Nonlinear evolution equations for thin liquid films with insoluble surfactants

Abstract

The dynamics of a free-liquid film with insoluble surfactants is followed until film rupture with a simple model based on three nonlinear evolution equations for the film thickness, the surfactants concentration and the tangential velocity of the fluid in the film. This model is derived asymptotically from the full Navier–Stokes equations for free films and incorporates the effect of van der Waals attraction, capillary forces and Marangoni forces due to gradients of surface tension. Different stability regimes are observed numerically for periodic and fixed boundary conditions and several initial conditions. Furthermore, the role of the relevant parameters (Hamaker constant, tension, Marangoni number) on the rupture time is assessed and comparison is made with the flow dynamics for a liquid film with insoluble surfactants on a solid substrate.