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Applied Thermal Engineering

journal homepage: www.elsevier.com/locate/apthermeng

A comprehensive comparison between substrate heating and light heatinginduced nanofluid droplet evaporations

Xin Yana, Jinliang Xua,b, Zhijun Menga, Jian Xiea,b,⁎

a Beijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy Utilization, North China Electric Power University, Beijing 102206, Chinab Key Laboratory of Power Station Energy Transfer Conversion and System of Ministry of Education, North China Electric Power University, Beijing 102206, China

H I G H L I G H T S

• Nanofluid droplet evaporations heated by light plasmonic and substrate are studied.

• Two heating modes behave different flow fields and temperature fields in droplet.

• Distinct flow fields lead to different nanoparticle patterns for two heating modes.

• Droplet volume variation has different trends for two heating modes.

• Surface area decreasing and temperature rise determine the volume variation trend.

A R T I C L E I N F O

Keywords:Sessile dropletNanofluidEvaporationSubstrate heatingPlasmonic heating

A B S T R A C T

A comprehensive comparison between substrate heating and light plasmonic heating induced nanofluid dropletevaporations is presented. The substrate temperature was kept as 36.5 °C for substrate heating, but a 1400 W/m2

irradiation flux emitted by a xenon lamp was used for light heating. Both two heating modes yield constantcontact diameter evaporation. Because light irradiation reorganizes nanoparticles to generate dynamicallyvaried heat source in nanoscale due to the plasmonic effect, the two heating modes are found to display threedifferences. First, droplet surface temperature decreases monotonically from contact line to apex for substrateheating, but for light irradiation, droplet surface temperature displays nonmonotonic variation including acontact line region CLR and a bulk volume region BVR. Temperature gradient is significant in CLR but does notexist in BVR. Second, the substrate heating generates both radial flow and Marangoni flow in the whole droplet.Thus, coffee-ring and dispersed nanoparticles are observed on substrate. On the other hand, for light heating, theMarangoni flow is only confined in CLR due to the local temperature gradient there, creating most of nano-particles deposition near the contact line. Third, because the droplet surface area decreases versus time, theevaporation rate reduces to behave the non-linear variation of droplet volume for substrate heating. The si-tuation is changed for light heating induced droplet evaporation. The enhanced plasmonic heating in CLR due tonanoparticles deposition there offsets the effect of droplet surface area decreasing. Thus, light heating wouldgive rise to the constant droplet evaporation rate, which is distinct to substrate heating. This work enhances thefundamental understanding of the droplet evaporation dynamics under the condition of light heating inducedplasmonic heating effect.

1. Introduction

The sessile droplet evaporation is an important phenomenon innature and industries, such as 3D printing [1], pesticide spraying [2],biosensor [3], DNA mapping [4], and droplet-based microfluidics [5,6].In practical applications, the droplet evaporation may be heated bysubstrate or light. Both two heating methods induce complicated

droplet evaporation phenomenon, due to the coupling between flowfield and temperature field within the droplet [7–10].

The substrate heating induced droplet evaporation has been widelyinvestigated by many authors. Picknett [11] defined two evaporationmodes: constant contact angel CCA mode and constant contact diameterCCD mode. The CCA mode varies contact diameters by keeping aconstant contact angle, while the CCD mode is inverse to CCA regarding

https://doi.org/10.1016/j.applthermaleng.2020.115389Received 10 September 2019; Received in revised form 31 March 2020; Accepted 22 April 2020

⁎ Corresponding author at: Beijing Key Laboratory of Multiphase Flow and Heat Transfer for Low Grade Energy Utilization, North China Electric Power University,Beijing 102206, China.

E-mail address: xiejian90@ncepu.edu.cn (J. Xie).

Applied Thermal Engineering 175 (2020) 115389

Available online 23 April 20201359-4311/ © 2020 Elsevier Ltd. All rights reserved.

