Linear stability of two-dimensional combined buoyant-thermocapillary flow in cylindrical liquid bridges

Abstract

The combined buoyant-thermocapillary flow in cylindrical liquid bridges of unit aspect ratio is calculated by a mixed finite-difference--Chebyshev-collocation method. Gravity is assumed to be parallel or antiparallel to the cylinder's axis. For dominating thermocapillarity the two-dimensional basic flow is unique at the onset of instability. It is shown that additional buoyant body forces act stabilizing on the axisymmetric flow in high Prandtl number fluids for both heating and cooling from below. For heating from below, the onset of time-dependent convection is delayed to higher Marangoni numbers than for cooling from below, in agreement with previously unexplained experimental findings. In the absence of thermocapillary effects two axisymmetric convective solutions bifurcate from the conducting basic state. This perfect pitchfork bifurcation is perturbed by weak thermocapillary forces. The linear stability of all three axisymmetric base states is investigated numerically for Pr=4, a Prandtl number typical for model experiments.