Thermocapillary convection in liquid bridges with undeformable curved surfaces

Thermocapillary convection in differentially heated cylindrical liquid bridges is investigated by two- and three-dimensional numerical simulations. The nondeformable free surface is either flat or curved as determined by the fluid volume and the Young-Laplace equation. With Prandtl numbers of I and 4 and a flat surface, our computed results for onset of oscillations are in good agreement with linear theory. Convection is steady and axisymmetric at sufficiently low values of Reynolds number with either flat or curved interfaces. Only steady convection is possible at all Reynolds numbers considered in strictly axisymmetric computations. Transition to oscillatory three-dimensional motions occurs as the Reynolds number increases beyond a critical value, dependent on the Prandtl number and liquid volume. Rotating waves with wave numbers of 1 or 2 are observed. The critical wave number depends on the Blot number. Heat loss from the free surface stabilizes the How, and the critical Reynolds number increases with increasing Biot number. With nonzero Biot number, two different branches can exist in the stability diagram. The numerical results are in, reasonable agreement with experiments.