Concentration‑driven convection in an inclined porous layer with weak pore clogging

Abstract

This work is devoted to the mathematical modeling of impurity transport through a porous medium. The model takes into account the deposition of impurity particles on the pore walls and subsequent clogging of the pores. Pore clogging is assumed to be weak, such that the influence of adsorbed particles on the system’s dynamics is taken into account only through changes in the permeability of the medium. The mixture filtration process is described within the Darcy–Boussinesq approximation; the equations are derived from the conservation laws for mass and momentum. The deposition of impurity particles is described within the framework of the linear MIM (mobile–immobile) approach. The change in permeability of the medium is linked to the change in porosity via the Kozeny–Carman relationship. The model is applied to study concentration-driven convection in an inclined layer of the porous medium. It is shown analytically that the base state of the system corresponds to the regime of steady state filtration along the layer. The stability of the base state with respect to small perturbations of two types — spiral and plane — is investigated numerically. The study has found that depending on the type of perturbations, both monotonic and oscillatory instability modes can be observed. Taking into account weak pore clogging leads to an increased stability of the system and a decreased frequency of the oscillatory mode. Increasing the inclination angle of the layer causes an additional increase in the stability of the base state, and this effect does not depend on the type of applied perturbations.