T

contact angles and diameters. Based on the assumption of quasi-steadyevaporation dominated by vapor diffusion, Popov [12] established acomplete theoretical model to predict droplet evaporation. For dropletsurface temperature measurement, an infrared thermography techniqueis introduced [13]. On a heated substrate, temperature differences be-tween droplet apex and contact line decrease gradually [13]. With ahigher substrate temperature, the model introduced by Popov [12]could not predict the experimental data precisely due to thermal effects[14]. With particles involved in droplet, the “coffee-ring” pattern wasformed because of the radial flow from droplet center to contact line[15]. The thermal properties of substrate and fluid can alter flow fieldto influence particle deposition [7]. Various particle patterns are re-viewed in Refs. [7,16].

Very few studies are reported on the light induced droplet eva-poration. Jiao et al. [17] used a 1550 nm infrared laser to heat waterdroplets on a hydrophobic surface. The droplet surface temperature andaverage evaporation rate increase quasi-linearly versus laser powers.Small satellite droplets come from condensed vapor are observed nearthe three-phase contact line [17]. Kita et al. [18] used a laser to heat apure water droplet. Marangoni flow and double-circulation vortex arecaptured by an infrared thermal camera. Hordy and Ta [19,20] de-monstrated the thermal response and evaporation rate of the nanofluiddroplet heated by a laser. Different from the substrate heating, the lightplasmonic heating induced droplet evaporation involves the compli-cated coupling between the heat source and the flow field in droplet,which is not well understood presently.

Recently, the nanofluid droplet evaporation with light plasmonicheating was experimentally studied [21]. It is found that the dropletevaporation rates behave a sharply increased regime and a constantregime when crossing a critical nanofluid concentration ci, cr. The ci, crrepresents the sufficient nanoparticles deposited at the region nearcontact line to generate heat. For nanofluid concentration >c ci i, cr, theredundant nanoparticles will be buried under the effective particlelayers to be useless. In Ref. [21], droplet evaporation with substrateheating is just mentioned to highlight the unique characteristics of lightplasmonic heating droplet evaporation.

In this paper, both light plasmonic heating and substrate heatingdroplet evaporation are investigated, which aims to get a comprehen-sive comparison between two heating methods. The experiment showsthat two heating methods have significant differences in the evapora-tion dynamics, surface temperature distribution, flow field and nano-particle deposition. To explain the different mechanisms of dropletevaporation between two heating methods, a vapor diffusion modelcoupled with energy and flow analysis is discussed.

2. Experimental section

Fig. 1 shows the schematic diagram of the experimental setups forsubstrate heating and light plasmonic heating. The main apparatusesconsist of a high-speed camera, an infrared camera, a micro-syringepump, a PMMA cloak, a Xe lamp (solar simulator) and a resistanceheater, etc.

The gold nanofluid droplet is generated by a micro-syringe and thenplaced on the clean quartz glass substrate. For all cases, the volume ofdroplets Vi is 1.98 ± 0.02 μL and the concentration of nanofluid ci is100 ppm. To prevent air disturbance, droplet evaporation process tookplace in a cylinder PMMA cloak. For light plasmonic heating, the ir-radiation intensity of Xe lamp is 1400 W/m2. For substrate heating, thetemperature of substrate Tw is 35.6 °C with which the droplet lifetime issimilar to the cases of light plasmonic heating. During the dropletevaporation, the ambient temperature and humidity are 25.0 ± 3.0 °Cand 30 ± 3%, respectively.

The droplet evaporation process was recorded by a high-speedcamera (Keyence, VW-9000), which behaves a spatial resolution of4.7 μm. Based on the recorded images, contact diameters D and contactangles θ are obtained by processing image files using MATLAB. HavingD and θ, droplet volume V at time t is

= − +V θ θθ

Dcos 3 cos 224sin

π3

33

(1)

The droplet surface temperature was measured by an infrared camera(Infrc Tec, ImageIR 5380), which has a temperature resolution of 0.02 Kat a spectral range of 3–5 μm. The measuring principle and data pro-cessing of droplet surface temperature were described in Ref. [21].

