The onset of concentration convection in a long rectangular domain of a porous medium

Abstract

We solve a problem of the convective flow stability in an elongated rectangular region of a porous medium. The transport of a mixture is described using the MIM (mobile-immobile media) approach. This approach consists in dividing the concentration of the solute into mobile and immobile components. The effect of density inhomogeneity on the flow of a solution in a porous medium is taken into account by the filtration equation within the Darcy-Boussinesq approximation. The problem is solved numerically with the use of the finite difference method. The fields of pressure and concentration are obtained. The influence of the parameters of the problem on the disturbance profiles is analyzed. A modified problem of stability is solved. The modification is necessary for finding the oscillatory convective mode. To obtain the solution, the spectrum of Lyapunov exponents is calculated with Gram-Schmidt orthogonalization. Neutral curves are found that make it possible to detect the threshold for the onset of convection. The ranges of parameters in which oscillatory perturbations are realized are obtained. The effect of sorption parameters on the occurrence of oscillations is analyzed.