Experimental Droplet Study of Inverted Marangoni Effect of a Binary

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Experimental droplet study of inverted Marangoni effect of a binary liquid mixture on a non-uniform heated substrate. Safouene Ouenzerfi, and Souad Harmand Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b04539 • Publication Date (Web): 16 Feb 2016 Downloaded from http://pubs.acs.org on February 20, 2016

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Langmuir

Experimental droplet study of inverted Marangoni effect of a binary liquid mixture on a non-uniform heated substrate Safouene Ouenzerfi, Souad Harmand *

LAMIH, UMR CNRS 8201, Université de Valenciennes et du Hainaut-Cambrésis

KEYWORDS: Marangoni effect, Surface tension, Infrared camera, self-rewetting fluids, Temperature gradient

ABSTRACT: We present an experimental study on the inversion of the Marangoni effect of a binary mixture droplet under a horizontal temperature gradient. In particular, we studied the dynamics and the evaporation behavior under these conditions. We show that a binary mixture (97% water - 3% butanol) droplet tends to migrate to warmer areas as opposed to spreading in pure fluids. During the evaporation process, we distinguish three stages of evaporation that are correlated to the dynamics of the droplet.

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INTRODUCTION Because of its practical and fundamental importance, droplet evaporation with its complicating features of surface regression, transient energy and species diffusion has been the subject of a large number of analytical [1, 2], experimental [3, 4] and computational [5, 6] studies over the timespan of several decades. In particular, numerous studies [7, 8] have been performed to understand the influence of the surface and substrates on the evaporation process of sessile drops. For instance, Sobac et al. [9] who conduct experiments with five fluids (methanol, ethanol, propanol, toluene and water) and four coatings (PFC, PTFE, SiOC and SiOx), reveal that the more wet and pinned a drop, the shorter the evaporation time. Some researchers extend the wettability separate from the evaporation process to control the droplet motion using a surface tension gradient. A gradient in surface tension resulting from nonuniformity in chemical composition, thermal gradients or electric fields [10, 11] causes an imbalance of tangential stresses at fluidic interfaces resulting in local or bulk flow or deformation. Flow under the effect of surface tension gradients is termed Marangoni flow after the observations made by Carlo Marangoni, who studied the spreading of oil on the surface of water [12]. Thermocapillary driven motion has been the subject of different experimental, numerical and theoretical research in the last decade. The idea of using a temperature difference as a driving force for moving drops was first discussed by Bouasse [13], who performed experiments with an oil drop on a slightly tilted metal wire. The drop moved upwards (against gravity) when the lower end of the wire was heated. Following this pioneering work, Brzoska [14] and Chen [15] studied droplet motion on non-wettable surfaces (silanized silicon wafers) with horizontal temperature gradients. They concluded that contact angle hysteresis is responsible for droplet


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pinning when the thermal gradient imposed on the substrate is below a threshold predicted by the theoretical work of Nadim [16]. One of the earliest theoretical studies was conducted by Brochard et al. [10]. Following that work, several theoretical models have been performed [17], from 2D investigation [16] to 3D modeling [18]. Numerically, Hu et al. investigate in [19] how the localized heating from a laser can block the microfluidic droplet motion through the induced thermo-capillary forces and explained [20] that the orientation of the droplet migration caused by the thermo-capillarity strongly depends on the contact angle between the droplet and the substrate surface. These studies are of central importance in the design of devices ranging from microfluidics to bio-chemical sensing [21]. For cooling system applications (e.g. a heat pipe), when a temperature gradient is applied along the pipe axis, surface tension-driven flows arise that travel from the hot side to the cold side (due to the Marangoni effect) and therefore oppose the liquid flow directed from the condenser towards the evaporator. This reduces the amount of liquid supplied to the evaporator, decreasing heat transfer, and leading to dry-out at lower power inputs [22]. Recently, others researchers [23] suggest replacing common pure liquids used in conventional heat pipes by an aqueous solution of long chain alcohols. Such fluids are also called selfrewetting fluids, in which the dependency of the surface tension with temperature is inversed in some ranges and the Marangoni forces are inversed as well [23-25]. To the best of our knowledge, few investigators [26-28] have studied the inversion of the Marangoni effect for a sessile droplet or bubble under a temperature gradient. For instance, Tripathi et al. [27] discussed modeling on the motion of a bubble driven by in a tube with a nonuniformly heated walls in inversed Marangoni situations. Liu et al. [28] consider numerically the inverted Manrongoni in a droplet. In this work, we present, for the first time, an experimental


