Stability of homogeneous seepage of a liquid mixture through a closed region of the saturated porous medium in the presence of the solute immobilization

The linear stability problem of homogeneous vertical seepage of the liquid mixture through a closed region of porous medium is investigated. The problem is solved taking into account immobilization of the solute by the porous medium, which is described within the MIM approach based on the second-order kinetics model allowing for the saturation of the solid matrix of porous medium with immobilized solute. The stability of the homogeneous vertical seepage mode to two-dimensional perturbations has been considered for the case of square porous domain. It is assumed that the lower and upper boundaries are maintained at fixed different concentrations of solute and the lateral boundaries are impermeable to the mixture. It has been found that due to consideration for the solute immobilization the perturbation spectrum of the homogeneous vertical seepage mode exhibits oscillatory perturbations which are absent in the case of using the classical diffusion model. Neutral curves for the space of the respective parameters and plots of neutral perturbation frequency as the function of governing parameters have been obtained numerically. It has been shown that in the presence of the immobilization the stability of the examined seepage mode decreases as compared to the classical diffusion model. The numerical investigation has shown that the oscillatory mode of convection exists only in a certain range of parameters characterizing the intensity of sorption. The maps of oscillatory instability mode existence in the space of governing parameters have been obtained.