垂直排液过程不稳定性的数值模拟

doi:10.19596/j.cnki.1001-246x.8332

摘要/Abstract

摘要：

为分析线框排液实验中液膜表面出现的不稳定现象及其成因，针对含有不溶性活性剂的线框液膜排液过程，模拟液膜底部的不稳定现象，分析Marangoni效应、膨胀黏性和扰动波数因素的影响。结果表明：底部扰动在排液开始比较剧烈，而后快速减弱，到排液后期又逐渐增强。排液开始的扰动是由初始扰动引起，而排液后期的扰动与活性剂分布有关。较弱的Marangoni效应可增强表面扰动，而较强的Marangoni效应则减弱底部扰动，使液膜呈刚性，发生表面逆流现象；较高的膨胀黏性减慢液膜排液进程，降低表面速度，且能抑制Marangoni效应引起的逆流现象；波数较大的扰动使液膜在排液初期的扰动变强，但对排液后期的稳定性不产生影响。

关键词: 线框排液, 扰动, Marangoni效应, 膨胀黏性

Abstract:

To analyze instability on surface of liquid film in a wire-frame drainage experiment, we establish a three-dimensional mathematical model for drainage process of a wire-frame containing insoluble surfactants, and simulate instability at bottom of the liquid film. Influence of factors including Marangoni effect, dilational viscosity and disturbance wave number are analyzed. It shows that bottom perturbation is severe at beginning of drainage, then quickly weakens, and gradually increases in the late drainage. Perturbation at the beginning is caused by initial perturbation, and instability at the late of the drainage is related to the distribution of surfactant. A weaker Marangoni effect enhances the surface disturbance, while a stronger Marangoni effect inhibits the bottom perturbation, making the liquid film rigid and causing surface countercurrent. Higher dilational viscosity slows down the drainage process and reduces the surface velocity. It suppresses the countercurrent phenomenon caused by the Marangoni effect. A greater disturbance wave number makes the perturbation stronger in the early stage of drainage, while it does not affect the stability of late stage of the drainage.

Key words: wire-frame drainage, perturbation, Marangoni effect, dilational viscosity

中图分类号:

O354

肖寒, 李春曦, 苏浩哲, 叶学民. 垂直排液过程不稳定性的数值模拟[J]. 计算物理, 2021, 38(6): 661-671.

Han XIAO, Chunxi LI, Haozhe SU, Xuemin YE. Numerical Simulation on Instability of Vertical Liquid Drainage[J]. Chinese Journal of Computational Physics, 2021, 38(6): 661-671.

图/表 12

图1 垂直线框排液过程示意图

Fig.1 Schematic of the vertical wireframe drainage process

表1 有量纲参数取值

Table 1 Values of dimensional parameters

有量纲参数	符号	取值或变化范围
动力学弯月面长度/mm	l^*	0.36
液膜特征厚度/μm	d^*	10
动力黏度/(Pa·s)	μ	10^-3
表面黏度/(Pa·s·m)	μ^s + κ^s	10^-4~4×10^-2
剪切黏度/(Pa·s·m)	μ^s	10^-5~2.1×10^-4
密度/(kg·m^-3)	ρ	10³
特征速率/(m·s^-1)	U^*	9.8×10^-4
扩散系数/(m²·s^-1)	D_s^*	10^-10~5×10^-8

表2 无量纲参数取值范围

Table 2 Values of dimensionless parameters

无量纲参数	符号	取值或变化范围
小量	ε	0.028
Marangoni数	M	7~350
Peclet数	Pe	100~30 000
表面黏度	S	7~300
剪切黏度	S′	0.1~10

图2 液膜表面扰动演化过程

Fig.2 The evolution process of liquid film surface disturbance

图3 液膜厚度和活性剂浓度的时空分布

Fig.3 Temporal and spatial distribution of liquid film thickness and surfactant concentration

图4 Ma=10和50时的液膜厚度分布

Fig.4 Liquid film thickness distribution at Ma=10 and 50

图5 Ma=10和50情形的厚度和浓度分布

Fig.5 Thickness and concentration distribution at Ma=10 and 50

图6 S0=40和90情形下的液膜厚度分布

Fig.6 Distribution of liquid film thickness at S0=40 and 90

图7 S0=40和90情形下的液膜厚度和浓度分布

Fig.7 Liquid film thickness and concentration distributions at S0=40 and 90

图8 液膜厚度分布

Fig.8 Distribution of liquid film thickness

图9 (a) 扰动能量E随时间t变化，横纵坐标均为对数形式；(b)稳定性因子β′随扰动数k变化

Fig.9 (a) The perturbation energy E as a function of time t, horizontal and vertical coordinates are in logarithmic forms; (b) The growth factor β′ as a function of disturbance number k

图10 扰动波数k=4和k=6情形下的厚度和浓度分布

Fig.10 Thickness and density distributions at disturbance wave numbers k=4 and k=6

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