NUMERICAL CALCULATION OF THE THERMOCAPILLARY MOTION OF A BUBBLE UNDER MICROGRAVITY

Abstract

The migration of a gas bubble under the action of surface tension and friction is dealt with numerically in some detail. The bubble is immersed in an infinitely extended liquid medium. Within the liquid there exists a constant temperature gradient far away from the bubble. Since surface tension decreases with increasing temperature, the bubble will move in the direction of the higher temperature (Marangoni convection). For creeping convection flow the influence of the convective terms in the energy equation on the flow field and, in particular, on the speed of migration is investigated for higher Marangoni numbers (Mg > 0). For small Marangoni numbers (Mg < 3), analytical results concerning the speed of migration and obtained by Subramanian, as well as the classical solution by Young, Goldstein and Block, for creeping flow, are confirmed. Finally, for non-zero values of the Reynolds numbers and for larger values of the Marangoni numbers, the migration speed of the bubble has been calculated. The nonlinear governing partial differential equations (vorticity, stream function, energy) are solved by means of a finite difference method. In case of a constant Prandtl number it is shown that the bubble speed can be represented as a function of the Reynolds number.