Linear stability and energy mechanism analysis of thermocapillary-buoyancy convection in molten GaAs liquid bridges with varying radius ratios

The stability of thermocapillary-buoyancy convection in a molten gallium arsenide (GaAs) liquid bridge (Pr = 0.068) confined between two disks with varying radii was investigated using linear stability analysis and a perturbation energy-based approach within the framework of the spectral element method. The effect of the disk radius ratio (Γr) on flow stability was systematically examined, and the underlying instability mechanisms were quantitatively identified. Throughout the study, the disk radius ratio of the liquid bridge varied within the range 0.800≤Γr≤1.000. In a top-heated configuration, a distinct transition in instability type, from static bifurcation to oscillatory bifurcation, was observed at critical disk radius ratio Γr=0.970. This transition, notably absent in the molten silicon systems, highlights a unique feature of the molten GaAs liquid bridge under gravity. In a bottom-heated configuration, a transition occurred from the oscillatory bifurcation to the static bifurcation, which was a destabilizing change opposite to that of the top-heated liquid bridge. These transitions in instability type for both heating configurations are attributed to abrupt shifts in the relative dominance of inertia and thermocapillary mechanisms. Energy analysis revealed that the thermocapillary mechanism plays a considerably more significant role in destabilizing the molten GaAs liquid bridge than it does in molten silicon systems. Specifically, in the top-heating configurations with 0.920≤Γr≤1.000 and bottom-heating configurations with 0.800≤Γr≤0.830 and 0.939≤Γr≤1.000, the contribution of thermocapillary mechanism remains non-negligible. In addition, the buoyancy contribution to instability was found to be negligible across all examined cases.