Onset of convective instabilities in a binary liquid mixtures with fast chemical reactions in a porous medium

In this paper, we study the instabilities, which can occur when a horizontal sparsely filled porous layer saturated with a binary mixture with fast chemical reaction is heated from below or from above. Analytic expressions are found for the criteria for the onset of stationary and oscillatory convection in binary mixtures with chemical reaction. The reaction is assumed to be fast compared with the diffusion rate. We find that both a stationary instability and an oscillatory instability can occur as the first bifurcation, depending on the sign and the value of the heat of reaction. The effect of the Prandtl number, the separation parameter and the porous parameter are shown graphically. Some of the known results are derived as special cases.