The effect of thermal conductivity on enhanced evaporation of water

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The effect of thermal conductivity on enhanced evaporation of water droplet from heated graphene-PDMS composite surface Pratibha Goel, Moutushi Dutta Choudhury, Anas Aqeel, Xiying Li, Li-Hua Shao, and Huiling Duan Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00799 • Publication Date (Web): 06 May 2019 Downloaded from http://pubs.acs.org on May 7, 2019

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The effect of thermal conductivity on enhanced evaporation of water droplet from heated graphenePDMS composite surface Pratibha Goela,§, Moutushi Dutta Choudhuryb, Anas Bin Aqeela, Xiying Lia, Li-Hua Shaoc* and Huiling Duana* a

State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and

Engineering Science, College of Engineering, Peking University, Beijing 100871, P.R.China b

Department of Physics, Indian Institute of Science Education and Research, Mohali,

Punjab140306, India c

Institute of Solid Mechanics, Beihang University (BUAA), Beijing 100083, P.R.China

§

Present Addresses: Department of Chemistry, Imperial College London, SW7 2AZ, UK

*Address correspondence to [email protected], [email protected]

ACS Paragon Plus Environment

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ABSTRACT The dynamics of evaporating water droplet on heated graphene-polydimethylsiloxane (PDMS) composite are investigated experimentally and theoretically. By inserting graphene nucleates in PDMS, we report the effect of change in thermal resistance on the evaporation process of water droplet on the heated graphene-PDMS composite surface. By dispersing graphene within PDMS matrix, the evaporation of water droplet is enhanced. The graphene nucleate density over the surface was controlled by varying graphene wt% from 0 to 2% which in turn controls the thermal resistance and hence evaporation rate. Experimentally, the maximum evaporation rate of 0.0044 μl/s was observed for the sample of 2 wt% graphene-PDMS composite. The evaporation rate on 2 wt% graphene-PDMS composite surface is about 1.5 times higher compare to that of plain PDMS without graphene. Theoretical model confirms the initial contact angle and presence of thermal coupling between liquid droplet and the substrate play important role in evaporation dynamics. Thermal conductance increases three times with the increase in graphene wt% from 0.1 to 2.0 wt% in PDMS. The heat storing capacity of graphene is responsible for the enhanced evaporation. The experimental findings are in good agreement with theoretical results. These samples were found insensitive to degradation and may find potential applications where high efficiency and high heat flux are needed.

Keywords: droplet evaporation, thermal resistance, graphene, PDMS, thermal coupling


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INTRODUCTION Over the past few decades droplet drying became one of the mostly studied interdisciplinary subject for soft-condensed matter researchers because of its high impact on daily life and vast industrial as well as biological applications.1–4 The dynamic of droplet evaporation is greatly affected by substrate heating. Hu and Larson proposed a flow model which states that inside the droplet resulting Marangoni flow is due to the surface tension gradient.5 The droplet which makes larger contact angle with the substrate results into effective recirculation flow inside the droplet due to thermal convection. On the other hand, smaller contact angle changes the flow pattern and only capillary radial flow takes place for a pinned contact angle. The droplet evaporation dynamics have potential applications on DNA separation, particle separation and painting industry.1,3,6,7 Surface modification changes the evaporation dynamics which results into the change of flow inside the droplet. In the of evaporation process of droplet from heated surface, the contact angle (CA) of droplet changes in two different ways.8,9 A regular droplet on a hydrophobic surface alter its mode from constant contact radius (CCR) mode to constant contact angle (CCA) mode to de-pin from the three-phase contact line (TPCL). Sobac et al. summarized the substrate temperature and substrate thermal properties on a pinned drop evaporating from hydrophilic and hydrophobic surfaces.10 They have conducted an experiment and showed how contact line changes with increasing temperature even when the drop is pinned on the substrate. Heat transfer occurs by convection inside the drop and conduction in the substrate, driven by a latent heat contribution at the evaporating free surface. Thermal conductivity of the substrate plays an important role in evaporation dynamics of the droplet. For example, Dunn et al. showed experimentally and theoretically, the atmospheric pressure and thermal conductivity of the liquid and substrate have significant effects on evaporation rate of sessile droplets.11 Kim and Vermuri reported the onset of nucleate boiling of water at 30 % lower superheat on alumina


