A linear stability analysis of large-Prandtl-number thermocapillary liquid bridges

A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4  Pr  50). We focus on the relationships between the critical Reynolds number Re_c, the azimuthal wave number m, the aspect ratio Γ and the Prandtl number Pr. A detailed Re_c–Pr stability diagram is given for liquid bridges with various Γ. In the region of Pr > 1, which has been less studied previously and where Re_c has been usually believed to decrease with the increase of Pr, we found Re_c exhibits an early increase for liquid bridges with Γ around one. From the computed surface temperature gradient, it is concluded that the boundary layers developed at both solid ends of liquid bridges strengthen the stability of basic axisymmetric thermocapillary convection at large Prandtl number, and that the stability property of the basic flow is determined by the “effective” part of liquid bridge.