Parametric Excitation of Concentration Convection in a Closed Region of a Porous Medium in the Presence of Solute Particle Immobilisation

Mathematical modelling of the effect of fluid flow modulation on concentration convection in a closed region of a porous medium taking into account the immobilisation of impurity on pore walls has been carried out. Transport of impurity taking into account the effect of immobilisation (deposition) of impurity particles on pore walls is modelled in the framework of MIM approach, filtration of mixture in a closed region is considered in the Darcy-Boussinesq approximation. As a result, an exact solution of the problem has been obtained; the present solution describes one-dimensional filtration in the horizontal direction through the considered closed region of the porous medium. The stability problem of the obtained exact solution is solved in linear approximation. The method of solving the stability problem is developed on the basis of the Galerkin approach. Neutral curves in the parameter space of the problem are constructed, and the synchronisation of perturbations with external flow modulation is studied. The possibility of controlling excited convective modes by modulating the external fluid flow (pumping) is described.