Sub-Critical Interaction of Free Surface Motion and Thermocapillary Convection

Abstract

A numerical study is performed to analyze the effect of the first mode of vibration on subcritical thermocapillary convection in a floating-zone liquid bridge of high Prandtl number fluid. First, the onset of oscillatory thermocapillary flow at a certain critical Marangoni number with an insulated and nondeformable free surface is investigated. The onset of oscillatory flow in this case is characterized by a rotating hydrothermal wave. Then, motion is induced to the free surface of the liquid bridge corresponding to the first mode of vibration of a free–free beam that is similar in configuration to the liquid bridge under study. In this case, an insulated free surface and subcritical Marangoni number are maintained to avoid the hydrodynamic instability associated with the rotating hydrothermal wave. The amplitude of vibration is set at 1.1% and 2.25% of the floating-zone diameter for two series of analyses, whereas the frequency of vibration is varied over a wide range to study the interaction between the imposed vibration amplitude and frequency with thermocapillary convection inside the floating zone. It is found that amplified coupling between the flow and induced free surface motion occurs at a certain frequency () that is indicated by significantly enhanced flow and temperature oscillations. The oscillatory flow under these subcritical conditions is generally consistent with earlier studies done at supercritical conditions in a similar configuration. The possibility of free surface interaction resulting in oscillatory thermocapillary flow is demonstrated in this work.