3. Results and discussion

3.1. Evaporation geometry characteristic

At the initial time, the droplet contact angle θi and diameter Di

are ~ 84.8° and 2.1 mm for both two heating methods. The CCD modewas obtained for both two heating methods as presented in Fig. 2a. Dueto the large pinning energy barrier to fix the contact line on the sub-strate, the CCD stage covers most of droplet lifetime [22]. Duringdroplet evaporation, the residual surface energy of droplet increaseswith decreasing θ. Approaching the droplet dry-out, since the residualsurface energy overcomes the pinning energy barriers, the dropletcontact line suddenly de-pins and recedes from the initial location [22].The residual liquid forms a smaller droplet with a larger θ to keepevaporation until it dries out. In the following contents, we just discussthe droplet evaporation process in CCD stage for light plasmonicheating and substrate heating.

Fig. 1. Schematic diagram of the experimental setups for substrate heating and light plasmonic heating.

X. Yan, et al. Applied Thermal Engineering 175 (2020) 115389

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The change of droplet volume is important to understand the masstransfer rate. At the initial stage of substrate heating, the data of dropletvolume V versus time t is around the black straight line (see Fig. 2b).Afterward, the data of V versus t deviates from the straight line and thedroplet evaporation rate decreases. As a result, the evaporation dropletlifetime extends 48 s (see Δt = 48 s in Fig. 2b). The result in Fig. 2b issimilar to the conclusion that the V–t would be non-linear whenθi > 45° [12,14]. In contrast, the light plasmonic heating induceddroplet evaporation perfectly follows the linear law of V–t. In Fig. 2c,the data of droplet volume are closely around a red straight line. Thedifferent trends of V–t for two heating methods are interesting andimportant. In this paper, we will investigate the cause of such distinc-tion gradually.

3.2. Droplet surface temperature and flow filed

Fig. 3 displays droplet surface temperatures. The substrate heatingand light plasmonic heating generate different surface temperaturefields. For substrate heating, as presented in Fig. 3a, temperature stra-tification is captured which is also reported by Fukatani et al. [23] andChandramohan et al. [24]. The highest temperature is at the contactline and unchanged. From contact line to apex, the temperaturemonotonically decreases which agrees well with the Fourier's law. Forlight plasmonic heating, droplet surface temperature displays

nonmonotonic variation to distinguish a contact line region CLR and abulk volume region BVR. Fig. 3b shows that the CLR has a highertemperature and a larger temperature gradient than the BVR, behavingthe boundary layer effect. With continuous light plasmonic heating, thewhole temperature of the droplet is slightly raised.

The flow field in droplet is closely depended on the droplet tem-perature field. We can speculate the flow field based on the temperaturefield and Ref. [7]. The flows in droplet are mainly two mechanisms: theMarangoni flow and the radial flow. The radial flow is caused by thenon-uniform evaporation flux distribution on droplet surface. Lagerevaporation flux at contact line than the droplet apex causes the radialflow from droplet center to contact line. The Marangoni flow is theresult of the droplet surface temperature gradient. Given the tempera-ture difference existing along the droplet surface, the liquid will moveopposite to the temperature gradient direction. It is noted that goldnanoparticles move with liquid in droplet.

The velocity of radial flow can be calculated as [25]

= =−

⎛⎝

− ⎞⎠

∞ −u J

ρD c T c f θ

RρrR

( ( ) ) ( )1

ς

rf

g s

f (2)

where J is evaporation flux at the contact line, ρf is nanofluid density.Dg is the diffusion coefficient of vapor, which is 2.56 × 10−5 m2/s at25 °C. cs(T) and c∞ are the vapor concentration at the gas–liquid in-terface and ambient, respectively. f(θ) and ζ are two parameters related

Fig. 2. The droplet evaporation dynamics for substrate heating and light plasmonic heating (a for droplet contact angle θ and diameter D versus time t, b and c fordroplet volume V versus time t).

