不混溶液体表面上蒸发液滴的动力学特性

doi:10.11949/0438-1157.20200110

摘要/Abstract

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

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

中图分类号:

TK 124

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.

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.

图/表 13

图1 三流体系统可能的润湿情况

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

图2 液滴放置于均匀加热的液体基底上的示意图

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

图3 初始时刻界面高度分布

Fig.3 Initial conditions of the interface height distribution

表1 典型参数的取值或变化范围

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	$T i *$	$K$	$2.93 × 102 ~ 3.43 × 102$

表1 典型参数的取值或变化范围

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	$T i *$	$K$	$2.93 × 102 ~ 3.43 × 102$

表2 无量纲参数定义及其数量级

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	$B o = ε 3 ρ 1 * g * L * 2 μ 1 * U *$	$10 - 1$

表2 无量纲参数定义及其数量级

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	$B o = ε 3 ρ 1 * g * L * 2 μ 1 * U *$	$10 - 1$

图4 液滴快速蒸发到最终形状的时间-空间演化

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

图5 h1最小值、h2最大值以及液滴半径xmax随时间的演化

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

图6 t=100时E对液滴形状的影响

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

图7 t=100时表面张力比对液滴形状的影响

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

图8 t=100时密度比对液滴形状的影响

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

图9 黏度比对最大液滴厚度(h2-h1)max、铺展半径xmax和接触角θ1和θ2的影响

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

图10 液-液和液-气界面温度与温度梯度的演化过程、

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

图11 不同表面张力比σ时铺展半径的时间演化对数图

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

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