The Benard-Marangoni Thermocapillary instability problem: on the role of the buoyancy

摘要

From an asymptotic analysis of the full convection problem in a horizontal weakly expansible viscous layer, bounded on the bottom by a flat heated solid surface and on the top by a free-surface subject to a temperature-dependent surface tension, we establish the following alternative: "Either the buoyancy is taken into account, and in this case the free-surface deformation effect is negligible and we rediscover the classical Rayleigh-Benard shallow convection rigid-free problem, or the free-surface deformation effect is taken into account, and in this case the buoyancy does not play a significant role in the Benard-Marangoni thermocapillary instability problem."