Influencing factors of film drainage of dip-coating process

doi:10.11949/j.issn.0438-1157.20181207

Abstract

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

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

CLC Number:

TQ 430.15

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.

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.

Figures/Tables 11

Fig.1 Schematic diagram of ?lms drainage

Fig.2 Schematic diagram of dip-coating film drainage

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

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

Fig.3 Characteristics of film drainage

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

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

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

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

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

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

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

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