A model of two-velocity particles filtration with variable injection

The filtration problems are actual in the design of underground storage facilities for hazardous waste. When the grout is injected into the porous soil, the fluid penetrates deep into the rock and, when solidified, blocks the pores. A model of suspension flow with 2-size particles moving with different velocities in a porous medium is considered. The proposed model of deep bed filtration generalizes the known equations of mass balance and particle capture kinetics for a fluid flow with various particles. The injection of a suspension with periodically changing concentration is considered. Exact and asymptotic solutions are obtained. The asymptotics rapidly converges to the numerical solution