平板浸涂过程中的液膜排液影响因素

doi:10.11949/j.issn.0438-1157.20181207

摘要/Abstract

摘要：

针对一端与活性剂溶液池相接的竖直平板浸涂液膜排液过程，基于润滑理论建立了液膜厚度、活性剂浓度及液膜表面速度的演化方程组，通过数值计算分析了Marangoni效应和表面黏度对液膜排液特征的影响。结果表明，Marangoni效应是影响液膜排液过程的重要因素，可导致液膜厚度增加，随Marangoni效应增强可得到更均匀的液膜。液膜表面速度随表面黏度增大而减小，较大的表面黏度将推迟表面速度逆流现象的发生，但其对膜厚均匀度几乎没有影响。

关键词: 浸涂, 液膜, 排水, 表面活性剂, Marangoni效应, 表面黏度, 界面张力

Abstract:

A mathematical model is established to investigate the gravity-driven draining process of a vertical thin liquid film containing insoluble surfactants, where the top of film is assumed to fix to a vertical plate and the bottom of film is connected with a surfactant solution pool. Lubrication theory is used to derive a coupled equation set for describing the evolution of the film thickness, surfactant concentration and surface velocity. The equation set is solved numerically by the FreeFem program based on finite element method. The characteristics of film evolution are examined and the effect of characteristic parameters on the process of film evolution is analyzed. Simulated results indicate that the Marangoni effect is a crucial factor affecting the film drainage process, the strong Marangoni effect, Ma, leads to the bodiness of the film thickness. Besides, for large values of Ma, both the film thickness and solute distribution tend to be more uniform. The effect of surface viscosity on the drainage of surfactant film cannot be neglected, the reduction of interfacial viscosity S results in the faster drainage process and the more rapidly decrease of film thickness. However, it has no effect on the uniformity of film thickness.

Key words: dip coating, liquid film, drainage, surfactants, Marangoni effect, surface viscosity, interfacial tension

中图分类号:

TQ 430.15

叶学民, 李明兰, 张湘珊, 杨少东, 李春曦. 平板浸涂过程中的液膜排液影响因素[J]. 化工学报, 2019, 70(6): 2164-2173.

Xuemin YE, Minglan LI, Xiangshan ZHANG, Shaodong YANG, Chunxi LI. Influencing factors of film drainage of dip-coating process[J]. CIESC Journal, 2019, 70(6): 2164-2173.

图/表 11

图1 液膜排液示意图

Fig.1 Schematic diagram of ?lms drainage

图2 浸涂液膜排液过程

Fig.2 Schematic diagram of dip-coating film drainage

表1 典型尺度参数和无量纲参数取值或变化范围

Table 1 Order of magnitude estimates for relevant physical parameters and nondimensional parameters

有量纲参数	符号	取值或变化范围	无量纲参数	定义	取值或变化范围
动力学弯月面长度/mm	l	0.36(0.0145~0.5)	小量	$∈ = d / l$	0.028
液膜特征厚度/μm	d	10(0~100)	Marangoni数	$M a = ∈ Γ 0 σ Γ μ U$	0.1~1500
扩散系数/(m²/s)	D ^s	10^-10~10^-8	Peclet数	$P e = U l D s$	0.1~10000
动力黏度/(Pa·s)	μ	10^-3	表面黏度	$S = (κ s + μ s) U / l 2 μ U / d$	10~3000
表面黏度/(Pa·s·m)	μ ^s+κ ^s	1.0×10^-4~4×10^-2
密度/(kg/m³)	ρ	10³
特征速率/(m/s)	U	7.7×10^-4

表1 典型尺度参数和无量纲参数取值或变化范围

Table 1 Order of magnitude estimates for relevant physical parameters and nondimensional parameters

有量纲参数	符号	取值或变化范围	无量纲参数	定义	取值或变化范围
动力学弯月面长度/mm	l	0.36(0.0145~0.5)	小量	$∈ = d / l$	0.028
液膜特征厚度/μm	d	10(0~100)	Marangoni数	$M a = ∈ Γ 0 σ Γ μ U$	0.1~1500
扩散系数/(m²/s)	D ^s	10^-10~10^-8	Peclet数	$P e = U l D s$	0.1~10000
动力黏度/(Pa·s)	μ	10^-3	表面黏度	$S = (κ s + μ s) U / l 2 μ U / d$	10~3000
表面黏度/(Pa·s·m)	μ ^s+κ ^s	1.0×10^-4~4×10^-2
密度/(kg/m³)	ρ	10³
特征速率/(m/s)	U	7.7×10^-4

图3 液膜排液特征

Fig.3 Characteristics of film drainage

图4 Ma=10，S=10，Pe=100时的液膜排液曲率特征

Fig.4 Characteristics of film curvature with Ma=10, S=10, Pe=100

图5 Ma=1，10，100，1000时垂直液膜的排液特征(t=10)

Fig.5 Characteristics of film drainage at Ma=1, 10, 100, 1000 when t=10

图6 Ma=1，10，100，1000时垂直液膜的排液特征(t=500)

Fig.6 Characteristics of film drainage at Ma=1, 10, 100, 1000 when t=500

图7 S=10，100，500，2000时垂直液膜的排液特征(t=5)

Fig.7 Characteristics of film drainage at S=10, 100, 500, 2000 when t=5

图8 当S=500和3000时液膜表面速度的演化过程

Fig.8 Evolution of film surface velocity at S=500, 3000

图9 S=10，100，500，2000时垂直液膜的排液特征(t=1000)

Fig.9 Characteristics of film drainage at S=10, 100, 500, 2000 when t=1000

图10 液膜厚度与表面速度的数值解与渐近分析解对比

Fig.10 Comparison of numerical and asymptotic solution of film thickness and surface velocity

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