Onset of Rayleigh-Benard-Marangoni convection in gas-liquid mass transfer with two-phase flow: Theory

Rayleigh and Marangoni instabilities in solute transfer between a gas phase and a liquid phase which are in parallel, laminar, stratified flow between two horizontal plates have been investigated theoretically. The effects of nonlinear velocity profiles of fluid flows and the nonlinear concentration profiles on the onset of Rayleigh-Benard-Marangoni convection in gas-liquid mass transfer of practical importance have been considered in the linear analysis of the general Rayleigh-Benard-Marangoni problem. In addition, the effect of surface convection and surface diffusion and the effect of surface viscosity of the surface active solute in the Gibbs adsorption layer, which were investigated separately by previous authors, have been combined together. To obtain the variations of the critical Rayleigh number and Marangoni number with the downstream distance of fluid flows, the restriction of the "frozen profile" has been released in the present study. For simplicity, the gas-liquid interface is assumed to be nondeformable.