Theoretical Analysis of Thermocapillary Flow in Cylindrical Columns of High Prandtl Number Fluids

Steady and oscillatory thermocapillary flows of high Prandtl number fluids in the half-zone configuration are analyzed theoretically. Scaling analysis is performed to determine the velocity and length scales of the basic steady flow. The predicted scaling laws agree well with the numerically computed results. The physical mechanism of oscillations is then discussed. It is shown that the deformation of free surface plays an important role for the onset of oscillations in that it alters the main thermocapillary driving force of the flow by changing the temperature field near the hot-corner region. This phenomenon triggers oscillation cycles in which the surface flow undergoes active and slow periods. Based on that concept a surface deformation parameter is derived by scaling analysis. The deformation parameter correlates available data for the onset of oscillations well.