Instability mechanisms of thermocapillary liquid bridges between disks of unequal radii

Abstract

In this paper, we explore thermocapillary liquid bridges between two disks of unequal radii with Prandtl numbers Pr of 0.0258 (mercury) and 0.068 (gallium arsenide) to gain insight into the underlying instability mechanism. In the context of Legendre's spectral element method, we determine critical conditions via linear stability analysis and then identify the instability mechanism through energy analysis. For the mercury bridge ( Pr =  0.0258), our analysis suggests that the flow instability undergoes an oscillatory bifurcation for radius ratios in the range of 0.5 ≤ Γr ≤ 0.66. In particular, we found three transitions between two-dimensional steady axisymmetric flow and three-dimensional stationary flow by further increasing the radius ratio to 0.73 ≤ Γr ≤ 0.76. For the gallium arsenide liquid bridge ( Pr =  0.068), the instability is always an oscillatory bifurcation in the whole computational interval. Furthermore, our observations identify six instability modes with different mechanisms. All instability modes in the mercury bridge ( Pr =  0.0258) are purely hydrodynamic, but the thermocapillary mechanism cannot be ignored in the gallium arsenide liquid bridge ( Pr =  0.068) because of the enhanced Pr effect.