Effect of First Vibration Mode on Sub-Critical Thermocapillary Convection in Floating Zone Liquid Bridge

Abstract

A numerical study has been done to analyze the effect of first mode of vibration on sub-critical thermocapillary convection in a floating zone liquid bridge of high Prandtl number fluid. First, onset of oscillatory thermocapillary flow at certain critical Marangoni number with insulated and non-deformable free surface was investigated. The onset of oscillatory flow in this case is characterized by a rotating hydrothermal wave. Then motion was induced at the free surface of the liquid bridge corresponding to 1 st mode of vibration of a free-free beam that is similar in configuration to the liquid bridge under study. In this case insulated free surface and sub-critical Marangoni number was maintained to avoid the hydrodynamic instability associated with the rotating hydrothermal wave. The amplitude of vibration was set at 1.1% and 2.25% of floating zone diameter for two series of analyses, whereas frequency of vibration was 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 flow and induced free surface motion occurs at certain frequency (~1 Hz) that is indicated by greatly enhanced flow and temperature oscillations. The oscillatory flow (flow and thermal pattern and oscillation frequency etc) under these sub-critical conditions is generally consistent with earlier studies in similar configuration. The possibility of free surface interaction resulting in oscillatory thermocapillary flow has been demonstrated in this work.