Model of suspension displacement in a porous medium

The displacement of monodisperse suspension by clean water in a porous medium, accompanied by the formation of deposit is considered. A flow of water is supplied at the inlet of the porous medium filled with suspension. The suspension is displaced by water moving at a constant velocity. A mathematical model of deep bed filtration of suspension in a porous medium based on size-exclusion mechanism of particle retention and pore clogging is formulated. It is proved that in the suspension area the solution depends only on time, and in the clean water area – only on the distance to the porous medium inlet. For constant initial conditions an exact solution of the problem is constructed. In the case of linear filtration coefficient, the analytic solution is given in explicit form. The properties of the obtained solutions are analyzed