A deeper insight into the dip coating process in the presence of insoluble surfactants: A numerical analysis

Abstract

A numerical investigation is carried out to study the effects of an insoluble surfactant on the dip coating of a flat substrate. Predictions of both the film thickness and the concentration of surfactant in the film as a function of the capillary number compare well with the solutions of a simpler asymptotic model based on the lubrication approximation. Streamline patterns confirm the existence of a stagnation point located in the bulk phase in the region of the dynamic meniscus ?a conjecture postulated forty years ago. The evolution of the flow patterns and the interfacial variables shows how the classical result of Landau and Levich is recovered as the coating speed is augmented. Finally, we show that the effect of inertia forces cannot be neglected when the viscosity of the coating liquid is low.