Danov KD, Valkovska DS, Ivanov IB
Faculty of Chemistry, Sofia University, 1 J. Bourchier Ave., Sofia, 1164, Bulgaria
J Colloid Interface Sci. 1999 Mar 15;211(2):291-303. doi: 10.1006/jcis.1998.5973.
Drainage of a partially mobile thin liquid film between two deformed and nondeformed gas bubbles with different radii is studied. The lubrication approximation is used to obtain the influence of soluble and insoluble surfactants on the velocity of film thinning in the case of quasi-steady state approach. The material properties of the interfaces (surface viscosity, Gibbs elasticity, surface diffusivity, and/or bulk diffusivity) are taken into account. In the case of deformed bubbles the influence of the meniscus is illustrated assuming simple approximated shape for the local film thickness. Simple analytical solutions for large and small values of the interfacial viscosity, and for deformed and nondeformed bubbles, are derived. The correctness of the boundary conditions used in the literature is discussed. The numerical analysis of the governing equation shows the region of transition from partially mobile to immobile interfaces. Quantitative explanation of the following effects is proposed: (i) increase of the mobility due to increasing bulk and surface diffusivities; (ii) role of the surface viscosity, comparable to that of the Gibbs elasticity; and (iii) significant influence of the meniscus on the film drainage due to the increased hydrodynamic resistance. Copyright 1999 Academic Press.
研究了两个半径不同的变形和未变形气泡之间部分可移动的薄液膜的排水情况。在准稳态方法的情况下，采用润滑近似来获得可溶性和不可溶性表面活性剂对液膜变薄速度的影响。考虑了界面的材料特性（表面粘度、吉布斯弹性、表面扩散率和/或体扩散率）。对于变形气泡，假设局部液膜厚度为简单近似形状，说明了弯月面的影响。推导了界面粘度大小值以及变形和未变形气泡的简单解析解。讨论了文献中使用的边界条件的正确性。控制方程的数值分析显示了从部分可移动界面到不可移动界面的过渡区域。对以下效应提出了定量解释：(i) 由于体扩散率和表面扩散率增加导致的流动性增加；(ii) 表面粘度的作用，与吉布斯弹性相当；(iii) 弯月面对液膜排水的显著影响，这是由于流体动力阻力增加所致。版权所有1999年学术出版社。