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study of the evaporation and motion on non-uniform heated substrate of a butanol-water binary mixture (a dilute aqueous solution of high carbon alcohols) at the droplet level (micro studies). The Marangoni effect arises when there is a variation in the surface tension along a liquid surface. It produces movement from regions of low surface tension towards those at high surface tension. Marangoni flow can be the result of concentration and/or temperature gradients. In a linear approximation the surface tension variation σ/ along the interface is related to the temperature and specie concentrations by [10]: = +

(1)

Usually, the effect is called the solutal Marangoni effect in the case of a concentration gradient and the thermo-capillary effect in the case of a thermal gradient. Onuki [29] develop a further formulation which involve the chemical potential. With a thermal gradient, a drop placed on a surface will move from the warm side to the cold side [10, 19] due to the dependence of surface tension on temperature. Surface tension decreases as temperature increases for the majority of pure fluids as shown in Figure 1 (for pure water and pure butanol). Therefore, in liquid systems with interfaces and temperature gradients, it is expected to observe surface flows directed from the cold to the hot regions, for temperatures higher than that of the minimum of the surface tension. In that case, the relationship between surface tension and temperature can be expressed linearly as presented by Karapt [26]: = + ( − )

(2)

where = | and denotes the surface tension at the reference temperature . The values of for different pure fluids are calculated in Table 1.


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Pure water

σ (mN/m)

Water-3%butanol solution

Pure butanol

70 60 50 40 30 20

T (˚C) 10 20

30

40

50

60

70

80

Figure 1: Surface tension-temperature behavior for pure fluids and a water butanol mixture Self-rewetting fluids (dilute aqueous solutions of high carbon alcohols), present a particular characteristic showing a decrease in the surface tension with increasing temperature at a specific critical temperature. In such cases, the Marangoni effect can be inverted and may lead to movement toward the hotter regions. In fact, because these solutions are non-azeotropic, the alcohol-rich component preferentially evaporates in the course of the liquid/vapor phase change. The surface tension gradient along the liquid-vapor interface, caused by both temperature and concentration gradients, is therefore expected to spontaneously transport liquid toward hot spots or dry patches on the heater surface. Basically, a nonlinear constitutive relation relates the interfacial tension to temperature. We choose the following model to describe this relation [26]: = + ( − ) + ( − )

(3)

where = . Surface tensions of several fluids, pure liquids and binary mixtures have been evaluated at different temperatures using the pendant droplet method. In particular, in this work solutions


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with a small concentration of butanol (3%) in water have been investigated. The measurements have been performed in the temperature range 20–80°C (Figure 1), and the values of and for each fluid are expressed in Table 1. Fluids

Pure water

Pure butanol

Water and 3% butanol

(mN/m)

76.379

26.295

62.525

C1

-0.1718

-0.0831

-0.9941

C2

-

-

0.0101

Table 1: Model’s coefficients for the relationship surface tension-temperature The main topic of this paper is an experimental fundamental consequence of the inversion of the Marangoni effect as movement toward the hotter regions and its effect on the evaporation of sessile drops. In the first part, we explain the principle of the Marangoni effect for both pure and self-rewetting fluids. We also present a key modeling of the displacement based on balance equilibrium equations. Experimental analysis for inversion of the direction of droplet motion for a butanol-water solution are presented in the second section. We discuss as well the evaporation process in such a binary mixture. Finally, section three contains concluding remarks.

MODELING When the droplet is deposited on the surface, two temperature gradients are established. The first one is related to the liquid/solid surface, and the second one results in tangential stresses along the liquid/gas interface. Thus, we account for three Marangoni forces, as shown in Figure 2.


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Figure 2: Force balance on the droplet -

Marangoni forces exerted at the solid/liquid surface

We estimate the force exerted by the solid on the drop due to and at the contact line which we note . We assume the footprint of the drop to be a circle (see Figure 2). The solid-gas and solid-liquid interfacial tensions cannot be estimated directly but are estimated as a function of the liquid-gas interfacial tension γ using Young’s equation: − = . cos where

!