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nano-porous coatings compared to a plain surface.12 Ujereh et al. attached arrays of carbon nanotubes to silicon and copper substrates and used them in boiling experiments with FC-72 to find a heat-transfer-coefficient which results into enhancement upto 450 %.13 Recently, it has been reported that increase in pool boiling heat transfer can be achieved by imparting inplane variation in surface temperature onto flat surface using low conductivity material.14 However, they have used sophisticated instruments such as electrical discharge machining (EDM) for fabrication of samples. In this work, we have experimentally probed the effect of in-plane variation in thermal conductivity of graphene-polydimethylsiloxane (PDMS) composite surface on evaporation of water droplet. The graphene on the surface of graphene-PDMS composite substrate acts as a bubble nucleation centre by storing heat and results into the enhancement of water droplet evaporation. The experimental results are in good agreement with the values obtained from theoretical model.

EXPERIMENTAL SECTION Graphene-PDMS composite preparation Research grade graphene (5-50 μm) was purchased from Suzhou Hengqiu Nano Reagent and were used in original form. PDMS silicone elastomer obtained from Dow Corning (Sylgard 184) was used as the host matrix. A series of graphene-PDMS composite samples were fabricated by varying graphene amount from 0 to 2.0 wt% in the base polymer. The desired amount of graphene was added into the base polymer and thoroughly mixed by using glass rod for 5 min to facilitate the uniform distribution. A cross-linker was then added at a ratio of 1:10 to the PDMS base polymer and further mixed for 5 min. To remove the trapped air bubbles, the prepared liquid polymer mixture was degassed for about 30 min. Small amount (5 g per slide) of prepared liquid mixture were spin coated on the glass slide at 350 rpm for 90 s. The


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slides were then cured at 60 ºC for about 4 h to cross link the polymer. Once cured, the graphene-PDMS composites were peeled off from glass slide and cut into 1 cm x 1 cm pieces. The thickness of the samples was about 350 μm. Droplet evaporation measurement To study the effect of varying in-plane thermal conductivity on evaporation process of sessile liquid droplet, a droplet of deionized (DI) water of 3 μl in volume were deposited on the samples (varying graphene wt%) kept at surface temperatures (Ts) of 60 ºC. The sample was heated from below via a custom designed thermoelectric heater. The evaporation of droplet was recorded in the closed chamber with the opening at the top for inserting the water droplet. The environmental temperature was maintained at 26 ± 1 ºC and relative humidity was 60 ± 5 %. During evaporation, the front section (planer view) was recorded at 1 frames/s by using a video camera with suitable objective. The frames were extracted from the video by using Virtual Dub software (USA). From the recorded images of the water droplet the CA, droplet height and contact area radius were measured by using ImageJ software (National Institute of Health, USA).The measurements were repeated three times at different position of each sample while keeping the substrate temperature (T) and initial volume of the droplet constant. Sample Characterisation AFM (Bruker Dimension Icon) was used to record the surface topography and root mean square (rms) roughness of the fabricated samples. Since the graphene is not just present on the surface but thoroughly mixed in liquid PDMS, the samples are robust and insensitive to degradation. To test the adhesion of the graphene present on the surface, scotch tape was applied on the surface. After that, mechanical pressure was applied by hands to enhance the adhesion of tape to the sample. Then the tape was quickly (1 s) peeled off. No graphene residue was seen on the tape surface, indicating an excellent adhesion of the surface graphene with the sample. This confirms the samples are insensitive to delamination. This test was done three


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times at different places on the sample. Optical Microscope (Olympus) was used to capture the magnified image of the samples.

RESULTS AND DISCUSSION Figure 1 shows the extracted frames from the videos of evaporation of droplet on plain PDMS and graphene PDMS composite with varying wt% of graphene. The evaporation rate was highest for 2 wt% graphene-PDMS composite. There are bubble appears inside the droplet on graphene-PDMS composite surfaces.

Figure 1: Evolution of water droplet with time on graphene-PDMS composite surface with varying wt% of graphene (a) 0 wt%, (b) 0.1 wt%, (c) 0.5 wt%, (d) 1.0 wt%, and (e) 2.0 wt%.


