Linear Rayleigh-Taylor stability of viscous fluids with mass and heat transfer

Abstract

The linear Rayleigh–Taylor stability of superposed viscous fluids with interfacial transfer of mass and heat is first considered for layers of finite thickness. A dispersion relation is obtained. It is then employed to derive stability and instability criteria for the case of two semi-infinite layers as well as the case where one of the layers is finite. From these criteria one arrives at a critical dispersion relation and a new critical wavenumber. This new critical wavenumber is distinct from the classical value owing to the presence of a parameter which depends, in a very simple manner, upon the kinematic viscosity of the fluids, the surface tension and the rate of interfacial transfer of mass and energy. Also it is found that the stabilizing effect of the surface tension is neither affected by the arrangement of the system nor the direction of the temperature gradient. However, the effects of the viscosity and the gravity will depend upon the relative positions of the superposed fluids and the direction of the temperature gradient at the interface.