!

(4)

is the equilibrium contact angle.

Integrating the circle surface, we get = "#

$ cos

%$!

= "#

$ $& . cos $&

%$(5)

!

where & is the substrate temperature given by: & = '. % + & .We note

(

= )


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= ' "# ) . cos -

!

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(6)

Marangoni forces exerted at the liquid/gas interface

We present below the temperature distribution measurements on the liquid/gas interface. We distinguish two different gradients of temperature so two opposing Marangoni forces in the interface because the rim of the droplet is cooler. However, the gradient toward the hotter regions is higher so the direction of total force is positive (towards higher T).

Figure 3: forces’ projection Basically, spatial variation in the surface tension results in added tangential stresses. We define as the Marangoni forces exerted in the interface in spherical coordinates. We distinguish the pulling stress in the direction of low temperature and ) the one directed to high temperature side. The projection of the pulling stress along the y axis is given by [17]: *+, *

-

- -1 . sin ( 1 -.

= -. . sin ( ) = -

)

(7)

where Ti is the droplet temperature at the liquid/gas interface. Integrating over the droplet surface (in Cartesian coordinate), we obtain the total pulling Marangoni force in the liquid /gas interface: = 2"#

3333 %

(8)

where


8

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7

3333 8 = 5 sin 6 ( ) .$ %4 8 %

There are also two main forces that influence the motion of the droplet: the friction force (9 ), and the hysteresis force () ). Considering a laminar approximation of the flow: 9 = −6. ". R.η. v(t)

(9)

where R is the radius of the droplet, η is the kinematic viscosity and v(t) the velocity of the droplet motion. The hysteresis forces are given by [21]: ) = 2#(>?@ where

ro

and

A

− >?@ ao

B )

(10)

are the position-dependent receding and advancing contact angle,

respectively, and 2C(>?@

A

− >?@

B )

is the resistance force due to contact angle hysteresis.

Equations (11) and (12) describe the equilibrium balance of forces interacting in the motion of the droplet: E

D F = + + 9 + )

GHI

J F

(11)

K - J =2"# -. − 6. ". R.η. F +' ". # ) . cos

LM

where HI = N .

O6 PQR(S)T PQR (S)M RUV(S)M

!

− 2. #. (>?@

A

− >?@

, D is the displacement of the droplet and

B )

(12)

the contact angle.

EXPERIMENTAL SETUP The test bench is dedicated to the study of the dynamic and thermal behavior of a droplet placed on a substrate subjected to a linear temperature gradient to highlight the thermocapillary


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and Marangoni effects. The average diameter of the pure or binary mixture drops is approximately 4 mm. The studied substrates are both silicon and borosilicate glass (76 mm × 26 mm × 1 mm). We have to notice here that the CAH (contact angle hysteresis) is very high for such substrates and was estimated to be 15˚ using the tilted droplet measurement method for the silicon substrate [30]. To generate à linear temperature gradient, we use a Peltier element in the heat sink and a heating film on the hot spring at the same time (see Figure 3). The Peltier element is controlled by a water block system (see Appendix) to hold the set-temperature in the cold side. The heating film resistance have 7, 2 Ω as a resistance and is coupled to a power supplier 30V-6A. A conductive plate (aluminum with an insulating coating) is inserted to generate a linear temperature gradient. The substrate plate rests on the conductive copper plates. The temperature gradient is transposed into the substrate and remains linear. Temperatures for the heat sources are 120°C for the hot source and 0°C for the cold source. Thus we obtained, over 120 mm, a linear temperature profile with a slope of 0.5 K/mm, ranging from 20 ° C to 80 ° C. The distribution equation of the temperature, T, along the wall is given in Figure 4. Peltier

Y

Heater

Tw(˚C)

Tw = 0.5428y + 18.141

90 80 70 60 50 40 30 20 10 0 10

30

50

70

90

110

Y(mm)

Figure 4: Temperature gradient distribution along the substrate (infrared camera sketch)


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A controllable syringe pump was used to deposit correctly the droplet. The evolution of the drop dynamics is followed by a thermal infrared camera from FLIR sc7000 S systems with a resolution of 30 µm per pitch. A high speed USBEYE CCD camera was placed in front of the sample to be observed as shown in Figure 5. It is able to record 160 frames per second. The emissivity of the silicon substrates was measured to be (0.66).

