Thermocapillary Convection in Liquid Bridges with Undeformable Curved Surfaces

Abstract

Thermocapillary convection in differentially heated cylindrical liquid bridges is investigated by two- and threedimensional numerical simulations. The nondeformable free surface is either e at or curved as determined by the e uid volume and the Young ‐Laplace equation. With Prandtl numbers of 1 and 4 and a e at surface, our computed results for onset of oscillations are in good agreement with linear theory. Convection is steady and axisymmetric at sufe ciently low values of Reynolds number with either e at or curved interfaces. Only steady convection is possibleat all Reynoldsnumbersconsidered in strictly axisymmetriccomputations. Transition to oscillatory threedimensional 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 Biot number. Heat loss from the free surface stabilizes the e ow, 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.