Large-Scale Liquid Motion in Free Thermocapillary Films

Abstract

Thermocapillary flows in thin films are considered which are differentially heated from lateral side walls. The competition between two different types of motion is addressed. One type is the so-called return flow in which a return flow opposes the thermocapillary free-surface flow to preserve mass conservation. The other type of motion is a large-scale flow which arises as a plug flow in which the velocity is independent of the coordinate perpendicular to the film. We provide physical arguments, based on the minimization of the surface energy, for the preference of the large scale flow over the return flow as the film thickness decreases. The large scale motion arises as a cellular flow with alternating vorticity perpendicular to the film surface. The direction of rotation of these vortices is not determined when the film is adiabatic and of constant thickness. If, however, the film thickness varies perpendicular to the applied temperature gradient the flow direction is dictated by the minimization of the surface energy. Our predictions are consistent with independent experiments and numerical simulations.