Figure 5: Experimental setup for dynamic and thermal measurements RESULTS AND DISCUSSION 1- Droplet on the substrate side at T>Tc a- Dynamics In the present study, we deposit a 4 mm droplet diameter from a water and 3% butanol solution on a silicon substrate with a thermal gradient as described in the previous section. The droplet is placed in the region where T >Tc, corresponding to 63X, where Tc is the critical temperature from which the linear surface tension relation is inverted. Figure 6, providing simultaneous CCD


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camera and infrared snapshots, shows clearly that the droplet spreads and migrates toward the hotter regions against the standard temperature gradient. The motion of sessile droplets on such a non-isothermal solid wall is mainly driven by thermocapillarity. When the liquid droplet contacts a thermal gradient surface, the surface tension on the hot side is stronger than on the cold side. = + is mainly a result of the temperature-induced surface tension gradient. When FT is large enough to overcome the hysteresis forces, the droplet is pushed across the thermal gradient. The motion of the droplet is also accompanied by a considerable shift between the right and left contact angles. It is shown in Figure 7 that the difference between the two contact angles, ∆ , attains a maximum at the moment of migration of the drop toward hotter regions (t=4 s and t=16 s). This shift implies that the droplet is considerably deformed at this moment. We emphasize that the displacement is asymmetric. This is due to the asymmetric evaporation rate between the two edges caused by the right edge being hotter. Hence we can explain why the droplet seems to be moving only on the cold side. The rapid and asymmetric evaporation rate makes the visualization of the migration more difficult but not impossible [10].


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Figure 6: CCD and infrared camera snapshots for T>TC at different instants

Figure 7: Contact angle behavior of the droplet


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The deformation of the droplet can also be analyzed when we observe the following parameters in phase: volume, diameter and height, as described in Figure 8. For a constant volume (at time = 5 s, for example), the diameter decreases instantaneously when the height rises locally; the droplet deforms and moves.

Figure 8: Evaluation of the height, diameter and volume during the evaporation process for the water -3% butanol droplet b- Evaporation process We investigate, in Figure 9, the temperature distribution of the droplet along the position axis as a function of time. The curve presents as well the region that the droplets occupy. Thus, we can also observe the migration aspect in this graph by following the evolution of Y!ZF , which designates the end tip of the droplet. We can also estimate the time at which the displacement is stopped. This instant corresponds to the absence of the butanol residues because we suppose that the butanol evaporates first [31]. Basically, in the evaporation process of a binary mixture sessile


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drop, we observe three different stages related to the binary volatility of the mixture. The first stage corresponds mainly to the evaporation of pure alcohol, the second is a transitional stage where both components evaporate, and the third corresponds to the evaporation of pure water. After depositing the drop onto the substrate, the butanol molecules tend to move towards the solid and the liquid/air interface (especially the contact line regions) because of the lower surface tension of butanol and the stronger hydrophobicity of these interfaces. Thus, a convective concentration Marangoni flow (a solutal Marangoni flow in the vertical direction due to the variation in concentration) is created, replenishing the interface with butanol molecules from the center. Following Sefiane et al. [31], the first stage is characterized by a clear disturbed vortex, probably related to the movement and evaporation of butanol substances in principle. When the interfacial component (in this case butanol) is depleted, the intensity of the solutal Marangoni flow abruptly declines and we define the onset of the second, transitional, stage in which the two compounds evaporate. In the last stage, the butanol residues have nearly disappeared, and we observe a normal droplet water evaporation process. We can distinguish the three stages in Figure 10, showing the volume evaporation versus time. For the first 20 s, the evaporation rate is slow (with the smallest slope) which can be explained by the strong presence of butanol substances at the interface. The second stage presents a higher slope, indicating a higher evaporation rate, and ends at t = 80 s. The last region is similar to the characteristic of pure water evaporation with highest slope. This behavior can also explain why the migration of the droplet stops at around t=20 s corresponding to the decline of the Marangoni force in the horizontal direction.