Fig. 3. The spatial distribution of drop surface temperature, showing different nature between substrate heating and light plasmonic heating (a: isothermal diagramof substrate heating drop evaporation for ci = 100 ppm and Tw = 35.6 °C; b: isothermal diagram of light plasmonic heating drop evaporation for ci = 100 ppm andqr = 1400 W/m2).

X. Yan, et al. Applied Thermal Engineering 175 (2020) 115389

3

to θ, f(θ) = (0.27θ 2 + 1.30)(0.6381 − 0.2239(θ − π/4)2) andζ=0.5(π− 2θ)/(π− θ) [7]. R is the contact radius (R= 0.5D) and r isthe radius of concerned location (r ≤ R). At contact line, →r R 1. Forthe specific cases in Fig. 3, we set θ = 84.8° = 0.471π andR = 1.05 mm at the initial time, the ur for substrate heating and lightplasmonic heating equal to 0.00653 mm/s and 0.00526 mm/s, re-spectively.

The Marangoni flow can be characterized by the Marangoninumber, which is defined as [7]

=Ma σT

l Tμα

dd

Δ(3)

where dσ/dT, μ and α are the surface tension gradient, dynamic visc-osity and thermal diffusion coefficient of water. The values of thesephysical properties are 1.657 × 10−4 N/(m·K), 1.005 × 10−3 Pa·s and1.4 × 10−7 m2/s, respectively. In Eq. (3), l is the arc length fromcontact line to the point with the lowest temperature. And ΔT is thetemperature difference within arc length l. For a specific case of sub-strate heating with l= 1.4 × 10−3 m and ΔT= 3.1 °C at t= 1.5 min inFig. 3a, Ma equals to 5111. The Marangoni flow is well established inthe whole droplet forMa > 100 [7]. The flow direction is from contactline to droplet apex. The Marangoni flow coupling with the radial flowyields the flow pattern in Fig. 4a, which causes the nanoparticle patternin Fig. 4c. Lots of nanoparticles are dispersedly distributed at the con-tact area, because Marangoni flow re-carries nanoparticles into thecenter of droplet.

For light plasmonic heating case in Fig. 3b, the l = 3.4 × 10−4 mand ΔT = 1.6 °C at t = 1.5 min are applied to have Ma = 641, which isalso larger than 100. In contrast to substrate heating case, the Mar-angoni flow is limited in CLR, because ΔT only exists in CLR. Mean-while, the radial flow is still established to let liquid travel from droplet

center to CLR. The flow map is established as presented in Fig. 4b. Theradial flow continuously transports the nanoparticles from dropletcenter to CLR. And the Marangoni flow traps the nanoparticles in CLRforming nanoparticle pattern as shown in Fig. 4d. There are almost allnanoparticles near contact line, and few nanoparticles in the center ofcontact area.

3.3. Energy analysis in droplet

Concerning the substrate heating, the heat transfers from substrateto droplet apex as shown in Fig. 5a. The gold nanoparticles have littleimpact on droplet evaporation process. The droplet evaporation raterelies on the thermal conductivity of liquid and temperature differencebetween substrate and air.

The light plasmonic heating induced gold nanofluid droplet eva-poration is more complex. The electron in gold nanoparticles could beresonant with incident light, called plasmonic effect, which promotesthe light energy absorption [26]. The nanoparticles will transfer lightenergy to thermal energy and warm up the liquid around them. Goldnanoparticles can be regarded as little moving heat sources. The na-noparticle distribution has a significant influence on droplet evapora-tion. Since most of the gold nanoparticles distribute in CLR, the heatgeneration is rich in CLR and weak in BVR.

The above analysis matches the temperature field shown in Fig. 3bthat CLR has a higher temperature than BVR. The ratio of the CLRvolume to droplet volume can be scaled by (δ/Lc)3. See Fig. 6, δ is thearc length of the CLR and Lc is the stretched length along the dropletcircumference. The magnitude of (δ/Lc)3 is in the range of 0.9–3.1% fordroplets with ci = 100 ppm, demonstrating the CLR volume is twomagnitudes smaller than the whole droplet for light plasmonic heating,which is recognized as the boundary layer effect.

