Convective stability of horizontal filtration flow through a closed domain of porous media with clogging

The present paper is devoted to the study of horizontal filtration flow through a closed porous domain with the extraction of some impurities from the mixture by immobilizing them. Usually, the filter is damaged after some time of use because of clogging. Here, we generalize the mathematical model for immobilization and clogging. The investigation of the transition of instability modes from monotonous to oscillatory and the influence of clogging on these phenomena are presented. It is shown that the oscillatory mode is observed in long domains or at moderate intensity of the external horizontal flow. At low flow intensities, the convective cells are stationary and there is no reason for oscillations. At high intensities, the external flow suppresses the convective oscillations. It is found, that the interval of flow intensity values, in which oscillations are observed, grows with increasing domain length, and for thin domains large intensities are needed to excite the oscillatory mode. Clogging leads to the stabilization of horizontal flow with respect to convective perturbations and sometimes to the dumping of the oscillations. The critical curves and instability maps in a wide range of the problem parameters are obtained and analyzed. For the limiting cases, a comparison with the results of the well-known Horton-Rogers-Lapwood problem (HRL) has been made.