The solution of shear stress discontinuity in film drainage model

Abstract

The Stokes–Reynolds–Young–Laplace (SRYL) model of film drainage for pure liquid and surfactant solution systems have been numerically solved with a simplified Young-Laplace equation in several literatures. However, with this simplification, the calculated profile of the tangential shear stress τb at the gas sides had an unphysical increment at the boundary of the computational domain, which violated the continuity in shear stress especially when inhibitory effect of surfactants on film drainage was considered. In this work, an improved model of film drainage was proposed by modifying the simplified Young-Laplace equation and artificial initial shape of the liquid film. The underlying reason for unreasonable τb caused by the simplified Young-Laplace equation was analyzed. This improvement avoided the unphysical sharp increase of τb at the boundary of the computational domain for both pure liquid and surfactant solution systems, which was critical to extend the SRYL model of film drainage to some complex systems.