Fig. 4. Physical pictures and nanoparticles patterns for different heating modes (a: substrate heating induced drop evaporation, b: light plasmonic heating induceddrop evaporation, c: nanoparticles pattern for substrate heating case, d: nanoparticles pattern for light plasmonic heating case).

X. Yan, et al. Applied Thermal Engineering 175 (2020) 115389

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3.4. Vapor diffusion from droplet surface

The droplet vapor diffusion model is discussed here to explain dif-ferent volume variation trends for two heating methods. The dropletcan be regarded as a spherical cap because the contact area radius R issmaller than the capillary length of water ~2.7 mm. The coordinatesystem is established as shown in the inset of Fig. 7a. Since the droplet

lifetime is scaled as several minutes, the droplet evaporation is assumedto be a quasi-static process. The evaporation rates of BVR and CLR arecalculated as the integration of evaporation flux for each area [25]:

∫

∫

= − +

= − +

− ∂∂

− ∂∂

( )( )

Q rR J θ r r

Q rR J θ r r

2π ^ ( )(1 ^ ) 1 d^

2π ^ ( )(1 ^ ) 1 d^

γ ζ θ Hr

γζ θ H

r

s,BVR 02

02 ( ) 2

s,CLR1 2

02 ( ) 2

(4)

where J0 is the evaporation flux at the droplet center that related to thecontact angle θ (t) and droplet surface temperature Ts. It is noted thatEq. (4) is introduced to solve the isothermal case of sessile drop eva-poration. However, the droplet surface temperature has a slight risewith time for light plasmonic heating. To be more suitable for realconditions, the Ts of BVR and CLR at time t obtained from the experi-ment are used to determine the corresponding Qs,BVR and Qs,CLR , re-spectively. We defined ̂ ≡r r R. γ = r1/R and r1 is the radius of theboundary between CLR and BVR. ζ(θ) is a parameter reflecting the

nonuniform distribution of the evaporation flux. The term + ∂∂( )1 H

r

2in

the integration kernel can be approximated as ̂− −r(1 ) ν θ2 ( ) [25]. ThenEq. (4) was integrated to obtain

=

=

− −−

−−

−

−

Q

Q

R J θ γθ

R J θ γθ

s,BVRπ ( )[1 (1 ) ]

1 Λ( )

s,CLRπ ( )(1 )

1 Λ( )

θ

θ

2 0 2 1 Λ( )

2 0 2 1 Λ( )

(5)

where Λ(θ) = ζ(θ) + ν(θ) ≈ 0.2239(θ − π/4)2 + 0.3619 [25]. The J0(θ) can be expressed by [25]

=−

+ −∞J θD c T c

Rθ θ( )

( ( ) )(0.27 1.30)(1 Λ( ))0

g s 2(6)

Noting that θ is given in radians. Combining Eqs. (5) and (6), we obtain

= − +

× − −= − +

× −

∞

− −

∞

− −

Q RD c T H c θ

γQ RD c T H c θ

γ

π ( ( ) )(0.27 1.30)

[1 (1 ) ]π ( ( ) )(0.27 1.30)

(1 )

θ

θ

s,BVR g s a2

2 0.6381 0.2239( π 4)

s,CLR g s a2

2 0.6381 0.2239( π 4)

2

2(7)

Thus, the overall evaporation rate is calculated as

= +Q Q Qt s,BVR s,CLR (8)

Assuming the droplet surface temperature is uniform and un-changed, based on Eqs. (7) and (8), Qs,CLR/Qt is obtained as shown inFig. 7a. With θ decreasing, Qs,CLR/Qt increases from 41.0% to 68.5%.The evaporation rate in CLR plays a key role in droplet evaporation.Thus, for substrate heating, droplet surface temperature is supposed tobe uniform and equal to the temperature at contact line. The Qt iswritten as [25]

