The effect of gas-phase transport on Marangoni convection in volatile binary fluids driven by a horizontal temperature gradient

Abstract

Recent experimental and numerical studies of convection in confined layers of volatile binary liquids with a free surface subjected to a horizontal temperature gradient have observed a reversal in the direction of interfacial flow as the concentration of air in the vapor space above the liquid is decreased. These observations suggest that transport in the gas phase has a significant effect on the balance between thermocapillary and solutocapillary stresses, the competition between which determines the flow direction. In order to develop a quantitative description of the flow reversal, we use the two-sided (liquid/gas) transport model introduced previously to obtain approximate analytical solutions for the interfacial temperature and composition of the liquid, hence predict thermocapillary and solutocapillary stresses, and the flow direction. Therefore, our solutions provide useful guidelines for choosing the optimal binary coolants composition and operating conditions for thermal management applications. Despite the complex nature of this problem, we have found that the mass transport in the gas phase is effectively one-dimensional and independent of the flow in moderate to large aspect-ratio cavity for sufficiently low temperature gradients, which allows this problem to be simplified and solved analytically in a sequential manner. Our theoretical predictions agree well with the results of numerical simulations, which indicates that the analytical analysis captures the essential physics of the problem.