Dynamics of volatile drop on surface of another immiscible liquid

doi:10.11949/0438-1157.20200110

Abstract

Abstract:

Aiming at the dynamic process of evaporated droplets on the surface of immiscible and uniformly heated liquid, a set of dimensionless equations are derived based on the lubrication theory. The dynamic characteristics of evaporated droplets were studied by numerical simulation. The results show that the evolution process of the droplets can be divided into two stages: the advancing stage of the droplets dominated by spreading and the backward stage of the continuous fluctuating oscillation dominated by evaporation. The fluidity of droplets is stronger at low viscosity ratio, which leads to more rapid spreading. The increase of viscosity ratio will lead to the decrease of spreading and shrinkage rate. Evaporation affects the interfacial tension and droplets spreading by affecting the temperature distribution of the droplets interfaces. Compared with the pinning phenomenon of drop evaporation on the solid surface, the spreading of evaporated droplets on the immiscible liquid surface is depinned and accompanied by obvious deformation of the liquid substrate.

Key words: evaporation, drop, contact line, interface tension

摘要：

针对不混溶均匀受热液体表面上蒸发液滴的动力学过程，基于润滑理论推导出了无量纲方程组。采用数值模拟方法，探究了蒸发液滴的动力学特性。结果表明，蒸发液滴的演化过程分为两个阶段：由“铺展主导”的液滴前进阶段和由“蒸发主导”的持续脉动振荡的后退阶段。液滴在低黏度比下的流动性更强，导致铺展更加迅速，黏度比的增加会导致铺展和收缩速率的降低。蒸发通过影响液滴界面的温度分布进而影响界面张力以及液滴铺展。相较于固体表面液滴蒸发出现的钉扎现象，蒸发液滴在不混溶液体表面上的铺展是去钉扎的，并且伴有液体基底的明显变形。

关键词: 蒸发, 液滴, 接触线, 界面张力

CLC Number:

TK 124

Chunxi LI, Liyu ZHUANG, Zhixian SHI, Xuemin YE. Dynamics of volatile drop on surface of another immiscible liquid[J]. CIESC Journal, 2020, 71(8): 3500-3509.

李春曦, 庄立宇, 施智贤, 叶学民. 不混溶液体表面上蒸发液滴的动力学特性[J]. 化工学报, 2020, 71(8): 3500-3509.

Figures/Tables 13

Fig.1 Three possible wetting conditions for a three fluid system

Fig.2 Sketch of a drop resting over uniform heated liquid substrate

Fig.3 Initial conditions of the interface height distribution

Table 1 Order of magnitude estimates for the relevant physical parameters

有量纲参数	符号	单位	取值
液膜最大厚度	$H *$	$m$	$10 - 4$
液膜特征长度	$L *$	$m$	$10 - 3$
黏度	$μ *$	$P a ? s$	$10 - 3$
液体密度	$ρ *$	$k g ? m - 3$	$103$
蒸气密度	$ρ 2 v *$	$k g ? m - 3$	1
汽化潜热	$L a *$	$k J ? k g - 1$	$103$
比热容	$C p *$	$k J ? k g - 1 ? K - 1$	1
热导率	$λ i *$	$k W ? m - 1 ? K - 1$	$10 - 3 ~ 10 - 2$
界面张力	$σ i *$	$N ? m - 1$	$10 - 2$
温度	$T i *$	$K$	$2.93 × 102 ~ 3.43 × 102$

Table 1 Order of magnitude estimates for the relevant physical parameters

有量纲参数	符号	单位	取值
液膜最大厚度	$H *$	$m$	$10 - 4$
液膜特征长度	$L *$	$m$	$10 - 3$
黏度	$μ *$	$P a ? s$	$10 - 3$
液体密度	$ρ *$	$k g ? m - 3$	$103$
蒸气密度	$ρ 2 v *$	$k g ? m - 3$	1
汽化潜热	$L a *$	$k J ? k g - 1$	$103$
比热容	$C p *$	$k J ? k g - 1 ? K - 1$	1
热导率	$λ i *$	$k W ? m - 1 ? K - 1$	$10 - 3 ~ 10 - 2$
界面张力	$σ i *$	$N ? m - 1$	$10 - 2$
温度	$T i *$	$K$	$2.93 × 102 ~ 3.43 × 102$

