In this paper we study 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 round cylinder with filtration process in the axial direction. The cylinder is filled with sorbent i.e. absorbent material that passed through dirty water or liquid solutions. We can 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 reducing the 2-D axisymmetrical mass transfer problem decribed by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order. We consider also model 1-D problem for investigation the depending the concentration of water and sorbent on the time.
Kangro, I., & Kalis, H. (2018). On mathematical modelling of the solid-liquid mixtures transport in porous axial-symmetrical container with Henry and Langmuir sorption kinetics. Mathematical Modelling and Analysis, 23(4), 554-567. https://doi.org/10.3846/mma.2018.033
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