Numerical algorithm for the problem of the technological process of filtering low-concentrated suspensions

The paper presents a mathematical model in the form of a second-order nonlinear differential equation with initial and boundary conditions and a numerical method for solving the problem based on the finite-difference method of the technological process of filtration of low-concentration suspensions to determine the ranges of variation of the ion-exchange filter parameters, as well as the results of computational experiments. When developing a mathematical model, the following main filter parameters and physico-mechanical properties of solutions (liquids) were taken into account: filtration rate, rate of sedimentation of gel particles on the pores of the filter, filter porosity, filter layer thickness, kinetic coefficient, dynamic viscosity coefficient and outlet concentration of the suspension. The developed mathematical model and a numerical solution method allow determining the deposition rate of gel particles in the pores of the filter, the outlet concentration of the solution and changes in the concentration of the driving solution of the ion-exchange filter.