Effect of wall slip on vertical film drainage in presence of soluble surfactants

Abstract

A mathematical model is established to investigate a vertical gravity-driven drainage flow containing a soluble surfactant when considering the effect of wall slip. The lubrication theory is employed to obtain the evolution equations describing film thickness, surface velocity, surfactant concentrations at the air–liquid, solid–liquid interface, and in the bulk. The influence of constant slip length bc and variable slip length bs varying with surfactant concentration on the drainage dynamics is investigated compared with the case of no-slip bo, and the mechanism of the film thinning and the backflow caused by wall slip is examined. Simulated results show that the wall slip has a significant impact on the dynamics of the film drainage compared with the no-slip case. For the case of constant slip length, the wall slip accelerates the film thinning in the early stage. At the middle stage, the wall slip enhances the Marangoni effect and surface velocity rapidly decreases, causing a surface backflow phenomenon at the film bottom; the higher the slip length, the more obvious surface backflow. In the late stage, surface backflow weakens, and the film thickness is less than that of bo. For the case of variable slip length, in the early stage, the film thickness and surface velocity are between those of bo and bc; at the middle stage, a weak surface backflow is evolved at the film bottom; in the late stage, the film thickness is close to that of bc, and the surfactant concentration is lower than those of bo and bc.