Linear stability of buoyant thermocapillary convection for a high-Prandtl number fluid in a laterally heated liquid bridge

Abstract

The buoyancy effect on the stability of axisymmetric buoyant-thermocapillary flow is investigated in a laterally heated high-Prandtl-number liquid bridge using linear stability analysis. Target geometry is the so-called full-zone (FZ) model in which the liquid is sustained between the coaxial cylindrical disks of the same diameter. The disks are maintained at the same temperature, and the mid part of the liquid bridge is heated, resulting in a non-uniform temperature distribution over the free surface. In that model, axisymmetric basic flow exhibits reflection symmetry around the midplane, and two identical toroidal vortices are formed in the upper and lower halves in zero-gravity conditions. However, the buoyancy breaks this symmetry in gravity conditions. There are two different types of perturbation in the FZ model, the symmetric and antisymmetric modes around the mid plane of the liquid bridge. When increasing the Rayleigh number Ra, the buoyancy strongly stabilizes the basic flow for the antisymmetric oscillatory mode and has a weak destabilizing effect on the symmetric oscillatory mode. Therefore, when Ra exceeds a certain threshold value, the most dangerous mode switches from the antisymmetric oscillatory mode, the most dangerous mode under zero-gravity conditions, to the symmetric oscillatory mode. The neutral stability curve of the symmetric oscillatory mode folds with increasing Ra, wherein the critical Reynolds number suddenly drops. We reveal that such an abrupt change in the neutral curve is caused by the transition of the instability source from the vortex in the upper half of the liquid bridge to the one in the lower half by increasing the buoyancy effect. With a further increase in the Ra, the most dangerous mode switches from the symmetric oscillatory mode to the antisymmetric steady mode.