Table 2 Representation and order of magnitude estimates of the relevant dimensionless groups

无量纲参数	定义	取值
毛细数	$C i = ε 2 σ i + σ i m * S i *$	$10 - 3 ～ 10 - 1$
蒸发数	$E = λ h 2 * T 2 m * - T 2 o * ε ρ 2 * U * H * L a *$	$10 - 3 ～ 10 - 2$
Marangoni数	$Σ i = α T i T i m * - T i o * σ i o * - σ i m *$	0~1
蒸气反冲数	$R = λ h 2 * 2 T 2 m * 2 - T 2 s * 2 L a * 2 μ 2 * U * ρ 2 v * L *$	$10 - 3 ～ 10 - 1$
Bond数	$B o = ε 3 ρ 1 * g * L * 2 μ 1 * U *$	$10 - 1$

Table 2 Representation and order of magnitude estimates of the relevant dimensionless groups

无量纲参数	定义	取值
毛细数	$C i = ε 2 σ i + σ i m * S i *$	$10 - 3 ～ 10 - 1$
蒸发数	$E = λ h 2 * T 2 m * - T 2 o * ε ρ 2 * U * H * L a *$	$10 - 3 ～ 10 - 2$
Marangoni数	$Σ i = α T i T i m * - T i o * σ i o * - σ i m *$	0~1
蒸气反冲数	$R = λ h 2 * 2 T 2 m * 2 - T 2 s * 2 L a * 2 μ 2 * U * ρ 2 v * L *$	$10 - 3 ～ 10 - 1$
Bond数	$B o = ε 3 ρ 1 * g * L * 2 μ 1 * U *$	$10 - 1$

Fig.4 Spatial-temporal evolution of the fast evaporation of a drop to a final shape

Fig.5 Temporal evolution of minimal h1，maximal h2，and the drop half-width xmax

Fig.6 The effect of E on the drop shape at t=100

Fig.7 The effect of the surface tension ratio σ on the drop shape at t=100

Fig.8 The effect of the density ratio ρ on the drop shape at t=100

Fig.9 The effect of the viscosity ratio on the maximal drop thickness (h2-h1)max，spreading radius xmax and contact angles θ1 and θ2

Fig.10 Evolutions of liquid-liquid and liquid-gas interfaces temperatures and temperature gradients

Fig.11 Log-log plot of the temporal evolution of spreading radius for different surface tension ratio σ

