Combined buoyant-thermocapillary flow in a cavity

Abstract

We treat the problem of combined buoyancy-thermocapillary convection in a cavity with a free surface heated differentially in the horizontal. Attention is focused on the structure and strength of the flow for large Δ T , i.e. large Marangoni and Rayleigh numbers. In the combined problem, the boundary-layer scalings for buoyant and thermocapillary convection suggest that in the limit of large Δ T , thermocapillarity will dominate the large-scale flow. Accurate numerical solutions are used to study this question at fixed cavity aspect ratio and Prandtl number, with G = Ra/Ma as a parameter. For G = 1, the flow evolves toward its boundary-layer limit in a fashion identical to that for G = 0, i.e. pure thermocapillary flow. For G = 10, the evolution is from a buoyancy-dominated structure, through a transition, to a thermocapillary-dominated structure. We infer that thermocapillarity will ultimately dominate all such flows at sufficiently large Δ T , for any fixed values of G , the aspect ratio, and the Prandtl number.