Modelling of a Three-dispersed Suspension Filtration

The injection method of soil stabilization is one of the methods to improve the soil base during the road construction. This method consists in the introduction of special compounds into the ground with the help of special equipment. Such compositions, as a rule, are solutions of polymers or cement, which harden, forming a solid base. The advantages of the injection method of soil stabilization for roads include rapid completion of work, minimal environmental impact, the possibility of application in difficult geological conditions, as well as strengthening the soil base at great depth. Injection solutions penetrate into microcracks and micropores of soils, forming a deposition. The study of liquid filtration in a porous soil system is of great practical importance. The paper considers the filtration of liquid in a porous medium with three types of particles. In the considered problem, each of the three types of suspension particles is characterized by its linear filtration function. It determines the size-exclusion particle capture mechanism, in which particles whose diameter exceeds the size of the pores get stuck in them, the rest pass through them unhindered. Numerical solutions are obtained for the concentrations of suspended particles of three types, as well as the total deposition. Depending on the initial parameters of the problem, the concentrations of suspended particles are either monotonic functions or non-monotonic, reaching the maximum value. In this paper, asymptotic solutions are constructed for the concentrations of suspended and retained particles near the concentration front, which are compared with numerical ones. The solution is obtained at infinity using a traveling wave.