The Influence of Static and Dynamic Free-Surface Deformations on the Three-Dimensional Thermocapillary Flow in Liquid Bridges

Abstract

The liquid-phase transport of heat and mass during the float-zone crystal-growth process is strongly affected by the surface-tension-driven flow caused by thermal gradients. In the half-zone model of this process the basic toroidal thermocapillary flow can become unstable to a three-dimensional and time-dependent state if the temperature gradients along the liquid—gas interface are increased. The corresponding two- and three-dimensional flows are analyzed here with emphasis on flow-induced dynamic deformations of the interface. The problem is treated using an asymptotic expansion of all relevant variables in the limit of high surface tension. The magnitude of the flow-induced surface deflection is quantified and the relative importance of different mechanisms is established. It is shown that the deformations are passive during the transition to oscillatory flow in high-Prandtl-number liquids as along as the capillary number is sufficiently small.