EFFECT OF ASPECT RATIO ON THERMOCAPILLARY CONVECTION INSTABILITY OF GaAs MELT LIQUID BRIDGE

In this paper, we explore the effect of aspect ratio on the instability of thermocapillary convection in GaAs melt (Pr = 0.068) liquid bridge by using the linear stability analysis in the context of spectral element method. Besides, we provide physical insight on the underlying instability mechanism via energy analysis. Differing from the cases of typical low Prandtl number (such as Pr = 0.011) and typical high Prandtl number (such as Pr > 1), which correspond to stationary instability and oscillatory instability respectively, the instability of the thermocapillary convection of GaAs melt (Pr = 0.068) is of note due to its noticeable dependence on the aspect ratio (As). In particular, we observe two instability modes for the flow considered here with the variation of the aspect ratio. When the aspect ratio As ranges from 0.4 to 1.18, thermocapillary flow transits from two-dimensional axisymmetric steady convection to three-dimensional periodic oscillatory convection (oscillatory instability). While for 1.20 ≤ As ≤ 2.5, the stationary instability appears and the two-dimensional axisymmetric steady flow transits to three-dimensional steady flow. As for the instability mechanism of the thermocapillary convection, the liquid bridge of high Prandtl number is characterized by thermocapillary mechanism, while the case of low Prandtl number features the hydrodynamic inertia mechanism. Based on disturbance energy analysis, it is shown that the instability of the present thermocapillary convection arises from the combined action of the hydrodynamic inertial instability and thermocapillary instability, in which the hydrodynamic inertial instability mechanism is dominant, and the specific proportion of these two contributions varies with the aspect ratio.