Hydrodynamic instabilities in cylindrical thermocapillary liquid bridges

The hydrodynamic stability of steady axisymmetric thermocapillary flow in a cylindrical liquid bridge is investigated by linear stability theory. The basic state and the three-dimensional disturbance equations are solved by various spectral methods for aspect ratios close to unity. The critical modes have azimuthal wavenumber one and the most dangerous disturbance is either a pure hydrodynamic steady mode or an oscillatory hydrothermal wave, depending on the Prandtl number. The influence of heat transfer through the free surface, additional buoyancy forces, and variations of the aspect ratio on the stability boundaries and the neutral mode are discussed.