Particle Transport With Finite Filtration Time

Particle transport by a fluid flow occurs in many applied construction problems, including pumping mortar into porous soil, creating watertight diaphragm walls, and constructing dams and underwater structures. A model of deep bed filtration of suspensions and colloids in a homogeneous porous medium with a finite number of vacancies for retained particles is considered. A suspension of constant concentration is injected into the inlet of a porous medium containing clean water. If the sediment growth rate remains positive as the sediment concentration approaches the upper limiting value, the filtration process continues for a finite time. In this case, the filtration function that specifies the sediment growth rate in the mathematical model is not blocking. At each point of the porous medium, sedimentation begins from the moment the concentration front passes and ends after a finite period of time depending on the distance to the porous medium inlet. A global exact solution to the problem is constructed in the filtration domain, which consists of two zones. In the zone bordering the concentration front, the solution has a standard form, and in the zone adjacent to the upper limiting values of the concentrations of suspended and retained particles, it has the form of a traveling wave.