Oscillation of the surface of a liquid film on a horizontally moving substrate due to attractive force from an opposed cylindrical surface

Abstract

Oscillatory behavior of the surface of a liquid film on a substrate moving at a constant horizontal velocity is investigated numerically, where the film is confined by a cylindrical solid surface across a gas layer. The evolution of the film surface profile is governed by a thin film equation, in which the disjoining pressure derived from the van der Waals interaction is taken into account. In such a confined geometry, the disjoining pressure acts on the film surface as attractive force from the upper solid surface, and becomes spatially nonuniform because the upper surface is not parallel to the substrate surface. The film surface can oscillate when the substrate moves horizontally at a constant velocity under such circumstances, where the behavior depends on whether the substrate velocity is larger or smaller than a critical value.