The Dynamics of Thin Liquid Film

Abstract

The dynamics of a general three-dimensional thin film subject to van der Waals forces, surface tension and surfactant concentration effects is considered. Using an asymptotic analysis based upon the thinness of the film with respect to its lateral extent, evolution equations for the leading-order film thicknesses, transverse velocities and surfactant concentrations are obtained. Specializations to free and confined films of various geometries (planes, spheres, cylinders and catenoids) are presented, along with the results of stability analyses and numerical simulations. Similar techniques are applied to the analysis of the dynamics of a thin thread of liquid. For the special case of a two-dimensional free film without surfactants, the existence of a similarity solution near the point of rupture is considered. Finally, the motion of a general two-dimensional Stokes flow confined to a channel is studied. By performing a matched asymptotic analysis in the vicinity of the contact line, appropriate macroscopic boundary conditions are obtained. A coupled system of first-order ordinary differential equations which describe the evolution of the leading-order film surface allows for the numerical simulation of the flow.