, but also significantly enhances the evaporation rate of Ag nanofluid by comparing to the base fluid. Yang et al. [START_REF] Yang | Heat transfer properties of nanoparticle-in-fluid dispersions (nanofluids) in laminar flow[END_REF] reported the increase of heat transfer coefficient in laminar flow by application of graphite nanofluid and they supposed instinctive high thermal conductivity and interaction between nanoparticles to be possible reasons. Naphon et al. [START_REF] Naphon | Experimental investigation of titanium nanofluids on the heat pipe thermal efficiency[END_REF] applied deionized water, alcohol, and nanofluids (alcohol and titanium nanoparticles) as working fluid in heat pipe fabricated from straight copper tube and 10.60% higher thermal efficiency was gained with 0.10 vol.% nanoparticle loading compared to base fluid. You et al. [START_REF] You | Effect of nanoparticles on critical heat flux of water in pool boiling heat transfer[END_REF] investigated the critical heat flux (CHF) in pool boiling with aqueous Al 2 O 3 nanofluids whose concentration varies from 0 to 0.05 g/l. A dramatic enhancement of approximately 200% in CHF was observed with 0.005 g/l Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets addition of GO leads to a larger enhancement of thermal conductivity in base fluid, which possesses lower thermal conductivity [START_REF] Yu | Experimental investigation on thermal conductivity of nanofluids containing graphene oxide nanosheets[END_REF]. Additionally, Kim and Bang [START_REF] Kim | Effects of graphene oxide nanofluids on heat pipe performance and capillary limits[END_REF] reported thermal resistance decrease and heat transfer coefficient enhancement at the evaporator section of heat pipe with application of GO/water nanofluid. Azizi et al. [START_REF] Azizi | Experimental analysis of thermal performance in a two-phase closed thermosiphon using graphene/water nanofluid[END_REF] reported an improvement in thermal performance and overall heat transfer coefficient in two-phase closed thermosiphon filled with graphene/water nanofluid.

In the present study, we examined the potential of PEG-functionalized reduced graphene oxide (rGO-PEG) nanofluid in heat transfer enhancement. rGO-PEG was synthesized in a two-step process from GO. The droplet evaporation performance of rGO-PEG nanofluid, basic phenomenon in heat transfer, is investigated and compared with normal graphene oxide (GO) nanofluid and base fluid (water). The effects of nanoparticle concentration and substrate temperature on evaporation rate are also assessed in this study.

Experiment Method

Synthesis of GO and rGO-PEG

All chemicals were of reagent grade or higher and were used as received unless otherwise specified. Graphite flakes, chloroacetic acid, sodium hydroxide, poly(ethyleneglycol) bis-(3-aminopropyl) (Mw=1.5 kDa), mercaptoethanol, N-(3-dimethylaminopropyl)-N'ethylcarbodiimide (98%, EDC), acetonitrile, methanol and dichloromethane were purchased from Sigma and used as received. GO was prepared from native graphitic flakes according to the modified Hummer's method [START_REF] Fellahi | Silicon nanowire arrays-induced graphene oxide reduction under UV irradiation[END_REF]. Carboxylated rGO (rGO-COOH) was synthesized from GO as described by Turcheniuk et al. [START_REF] Turcheniuk | Infrared photothermal therapy with water soluble reduced graphene oxide: shape, size and reduction degree effects[END_REF]. In short, Chapter 5 Effect of Multi Factors on Evaporation Performance of Graphene Nanofluid Droplets sodium hydroxide (NaOH, 1.4 g) and chloroacetic acid (Cl-CH 2 -COOH, 1 g) were added to 50 mL of an aqueous solution of GO (20 mg) and sonicated at 35 kHz for 2 h at 80°C to convert hydroxyl groups present on GO to COOH via conjugation with acetic acid moieties and partially reduce GO to rGO. The rGO-COOH solution was quenched with HCl (20%), washed (four times) with distilled water until neutral pH and purified by repeated cycles of centrifugation (4000 rpm, 20 min)/rinsing.

Characterization results

Absorption spectra were recorded using a Perkin Elmer Lambda UV/Vis 950 spectrophotometer in plastic cuvettes with an optical path of 10 mm. The wavelength range was 200-800 nm. Zeta-potential measurements were performed using a Zeta-sizer Nano-ZS (Malvern Instruments Inc. Worcestershire, UK). Samples were diluted to 25 µg/mL and measured in Milli-Q water at pH 7.0. Micro-Raman spectroscopy measurements were performed on a Horiba Jobin Yvon LabRam HR micro-Raman system combined with a 473-nm (1 mW) laser diode as excitation source. Visible light is focused by a 100× objective. The scattered light is collected by the same objective in backscattering configuration, dispersed by an 1800 mm focal length monochromator and detected by a CCD camera. X-ray photoelectron spectroscopy (XPS) measurements were performed using a PHl 5000 VersaProbe -Scanning ESCA Microprobe (ULVAC-PHI, Japan/USA) instrument at a base pressure below 5×10 -9 mbar. Monochromatic AlKα radiation was used and the X-ray beam, focused to a diameter of 100 µm, was scanned on a 250×250 µm surface, at an operating power of 25 W (15 kV). Photoelectron survey spectra were acquired using a hemispherical analyzer at a pass energy of 117.4 eV with a 0.4 eV energy step. Core-level spectra were acquired at a pass energy of 23.5 eV with a

Results and Discussion

Experimental results at ambient conditions

In this research on evaporation performance, graphene oxide (GO, 0.25 mg/ml), and rGO-PEG (0.25 and 0.8 mg/ml) nanofluids were tested on a hydrophilic sapphire substrate. A droplet of pure water was also tested for comparison. The PEGylation of rGO was applied to improve solubility and stability of the graphene nanofluid and thus prevent its sedimentation. Fig. 5.3 shows photographs of GO and rGO-PEG nanofluid samples, three months after preparation. The GO nanofluid (Fig. 5.3(a)) has apparent graphene nanoparticle sediment at the bottom of the bottle, while the rGO-PEG nanofluid