Generalized Darcy’s Law in Filtration Theory
RUDN University, Moscow, Russian Federation
Published online: 14 February 2018
We study the hydrodynamics of flow in a porous medium modeling the grain filling in filters. Using the lattice approximation, we derive the structure of the current in porous media and obtain the transverse diffusion coefficient D which proves to be proportional to the diameter d of the grains as constituents of the medium. We consider the axially-symmetric stationary flow in a cylindrical filter and show that the vertical velocity takes its maximal value at the wall, this effect being known as the “near-wall” one. We analyze the solution to the Euler equation with the modified Darcy force, which depends not only on the velocity but also on the gradient of the pressure included in the Darcy coefficient. Finally, within the scope of the perturbation method, we derive the main filtration equation and discuss the influence of modifying the Darcy’s law on the efficiency of the filtration process.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).