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Figure 2 (a) and (b) shows the typical AFM images over 1.5 μm x 1.5 μm areas of plain PDMS and graphene-PDMS composite (2 wt%). The obtained rms roughness at different 1 μm x 1 μm areas are very small, 0.53 ± 0.05 nm and 1.38 ± 0.07 nm for plain PDMS and 2 wt% graphenePDMS composite surface, respectively. The rms roughness of other samples lies in between these two values for varying graphene quantity from 0 to 2 wt%. AFM imaging of the surfaces was conducted and repeated at many locations and showed similar values of rms. The purpose of the AFM imaging and rms data is to show that the roughness does not significantly change with the incorporation of graphene in PDMS. CA of water droplet was observed to be 114.9º ± 1.5º on flat PDMS surface. Maximum addition of graphene on the substrate changes negligible amount of CA (112.1º ± 1.5º) which further confirms that there is not much change in surface roughness as well as droplet geometrical configuration. The water droplet is in Wenzel state on flat PDMS surface and hence these surfaces could not trap vapor as the seed for the bubble nucleation for water droplet evaporation.

Figure 2: AFM image of (a) PDMS surface, and (b) 2 wt% graphene-PDMS composite surface. Inset in the figures shows the corresponding image of 3 µl droplet placed on the surfaces. Characteristics of droplet Evaporation The experimental finding reveals that evaporating droplet dynamics change with the presence of graphene in PDMS. The initial CA on different substrates does not diversify significantly i.e., the spreading coefficient is nearly the same for all the droplet on different substrate.


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Therefore, their initial shapes are clearly do not alter. Changes of radii or the contact angles are nearly same for all substrates (Figure 3). The mode of droplet evaporation is not only CCA or CCR modes. The contact angle (θ) varies non-linearly with time. For plain PDMS surface the relationship between θ and time t is: 𝜃 = 𝑎 + 𝑏. 𝑡 + 𝑐. 𝑡 *

(1)

The curve fitting provides 𝑎 = 106.523, 𝑏 = −0.06693and 𝑐 = 1.24 × 1056 . Whereas the contact radius r decays with t for simple PDMS substrate as, 𝑟(𝑡) = 𝐴 + 𝐵. 𝑡 + 𝐶. 𝑡 *

(2)

The value of parameters fitted as 𝐴 = 0.5618, 𝐵 = −2.96 × 1056 and 𝐶 = −2.37 × 105? .

Figure 3: (a) Contact angle and (b) contact radius of a water sessile droplet during evaporation from different substrates with different conductivity. The normalised volume(𝑉 ⁄𝑉A )vs t graph indicates clearly that evaporation curves are becoming steeper with increasing the amount of graphene in graphene-PDMS composite (Figure 4). The presence of graphene on the heated graphene-PDMS composite substrate changes remarkably the evaporation rate of a water droplet. Alrashdan et al. found that adding 10 % of graphene in paraffin could increase the thermal storage by 40 %.15 In similar way, the PDMS substrates


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also increases the thermal storage with the added graphene by remarkable amount. When the substrates are heated to 60 ºC, plain PDMS substrate is not able to change the upper substrate temperature within experimental time. The heat flux of the substrate increases with increasing

Figure 4: Experimentally observed trend of change in normalized volume with time for different substrate (varying graphene wt%). order of graphene. The heat flux depends on the thermal conductivity of the substrate as well as the ability of storing of heat energy of graphene nucleates. The bubble formation on graphene modified PDMS surface also confirms the heat storing capacity of graphene. With the increase in graphene nucleates on the surface, the number of bubbles formation also increases (video S1). Experimentally we have observed that dispersed graphene in PDMS increases thermal conductivity of the substrate and hence the evaporation rate of water droplet. The evaporation rate calculated from the experimental observation of rate of change of volume with time is given in table 1 which varies according to the thermal resistance (ɌD ) of the surface. Table 1: Evaporation rate of droplet with variation in graphene wt% in graphene-PDMS composite surface Weight percentage of graphene Evaporation rate (wt %) 𝑉̇ 𝑥 1056 (µl/s) 0.0 31.677 0.1 39.414 0.5 41.336 1.0 41.388 2.0 44.389


