Transient thermocapillary flow in thin liquid layers

Abstract

A spatially varying temperature distribution imposed on the free surface of a liquid leads to an effective tractive force on the surface because of the dependence of surface tension on temperture. A solution for transient flow in infinite thin layers is presented. The layer is thin enough so that inertial forces are negligible. The equations of motion are nondimensionalized by an explicit scaling procedure. Small-time and large-time solutions are obtained with variation of surface height as part of the solution.