Coupling effects of surface elasticity and disjoining pressure on film drainage process

Abstract

The aim of the present paper is to investigate the gravity-driven draining process containing insoluble surfactants, with the coupling effects of surface elasticity and disjoining pressure taken into consideration. A set of evolution equations including liquid film thickness, surface velocity and surfactant concentration, is established based on the lubrication theory. Assuming that the top of the liquid film is attached to the wireframe and the bottom is connected to the reservoir, the drainage stability is simulated with the FreeFem software. The characteristics of film evolution under the coupled effects of surface elasticity and disjoining pressure are examined, respectively. The simulated results show that the surface elasticity and the disjoining pressure have significant influences on the vertical thin film draining process. Under the effect of the surface elasticity alone, the initial film thickness increases with the elasticity increasing and the black film only forms on the top of the liquid film, but cannot stably exist and breaks quickly. The addition of the surface elasticity can increase the liquid film thickness and the drainage time, reduce the surface velocity, and rigidify the interface. When the disjoining pressure is applied merely, the surfactant flows into the reservoir continuously; hardly can the liquid film form a surface tension gradient and thus cannot form a countercurrent phenomenon. Under the coupling effect of the surface elasticity and disjoining pressure, a more stable liquid film forms. In the early stage of drainage, surface elasticity increases the film thickness, reduces the surface speed and generates the liquid countercurrent to slow the drainage process. When the black film appears, the electrostatic repulsion of the disjoining pressure is notable and makes the black film stable. The results obtained in the paper are in agreement with some of the experimental results in the literature. However, the elasticity-related surface tension and surfactant concentration model used is a simplified model. The nonlinear relationship between surface tension and surfactant concentration should be further considered in future theoretical models.