Modeling the Process of Filtering a low-Concentration Solution through a Porous Medium
DOI:
https://doi.org/10.71310/pcam.4_68.2025.10Keywords:
mathematical model, cylindrical filter, Navier–Stokes equations, Darcy’s law, Poisson equation, advection–diffusion, hydrodynamicsAbstract
This article presents an integrated mathematical model of radial filtration in a cylindrical filter, in which the flow movement is carried out from the outer layer to the inner cavity. Free flow areas are described by Navier-Stokes equations for incompressible fluid, where the filtration process through the porous layer is formalized based on Darcy’s law, and the pressure distribution is determined by the Poisson equation. The transfer of dissolved substances is modeled using the advection-diffusion equation. The model includes a mechanism for the evolution of porosity over time (sealing or clogging), which allows tracking the conjugate dynamics of the "pressure-velocity-porosityconcentration" parameters. The analysis showed that considering the vertical orientation of the cylindrical filter is a significant factor influencing the reduction of energy costs and increasing the selectivity of the process.
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