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T(˚C) 78 75 72

Y!ZF

69 66 63 60 57 -3

-2

-1

0

1

2

3

Y (mm) t= 0 s

t=20s

t= 60 s

t= 120 s

Substrate temperature

Figure 9: Droplet temperature distribution along Y axis.

V*10-9 (m3) 4.5

7

4

6

-dv/dt*10-11 (m3/s)

3.5 5 3 2.5

4

2

3

1.5 2 1 0.5

Stage I

Stage II

0 0

15

30

45

60

1

Stage III

0 75

90

105 120 135 150 t (s)

0

10

20

30

40

50

60 t(s)

Figure 10: Volume and evaporation rate profile for T>Tc


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As explained before in the model, the rim of the droplet is colder. This leads to the creation of two opposite thermal Marangoni flows. To study these effects, we calculate in Figure 11.a the thermal Marangoni number on the left (cold side of the substrate) and right (hot) sides. The Marangoni number is the nondimensional number that gives the ratio between the thermocapillary effect and the viscous forces, and it is given by [' =

* ) ∆ *

.

].^

where _ is the

length height of the droplet in m, ∆ is the maximum temperature difference across the system in K, ` is the dynamic viscosity in kg/s/m, and a is the thermal diffusivity in m2/s. We can observe in this figure that the thermal Marangoni effect is more important on the hot side. When the butanol substances evaporate, the difference between the two Marangoni numbers is considerably reduced. Thus, the thermal Marangoni force on the interface weakens and the migration of the droplet ends completely. Figure 11.b provides the evolution of the solutal Marangoni number as a function of time ['b =

* ) ∆ *b

.

].c

. The key number in this case is the same as the thermal Marangoni number but the

first term is δσ/δc, where c is concentration and α, the diffusivity, is used instead of thermal diffusivity. The solute Marangoni number decreases when the concentration of butanol is depleted. Thus, with the absence of butanol substances, the solutal Marangoni effect in the vertical direction slows down.


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Solute marongoni number

Thermal Marangoni number 3000

80000

2500

70000 60000

MaS

2000

MaT

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1500 1000

50000 40000 30000

500

20000

0

10000 0

20

40

t(s)

Marangoni number left

60

80

100

120

0

20

40

60

80

100

t(s) marangoni number right

Figure 11: Thermal and solutal Marangoni number profiles A complete infrared on-top-shooting is shown in Figure 12. Here we can also differentiate the three stages according the behavior of the agitated substances (vortices). During the first stage, we notice the existence of a turbulent transparent thin layer which probably corresponds to the migration of butanol substances to the top interface. From t= 25 s, a second behavior is observed in which the transparent layer disappears. We can correlate this stage to the transition phase. The third stage presents sharper shades and a faster shape change (high evaporation rate corresponding to the water rate).


18

120

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Figure 12: Infrared sessile droplet visualization and investigation of the presence of butanol residues c- Comparison with theory:

We consider 8 the temperature of the interface as given by experimental data: 8 = ' (d) ∗ (% + f(d)) + b(t) 8 = 2 ∗ ' (d) ∗ ( % + f(d)) %

(13) (14)


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where ' (d) is a function determined from infrared experimental data and D(t) is defined as the displacement function of the droplet. ' (d) = 32.22 ∗ d − 6783.3 ∗ d + 1.092 . 10m (Post processing curves from Figure 12) 7

3333 = 5 sin6 ( ) . (n2 ∗ ' ∗ # ∗ >?@ + 2 ∗ ' ∗ f(d)o) ∗ $ % 8

(15)

-

where - = ) (t) 1

K - -.

K - -.

7

= p sin6 ( ) . ) . n(n2 ∗ ' ∗ # ∗ >?@ + 2 ∗ ' ∗ f(d)o)o $

N

= 6 ∗ ) ∗ ' ∗ f(d)

Hence we obtain the following differential equation: GHI

J F

=

m.7 6

J

∗ # ∗ ) ∗ ' ∗ f(d) − 6. ". R.η. F + ' ∗ " ∗ # ∗ ) ∗ cos

!

(16)

We then solve the differential equation numerically considering ) , a linear relation of butanol concentration which is equal to zero when the butanol substances are completely evaporated. Figure 13 shows the position of the water and 3% butanol droplets versus time, compared to the theoretical results of a numerical solution of the equation above. The experimental position is compared to Y!ZF . It is seen that qualitatively the theory reproduces the main trend found experimentally in terms of direction (toward hotter regions).


