Open AccessGeneralizing Darcy’s law for filtration radial flows through porous media
Author(s) -
Yu. P. Rybakov,
N.V. Semenova,
Jurabek Shakarovich Safarov
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/675/1/012064
Subject(s) - darcy's law , filtration (mathematics) , porosity , porous medium , axial symmetry , mechanics , homogeneous , generalization , mathematics , physics , mathematical analysis , materials science , geometry , thermodynamics , pure mathematics , composite material
We study the filtration process in porous media and compare the filtration coefficients for two possible geometries of flows: cylindrical and radial ones. Solving balance equations for impurity concentration in the simplest axially-symmetric stationary case, one finds the radial filtration process more effective. Therefore, we restrict our attention to the radial filters with non-homogeneous grain filling. First, we describe the transverse diffusion effect and then suggest the generalization of the Darcy’s filtration law, its dynamical origin being stressed. Using the perturbation method, we find the structure of the Stokes stream function for some particular choices of the porosity.