On Mathematical Modelling of the Solid-Liquid Mixtures Transport in Porous Axial-Symmetrical Container with Henry and Langmuir Sorption Kinetics

In this paper we study the diffusion and convection filtration problem of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances. As an example we consider a round cylinder with filtration process in the axial direction. The cylinder is filled with a sorbent. We derive the system of two partial differential equations (PDEs), one expressing the rate of change of concentration of water in the pores of the sorbent and the other - the rate of change of concentration in the sorbent or kinetical equation for absorption. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM). This procedure allows us to reduce the 2-D axisymmetrical mass transfer problem described by a system of PDEs to the initial value problem for a system of ordinary differential equations (ODEs) of the first order. We consider also a 1-D model problem and investigate the dependence of the concentration of water and sorbent on the time.