The effect of surfactant on the flow of a thin liquid film over a spinning disc

Abstract

We examine the flow of a thin liquid film over a spinning disc in the presence of dilute insoluble surfactant. We use the integral method to derive a coupled system of equations that govern the axisymmetric evolution of the film thickness, radial flow rate, angular momentum and surfactant surface concentration; a linear equation of state is used for closure. This system of equations is parameterized by a modified Weber number, a Marangoni parameter, M, and a surface Peclet number, Pe s . Numerical solutions of these equations reveal that the presence of surfactant gives rise to Marangoni stresses which interfere with the mechanisms of wave growth. For M ∼ 0.1 , our results indicate that the formation of interfacial waves is suppressed.