= − +∞Q RD c T H c θπ ( ( ) )(0.27 1.30)t g s a2 (9)

The evaporation rates calculated by Eqs. (7)–(9) and got from theexperiment are compared in Fig. 7b and c. For substrate heating, thevariation trends of evaporation rate obtained by model and experimentare similar. The mean relative deviation σR, mean absolute relativedeviation σA and standard relative deviation σs of the rates got frommodel and experiment are 3.73%, 9.53% and 12.64%, respectively. Forlight heating, the experiment data fluctuates around 5.2 nL/s due to thelinear change of droplet volume. The evaporation rate obtained bymodel also fits the experiment data well. The σR, σA and σs are −4.87%,8.97% and 9.64%, respectively. Thus, the vapor diffusion model canreflect the physical processes of droplet evaporation well. There are twofactors determine the droplet evaporation rate. First, during dropletevaporation, droplet surface area decreases with time, suppressing thedroplet evaporation rate. This is a negative effect. Second, the increasein Ts elevates the droplet evaporation rate. This is a positive effect. Thecompetition between the two effects yields different droplet volumevariation trends. For substrate heating, the temperature near contact

Fig. 5. The contrast of heat generation and transfer for two heating methods.

Fig. 6. The analysis of CLR relative volume for light plasmonic heating dropletevaporation.

X. Yan, et al. Applied Thermal Engineering 175 (2020) 115389

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line is constant leading to only a negative effect on droplet evaporation,which causes the non-linear change of droplet volume. For light plas-monic heating, most of the gold nanoparticles are limited in CLR whichresults in the enhanced heat generation and temperature rise withinCLR. The negative effect and positive effect both exist yielding theconstant evaporation rate and linear variation of droplet volume.

The effects of light plasmonic heating and substrate heating onnanofluid droplet evaporation are rarely investigated. The availableexperimental data are limited. This study provides valuable experi-mental data for further theoretical analysis and numerical simulation ofdroplet evaporation.

4. Conclusions

The nanofluid droplet evaporations induced by substrate heatingand light plasmonic heating are compared comprehensively. The CCDevaporation takes place in both two heating methods. Due to differentheating methods, three different evaporation characteristics are iden-tified. First, droplet surface temperature decreases monotonically fromcontact line to apex for substrate heating. However, a nonmonotonicsurface temperature variation is shown for light plasmonic heating,which separates droplet into a contact line region CLR and a bulk vo-lume region BVR. The temperature gradient is significant in CLR but

weak in BVR. Second, the substrate heating owns the radial flow andMarangoni flow over the whole droplet, leading to lots of nanoparticlesdispersedly distribute at the contact area when droplet dry-out. Forlight plasmonic heating, the Marangoni flow is confined in CLR onlycaused by a large temperature gradient there. And the nanoparticlesjust deposit near the contact line. At last, the variation of volume is non-linear for substrate heating, since the decreasing droplet surface areareduces the droplet evaporation rate. By contrast, the linear law of dropvolume is observed for light plasmonic heating. The enhanced heatgeneration in CLR due to the nanoparticles' plasmonic effect thereovercomes the negative effect of droplet surface area decreasing. It isbelieved that this work will improve the development of fundamentalresearch and applications of droplet evaporation significantly.

Declaration of Competing Interest

The authors declare that they have no known competing financialinterests or personal relationships that could have appeared to influ-ence the work reported in this paper.

Acknowledgments

The authors acknowledge the support from National Natural Science

Fig. 7. Vapor dissipation rate via droplet surfaces (a: the ratio of evaporation rate of CLR to total evaporation rate, b and c: the comparison of evaporation ratesbetween experiment and model for substrate heating and light plasmonic heating. σR, σn and σA represent the mean relative deviation, mean absolute relativedeviation and standard relative deviation, respectively.)

X. Yan, et al. Applied Thermal Engineering 175 (2020) 115389

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Foundation of China (51806065 and 51821004) and FundamentalResearch Funds for the Central Universities (2018ZD02 and2018QN020).

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