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The quantitative agreement of the calculated and observed displacement as a function of time is reasonable, given the simplifications used in the theoretical model. Indeed, the droplet migration stops when the butanol presence is depleted. In fact, the thermal Marangoni force is correlated to the derivative of surface tension (equation. 11), which depends on the concentration of butanol in water and determines the direction, migration or pinning of the droplet.

Figure 13: Positions of the droplet as function of time

2- Droplet on the substrate side at T=Tc

Tc is the critical temperature at which the behavior of the surface tension – temperature dependence changes. In this part we investigate the dynamics of the droplet near this specific


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x 0.000000001

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1 2 3 temperature. First, we present the evolution of volume versus time to determine precisely when 4 5 the butanol mixture effect disappears to highlight the Tc response only. 6 7 8 As we can see in Figure 14, the third stage takes place at t= 103 s. Thus, we are interested in 9 10 the dynamics of the droplet during the two first stages we observe in Figure 15, which includes 11 12 CCD camera views and the contact angle profiles, an oscillatory behavior in which the droplet 13 14 15 deforms toward both hotter and colder regions. The difference between the two contact angles, 16 17 ∆ , is an important value that indicates the deformation of the droplet. This value fluctuates 18 19 20 between positive and negative. We assume that at this temperature the standard Marangoni 21 22 forces and inverted ones coexist, so the droplet does not migrate but deforms. This deformation 23 24 is intermediate and oscillates in both directions. 25 26 27V*10-9(m3) -dv/dt*10-11 283 (m3/s) 2.5 29 30 2.5 31 2 32 332 34 1.5 35 1.5 36 37 1 381 39 0.5 40 0.5 41 Stage I Stage II Stage III 42 0 430 0 20 40 60 80 100 44 0 15 30 45 60 75 90 105 120 135 150 165 t(s) 45 t (s) 46 47 48 49 Figure 14: Volume and evaporation profiles as a function of time 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

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Figure 15: Deformation and contact angle behavior at T close to Tc

CONCLUSION In this paper, we presented an experimental investigation of the dynamics and evaporation of a self-rewetting fluid at the droplet level. We studied and analyzed the movements of a water3%butanol droplet. Above a certain temperature, the surface tension-temperature dependence for these fluids is inverted. In addition, the Marangoni forces established in a temperature gradient are inverted as well. We designed and set up an experimental test bench including infrared camera control. We observed the migration of the droplet toward the hotter regions (inverted direction) and we measured the accompanying changes in contact angle. The displacementn rate of the droplet was reasonable but not important due to the high hysteresis angle effect of the substrate. Karapst et al. [26] present several results in term of displacement and contact angle , however we are not able to compare with since they consider that the surface temperature Ts is


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the same at the wall Tw. Experimentally , we prove the existence of temperature gradient at the interface as predicted by Brochard [10] which has been to take in account. An oscillating behavior characterizes the point where T=Tc, which characterizes the evenhanded of Marangoni forces at this point. In conclusion, this study improves understanding of the inverted Marangoni effect on the dynamics and evaporation of a droplet at the micro scale and promotes better comprehension of different applications (heat pipe cooling studies as an example).

AUTHOR INFORMATION Corresponding Author * [email protected] ACKNOWLEDGMENT We acknowledge financial support of this research from University of Valenciennes.

REFERENCES (1) Victor, V. A. Evaporation of small drops. J. Appl. Phys. 1991, 10, 7034–7036. (2) Erbil, H. Y. Evaporation of pure liquid sessile and spherical suspended drops: A review. Adv. Colloid Int. Sci. 2012, 170, 67. (3) Carle, F.; Sobac, B.; Brutin, D. Experimental evidence of the atmospheric convective transport contribution to sessile droplet evaporation. Appl. Phys. Lett. 2013, 102, 061603.


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TABLES OF CONTENTS GRAPHIC

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Surface tension behavior for self-rewetting fluids and displacement of the droplet toward hotter region demonstrating the inverted Marangoni effect.


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APPENDIX

Figure 16: Water cooling system


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Experimental Droplet Study of Inverted Marangoni Effect of a Binary

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