Rupture of a Surfactant-Covered Thin Liquid Film on a Flexible Wall

Abstract

The rupture of a surfactant-covered thin liquid film on a flexible wall is studied in this paper. Evolution equations for the deflections of the air-liquid and wall-liquid interfaces and surfactant surface concentration are derived using lubrication theory, and their linear and nonlinear stability characteristics are investigated. Our linear stability results indicate that increases in the level of damping, the longitudinal wall tension, and the relative magnitude of Marangoni stresses have a stabilizing influence. Numerical simulations of the evolution equations are used to investigate the nonlinear characteristics of the instability. In all cases considered, the surfactant concentration decreases in the rupture region as rupture is approached, and the resulting Marangoni flows retard but do not prevent rupture. Self-similar rupture is examined and power-law scalings are extracted for different parameter values. These appear to be unchanged from those for rigid substrates, evidently because the van der Waals forces that drive the instability dominate the rupture dynamics.