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The thermal conductivity of the substrates increases with the increasing graphene nucleate density. Graphene flocculate in the PDMS solution and after film formation they increase the opacity of the substrates. Accumulation of the graphene nucleates on the surface increases their heat storing capacity which enhances the evaporation rate of water droplet from the substrates. In the next section, we tried to justify our experimental views in terms of theoretical background of evaporation mechanism. Theoretical background of droplet evaporation incorporating thermal effects and comparison with experimental results For the cases of high energy surfaces, a droplet usually evaporates in CCR mode. It follows Langmuir equation of evaporation,16 GH GI

= −4𝜋

KLMNO P QRS

(3)

This equation is considered for a levitate droplet in air and molecular diffusion (D) of vapour molecules from the droplet to the surrounding gas is assumed to be a limiting mechanism. Here P is vapour pressure, which is very low, since the liquid is not very volatile. M is the molecular weight, r and ρ are the radius and density of the droplet respectively. R is the ideal gas constant and T is the temperature. Introduction of the substrate to the system changes the droplet shape as well as the evaporation mechanism. The evaporation rate is reduced by incorporation of the substrate. Picknett and Bexon introduced a factor which reflects the interaction between the droplet and the solid substrate f (θ), where θ is the contact angle of the liquid with the substrate.17 When a liquid droplet is deposited on the non-conducting solid substrate, the droplet is considering to be evaporated with saturation concentration Cs(Ta) and according to “isothermal diffusion theory” the rate of volume change takes the form,17 GHT GI

=−

UL(S)VW (SX ) Q

𝑟G (𝑡)𝑓(𝜃)


(4)

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The saturation concentration highly depends on the temperature, another temperature dependent part is D which is proportional to 𝑇 [⁄* .18 𝑟G (𝑡) is the time varying base-radius of the droplet interacting with the substrate. During evaporation, if the contact angle changes with time, then𝑓(𝜃) also changes with time. The most updated value of f (θ) for q < 90º is given by Hu-Larson which is equal to19,20 𝑓(𝜃) = 0.27𝜃 * + 1.3

(5)

But in the our case, the surface was partially hydrophobic with 𝜃 ≈ 120ᵒ and f (θ) term takes the form,21 q bc de^g *ah

^_` a

𝑓(𝜃) = (bc de^ a) + 4 ∫r

^_`g *Uh

tanhm(𝜋 − 𝜃)𝜏o 𝑑𝜏

(6)

where 𝜏 = 𝑡t𝑡 , 𝑡s is considered as a parameter which is involved to make the function f(θ) s

dimensionless and it depends on the geometrical configuration of the drop on the substrate. Interaction of drop with the heated substrate involves thermal coupling coefficient g which is first introduced by Sefiane et al. in 2011.22,23 The eq. (4) is modified by including a substrateliquid interface characteristic constant (thermal coupling coefficient) ` 𝑔 ’ as GH GI

=−

UL(S)VW (SX ) Q

𝑟G (𝑡)𝑓(𝜃)𝑔

(7)

The thermal coupling 𝑔 occurs between the solid substrate and the droplet. Vi is the initial volume which is deposited on the substrate and V(t) is the instantaneous volume of the drop. The energy balance equation for small section of the substrate is given by,22 GH

x

Ł = (𝑇w − 𝑇A ) Ɍ GI

yz

(8)

R (R c R )

Here Ɍ{| = R} c RO c RW is the equivalent thermal resistance. Rs, Rl and Rg are the thermal }

O

W

resistances of the solid substrate, liquid droplet and the gas, respectively. The resistance change in the present system is due to the change in resistance of substrate (Rs). Total heat transfers through the surface is considered by the contact area (S) of droplet with substrate which is


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given by 𝑆 = 4𝜋rG * . Ł is the latent heat of vaporization, Ta and Ti are the ambient temperature and interfacial temperature of the liquid droplet and solid substrate respectively. Therefore, we can clearly see from the theoretical background that the enhanced evaporation rates on graphene-PDMS composite surface with varying graphene wt% is mainly due to I.

The varying thermal resistance Ɍ{| with change of the substrate resistance Rs

II.

The diffusion coefficient D and

III.

Saturation concentration,𝐶D (𝑇A ) = 1 − 𝑎b (𝑇w − 𝑇A ) 𝑎b =

€

•‚W „⃒ƒ †ƒX T •ƒ

(9)

VW (SX )

Using eqs. (8) and (9) incorporate the temperature coupling and the final term of the volume evaporation rate of the droplet becomes, GH GI

=

ḢT

(10)

‰̇ ŠŁɌyz Œ bc w‡ ˆ T ‹

From eq. (4), the results extracted are plotted as shown in Figure 5 (solid curves).

