Viscous potential flow analysis of interfacial stability with mass transfer through porous media

The interfacial stability with mass transfer, surface tension, and porous media between two rigid planes will be investigated in the view of viscous potential flow analysis. A general dispersion relation is obtained. For Kelvin–Helmholtz instability, it is found that the stability criterion is given by a critical value of the relative velocity. On the other hand, in the absence of gravity the problem reduces to Brinkman model of the stability of two fluid layers between two rigid planes. Vanishing of the critical value of the relative velocity gives rise to a new dispersion relation for Rayleigh–Taylor instability. Formulas for the growth rates and neutral stability curve are also given and applied to air-water flows. The effects of viscosity, porous media, surface tension, and heat transfer are also discussed in relation to whether the system is potentially stable or unstable. The Darcian term, permeability’s and porosity effects are also concluded for Kelvin–Helmholtz and Rayleigh–Taylor instabilities. The relation between porosity and dimensionless relative velocity is also investigated.