Thermocapillary flow around hemispherical bubble

Abstract A hemispherical bubble, attached to a plate, is surrounded by an initially quiescent and isothermal liquid. By suddenly heating the plate, a thermal gradient over the bubble surface results. Because surface tension is temperature dependent, tangential stresses arise at the bubble surface. The liquid is viscous, and motion in the liquid phase begins. Such motion is an example of thermocapillary flow. This problem, besides being of interest from a fundamental point of view, is of possible concern in the design of space vehicles capable of storing cryogenic fluids for long periods of time in a weightless condition. Solutions to the problem are developed by numerical treatment of the governing equations. Flow and temperature fields, which depend upon the Prandtl and Marangoni numbers, were obtained for Prandtl numbers 1 and 5 and Marangoni numbers from 0 to 100,000. Results show that liquid is pulled toward the intersection of the bubble and the plate, then flows around the bubble surface, and leaves the bubble as a jet. The extent of the jet increases with increasing Marangoni number and decreases with increasing Prandtl number. Thermocapillary flow increases heat transfer (Nusselt number) over that obtained from conduction, but the increase is modest. The Nusselt number increases with the Marangoni number and is insensitive to the Prandtl number. At a Marangoni number of 40,000, the local Nusselt number was increased by a factor of 2. In order for thermocapillary flow to become a dominant heat transfer mechanism, the Marangoni number must exceed 100,000.