高径比对GaAs熔体液桥热毛细对流失稳的影响

采用基于谱元法线性稳定性分析方法, 研究了高径比对GaAs熔体(Pr = 0.068)液桥热毛细对流失稳的影响, 同时结合能量分析揭示了热毛细对流的失稳机制. 研究结果表明: 与典型低普朗特数(例如Pr = 0.011)熔体静态失稳模式和典型高普朗特数(例如Pr>1)熔体振荡失稳模式不同, GaAs熔体热毛细对流失稳模式依赖于液桥高径比(As). 随高径比的变化, GaAs熔体热毛细对流存在两种失稳模式. 高径比As 在0.4≤As≤1.18范围内, 热毛细对流失稳是从二维轴对称定常对流转变为三维周期性振荡对流(振荡失稳); 高径比在1.20≤As≤2.5范围内, 热毛细对流失稳是从二维轴对称定常流动转变为三维定常流动(静态失稳). 典型的高普朗特数熔体液桥热毛细对流失稳机制是热毛细机制; 典型的低普朗特数液桥热毛细对流失稳机制是水动力学惯性机制. 本文基于扰动能量分析的结果表明: GaAs熔体热毛细对流失稳同时包括水动力学惯性失稳机制和热毛细失稳机制的贡献, 其中水动力学惯性失稳机制占主导作用, 两种机制对热毛细对流失稳能量贡献的占比随高径比的变化而变化. 

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.