Effect of Prandtl number on the flow instabilities in thermocapillary liquid bridges between two coaxial disks with different radii

Abstract

The effect of Prandtl number on the instability of thermocapillary liquid bridges has been extensively studied, but the vast majority of efforts were put into typical cylindrical liquid bridge between two equal ends. The crystal growth practices have the propensity to form liquid bridges between unequal disks, thus the dependence of instability patterns and underlying mechanisms on the radius ratio is crucial but remains unclear. By fixing the radius ratio at Γr=0.5, we systematically explore the effects of Prandtl number and heating strategy, namely the upper heating and the bottom heating settings, on flow instabilities in thermocapillary liquid bridges between coaxial disks with different radii under microgravity through linear stability analysis based on spectral element method. In contrast to typical cylindrical liquid bridge (Γr=1), the present analysis indicates that the instability is always an oscillatory bifurcation even for small Prandtl number Pr=0.001 in the bottom heating scenario. What's more, the instability remains a stationary bifurcation and the critical Marangoni number experiences significant increase with the rise of Pr in the region of 0.001≤Pr≤1.2 for the upper heating situation. For all liquid bridges, the energy analysis results show that the instability under different Prandtl numbers can be roughly divided into three types.