On the Disturbance of a Thin Layer of Liquid by a Moving Obstruction

Abstract

We calculate the free surface shapes upstream and downstream of an obstacle obstructing a thin liquid layer on a moving surface, taking into account gravity and surface tension. We assume low Reynolds number viscous flow, a two-dimensional layer, and small ratio of vertical to horizontal length scale. The upstream and downstream shapes are very different. The upstream liquid piles up against the obstacle to provide an overpressure sufficient to drive the Poiseuille component of the lubrication flow under the obstacle. The downstream liquid is disturbed only by surface tension.