Figure 5: Comparison of experimental values (dots) of evaporation rate with theoretical values (solid curves) with consideration of contact angle of the droplet with substrate for 𝜃 > 90ᵒ. Where 𝐶{| represents the heat-conductivity of the substrate and is given by


Ɍ{| Ž𝑆 . {

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We have considered the non-linearity [eq. (1) and (2)] in f(θ) and rd. The trivial solution of eq. (4) gives 𝑉̇A . 𝑉̇A is the evaporation rate of the droplet in isothermal condition. From that we ••

GV

derived the solution of eq. (10), where 𝐶D (𝑇w ) = 1.93 × 105* ‘’ and € GSW„ ⃒ ST “SX = ••

1.11 × 105[ ‘’ ” and pressure is 1 bar.24 Latent heat is considered to be Ł = 2264705 𝐽⁄𝑘𝑔. We get different graphs considering different f(θ) for different range of θ. We get the curve (Figure 5) for the higher range of θ (q > 90º) for which we used eq. (6) in eq. (4). We can clearly see from curves in Figure (5), equivalent resistance of the substrate decreases with increasing of graphene amount in the substrate if we consider the base contact area of drop behaves in similar way for all cases of the substrates. Here we have calculated 𝑉̇ for graphenePDMS composite surfaces considering the evaporation rate graphene free substrate and theoretical volume is scaled with the initial volume of the corresponding droplets. We consider 𝐶 =

𝑅{| t , the contact surface area varies distinctively when we change contact angle q. We 𝑆

have considered the heat conduction of graphene, which varies from 2000 W/mK to 4000 W/mK and the case of simple PDMS (heat conductivity 0.15 W/mK), so the heat-conduction of the composite varies of the order of 104 times. In this case we found heat conduction increased of the order of 101 times (Figure 5) where we consider the drop-surface interaction section changes similarly for all cases. We also have to keep in mind that the surface is not purely made with graphene. It's a composition of graphene and PDMS. Therefore, the conduction must be much less than that of pure graphene. Using f(q) from equ. (6) gives much more agreeable results than f(q) of equ. (5) for supporting particularly this case. Here the evaporation rate of the droplet is 1.81. Another scaling parameter is used to make f(θ) a dimensionless quantity, 𝑡s = 832. Figure 5 showing the comparison of experimental results (dots) with the theoretical ones (curves). The comparison of the theoretical results are well in agreement with the experimental results.


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Figure 6 shows the optical micrographs of different samples which further confirms graphene nucleate density on surface increases with the graphene wt% and this provides the increment of thermal conductivity of the substrates. In this study we clearly observe that increase in graphene wt % from 0 to 2.0 % promotes the evaporation rate of water droplet by enhancement in heat-flux. Theoretical results support the fact that thermal coupling between liquid and substrate plays a crucial role in evaporation. The “thermal coupling” [ 𝑔 (eq. (7)] involves

Ɍyz xy

which decreases with increase in graphene

nucleate density in the substrate.

Figure 6: Optical microscopic image of the substrate with varying graphene amount.

CONCLUSION In this study we investigated the effect of variation in in-plane thermal conductivity on evaporation rate of water droplet from heated graphene-PDMS composite. By incorporating highly thermally conducting graphene nucleates in PDMS imparts in-plane variation in the surface temperature. With increase in graphene wt% from 0 to 2 % further promotes the evaporation rate by heat storing capacity of graphene nucleates and results into heat-flux enhancement. Theoretical results support the fact that thermal coupling between liquid to substrate plays most crucial role in evaporation dynamics. With increase in graphene nucleate


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density, the thermal conductance increases and hence the evaporation rate increases. The theoretical results are in good agreement with the experimental finding.

ACKNOWLEDGEMENTS PG gratefully acknowledges Peking University, China for postdoctoral fellowship. MDC would like to thank IISER Mohali, India for providing research fund.

Supporting Information Available The video S1 shows the contrast in evaporation of water droplet from heated PDMS surface (left) and graphene-PDMS (2 wt%) surface (right). This material is available free of charge via the internet at http://pubs.acs.org.

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The effect of thermal conductivity on enhanced evaporation of water

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