Theory on Thermal Instability of Binary Gas Mixtures in Porous Media

A theory is developed which predicts the instability of a horizontal layer of porous medium saturated with a binary gas mixture. The lower boundary of the system is maintained at a higher temperature and the upper one at low temperature. The transport equations and coefficients are developed on the basis of kinetic theory. A linear perturbation technique is employed to reduce the governing equations for momentum, heat, and mass transfer to eigenvalue differential equations which are solved by the Finlayson method, the combination of the Galerkin method and the Routh-Hurwitz stability criterion. Only neutral stationary stability is found to occur in the system. Its criterion can be predicted by a simple algebraic equation. Both the critical Rayleigh and wave numbers for the onset of convection are governed by five independent dimensionless parameters, two of which are most influential. The critical Rayleigh number may be lower or greater than that for pure fluid layer depending upon whether thermal diffusion induces the heavier component of the mixture to move toward the cold or hot boundary, respectively. The theory compares well with the experimental results.