References 31

1	Craster R V, Matar O K. On the dynamics of liquid lenses[J]. Journal of Colloid and Interface Science, 2006, 303(2): 503-516.
2	韦存茜, 严杰, 唐浩, 等. 灌注液体型光滑多孔表面制备及应用[J]. 化学进展, 2016, 28(1): 9-17.
	Wei C X, Yan J, Tang H, et al. Fabrication and application of slippery liquid-infused porous surface[J]. Progress in Chemistry, 2016, 28(1): 9-17.
3	Harkins W D. The Physical Chemistry of Surface Films[M]. New York: Reinhold Pub., 1952.
4	Foda M, Cox R G. The spreading of thin liquid films on a water-air interface[J]. Journal of Fluid Mechanics, 1980, 101(1): 33-51.
5	Sebilleau J. Equilibrium thickness of large liquid lenses spreading over another liquid surface[J]. Langmuir, 2013, 29(39): 12118-12128.
6	Nosoko T, Ohyama T, Mori Y H. Evaporation of volatile-liquid lenses floating on an immiscible-liquid surface: effects of the surface age and fluid purities in n-pentane/water system[J]. Journal of Fluid Mechanics, 1985, 161(1): 329.
7	Rahman M R, Mullagura H N, Kattemalalawadi B, et al. Droplet spreading on liquid–fluid interface[J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2018, 553: 143-148.
8	Shabani R, Kumar R, Cho H J. Droplets on liquid surfaces: dual equilibrium states and their energy barrier[J]. Applied Physics Letters, 2013, 102(18): 184101.
9	Sun W, Yang F. Evaporation of a volatile liquid lens on the surface of an immiscible liquid[J]. Langmuir, 2016, 32(24): 6058-6067.
10	Liu L, Xu C, Zhao L, et al. Experimental and theoretical study of evaporation of a volatile liquid lens on an immiscible liquid surface[J]. Langmuir, 2019, 35(40): 12979-12985.
11	Dussaud A D, Troian S M. Dynamics of spontaneous spreading with evaporation on a deep fluid layer[J]. Physics of Fluids, 1998, 10(1): 23-38.
12	Buffone C. Formation, stability and hydrothermal waves in evaporating liquid lenses[J]. Soft Matter, 2019, 15(9): 1970-1978.
13	Shimizu Y, Mori Y H. Evaporation of single liquid drops in an immiscible liquid at elevated pressures: experimental study with n-pentane and R113 drops in water[J]. International Journal of Heat and Mass Transfer, 1988, 31(9): 1843-1851.
14	Sebilleau J, Lebon L, Limat L, et al. The dynamics and shapes of a viscous sheet spreading on a moving liquid bath[J]. Europhysics Letters, 2010, 92(1): 14003.
15	Noblin X, Buguin A, Brochard-Wyart F. Cascade of shocks in inertial liquid-liquid dewetting[J]. Physical Review Letters, 2006, 96(15): 156101.
16	Noblin X, Buguin A, Brochard-Wyart F. Fast dynamics of floating triple lines[J]. Langmuir, 2002, 18(24): 9350-9356.
17	Aveyard R, Clint J H, Nees D, et al. Size-dependent lens angles for small oil lenses on water[J]. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 1999, 146(1/2/3): 95-111.
18	Wilkinson K M, Bain C D, Matsubara H, et al. Wetting of surfactant solutions by alkanes[J]. Chemphyschem A European Journal of Chemical Physics & Physical Chemistry, 2005, 6(3): 547-555.
19	Chen L, Jeng J, Robert M, et al. Experimental study of interfacial phase transitions in three-component surfactant systems[J]. Physical Review A, 1990, 42(8): 4716.
20	Style R W, Dufresne E R. Static wetting on deformable substrates, from liquids to soft solids[J]. Soft Matter, 2012, 8(27): 7177-7184.
21	Burton J C, Huisman F M, Alison P, et al. Experimental and numerical investigation of the equilibrium geometry of liquid lenses[J]. Langmuir, 2010, 26(19): 15316-15324.
22	Greco E F, Grigoriev R O. Thermocapillary migration of interfacial droplets[J]. Physics of Fluids, 2009, 21(4): 42105.
23	George D, Damodara S, Iqbal R, et al. Flotation of denser liquid drops on lighter liquids in non-Neumann condition: role of line tension[J]. Langmuir, 2016, 32(40): 10276-10283.
24	Phan C M, Allen B, Peters L B, et al. Can water float on oil?[J]. Langmuir, 2012, 28(10): 4609-4613.
25	Guan J H, Wells G G, Xu B, et al. Evaporation of sessile droplets on slippery liquid-infused porous surfaces (slips)[J]. Langmuir, 2015, 31(43): 11781-11789.
26	Brochard-Wyart F, Debrégeas G, de Gennes P G. Spreading of viscous droplets on a non viscous liquid[J]. Colloid and Polymer Science, 1996, 274(1): 70-72.
27	Gelderblom H, Stone H A, Snoeijer J H. Stokes flow in a drop evaporating from a liquid subphase[J]. Physics of Fluids, 2013, 25(10): 102102.
28	Bresme F, Quirke N. Computer simulation studies of liquid lenses at a liquid–liquid interface[J]. The Journal of Chemical Physics, 2000, 112(13): 5985-5990.
29	Kriegsmann J J, Miksis M J. Steady motion of a drop along a liquid interface[J]. SIAM Journal on Applied Mathematics, 2003, 64(1): 18-40.
30	Pujado P R, Scriven L E. Sessile lenticular configurations: translationally and rotationally symmetric lenses[J]. Journal of Colloid and Interface Science, 1972, 40(1): 82-98.
31	Hong J, Kim Y K, Kang K H, et al. Effects of drop size and viscosity on spreading dynamics in DC electrowetting[J]. Langmuir, 2013, 29(29): 9118-9125.

