Volume effect on the instabilities of thermocapillary flow in annular pools filled with silicon melt

The effect of melt volume on the instabilities of thermocapillary flow in annular pools filled with silicon melt (Prandtl number Pr = 0.011) was investigated by the linear instability analysis. With the increase of volume ratio V/V-0 from 0.584 to 1.343, the critical Marangoni number decreases steeply when the volume ratios are small, while increases slightly for intermediate volume ratios, and decreases again for large volume ratios. The wavenumber and oscillation frequency keep decreasing and a jump occurs at approximately V/V-0 = 1.2 corresponding to the second decrease of the critical Marangoni number. The energy analysis indicates that the flow instability is initiated by the hydrodynamic inertial instability mechanism.