Eur. Phys. J. Plus (2018) 133: 1
https://doi.org/10.1140/epjp/i2018-11804-8

Regular Article

Motion through a non-homogeneous porous medium: Hydrodynamic permeability of a membrane composed of cylindrical particles

Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004 (U.P.), Allahabad, India

^* e-mail: pramod547@gmail.com

Received: 16 October 2017
Accepted: 23 November 2017
Published online: 5 January 2018

Abstract

The present problem is concerned with the flow of a viscous steady incompressible fluid through a non-homogeneous porous medium. Here, the non-homogeneous porous medium is a membrane built up by cylindrical particles. The flow outside the membrane is governed by the Stokes equation and the flow through the non-homogeneous porous membrane composed by cylindrical particles is governed by Darcy’s law. In this work, we discussed the effect of various fluid parameters like permeability parameter , discontinuity coefficient at fluid-non homogeneous porous interface, viscosity ratio of viscous incompressible fluid region and non-homogeneous porous region, etc. on hydrodynamic permeability of a membrane, stress and on velocity profile. The comparative study for hydrodynamic permeability of membrane built up by non-homogeneous porous cylindrical particles and porous cylindrical shell enclosing a cylindrical cavity has been studied. The effects of various fluid parameters on the streamlines flow patterns are also discussed.