NONLINEAR EVOLUTION-EQUATIONS FOR THIN LIQUID-FILMS WITH INSOLUBLE SURFACTANTS

The dynamics of a free-liquid film with insoluble surfactants is follo wed until film rupture with a simple model based on three nonlinear ev olution equations for the film thickness, the surfactants concentratio n 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, capilla ry forces and Marangoni forces due to gradients of surface tension. Di fferent stability regimes are observed numerically for periodic and fi xed boundary conditions and several initial conditions. Furthermore, t he role of the relevant parameters (Hamaker constant, tension, Marango ni number) on the rupture time is assessed and comparison is made with the flow dynamics for a liquid film with insoluble surfactants on a s olid substrate.