[1]	Jingwei CHAO, Jiaxing XU, Tingxian LI. Investigation on the heating performance of the tube-free-evaporation based sorption thermal battery [J]. CIESC Journal, 2023, 74(S1): 302-310.
[2]	Huafu ZHANG, Lige TONG, Zhentao ZHANG, Junling YANG, Li WANG, Junhao ZHANG. Recent progress and development trend of mechanical vapor compression evaporation technology [J]. CIESC Journal, 2023, 74(S1): 8-24.
[3]	Xin WU, Jianying GONG, Long JIN, Yutao WANG, Ruining HUANG. Study on the transportation characteristics of droplets on the aluminium surface under ultrasonic excitation [J]. CIESC Journal, 2023, 74(S1): 104-112.
[4]	Wei SU, Dongxu MA, Xu JIN, Zhongyan LIU, Xiaosong ZHANG. Visual experimental study on effect of surface wettability on frost propagation characteristics [J]. CIESC Journal, 2023, 74(S1): 122-131.
[5]	Zhanyu YE, He SHAN, Zhenyuan XU. Performance simulation of paper folding-like evaporator for solar evaporation systems [J]. CIESC Journal, 2023, 74(S1): 132-140.
[6]	Xiaoqing ZHOU, Chunyu LI, Guang YANG, Aifeng CAI, Jingyi WU. Icing kinetics and mechanism of droplet impinging on supercooled corrugated plates with different curvature [J]. CIESC Journal, 2023, 74(S1): 141-153.
[7]	Lisen BI, Bin LIU, Hengxiang HU, Tao ZENG, Zhuorui LI, Jianfei SONG, Hanming WU. Molecular dynamics study on evaporation modes of nanodroplets at rough interfaces [J]. CIESC Journal, 2023, 74(S1): 172-178.
[8]	Aiqiang CHEN, Yanqi DAI, Yue LIU, Bin LIU, Hanming WU. Influence of substrate temperature on HFE7100 droplet evaporation process [J]. CIESC Journal, 2023, 74(S1): 191-197.
[9]	He JIANG, Junfei YUAN, Lin WANG, Guyu XING. Experimental study on the effect of flow sharing cavity structure on phase change flow characteristics in microchannels [J]. CIESC Journal, 2023, 74(S1): 235-244.
[10]	Yue YANG, Dan ZHANG, Jugan ZHENG, Maoping TU, Qingzhong YANG. Experimental study on flash and mixing evaporation of aqueous NaCl solution [J]. CIESC Journal, 2023, 74(8): 3279-3291.
[11]	Jinming GAO, Yujiao GUO, Chenglin E, Chunxi LU. Study on the separation characteristics of a downstream gas-liquid vortex separator in a closed hood [J]. CIESC Journal, 2023, 74(7): 2957-2966.
[12]	Xuanzhi HE, Yongqing HE, Guiye WEN, Feng JIAO. Ferrofluid droplet neck self-similar breakup behavior [J]. CIESC Journal, 2023, 74(7): 2889-2897.
[13]	Yuanyuan ZHANG, Jiangyuan QU, Xinxin SU, Jing YANG, Kai ZHANG. Gas-liquid mass transfer and reaction characteristics of SNCR denitration in CFB coal-fired unit [J]. CIESC Journal, 2023, 74(6): 2404-2415.
[14]	Zhengtao LI, Zhijie YUAN, Gaohong HE, Xiaobin JIANG. Study of the mechanism of internal circulation regulation during evaporation of NaCl droplets on hydrophobic interface [J]. CIESC Journal, 2023, 74(5): 1904-1913.
[15]	Simin YI, Yali MA, Weiqiang LIU, Jinshuai ZHANG, Yan YUE, Qiang ZHENG, Songyan JIA, Xue LI. Study on ammonia evaporation and hydration kinetics of microcrystalline magnesite [J]. CIESC Journal, 2023, 74(4): 1578-1586.