Axisymmetric Stokes Flow past a Swarm of Porous Cylindrical Shells

Abstract

The problem of an axisymmetric Stokes flow for an incompressible viscous fluid past a swarm of porous cylindrical shells with four known boundary conditions as Happel’s, Kuwabara’s, Kvashnin’s and Cunningham/Mehta-Morse’s is tackled. The Brinkman equation is taken for fluid flow through the porous region and the Stokes equation for fluid region in their stream function formulation are used. Drag force experienced by the porous cylindrical shell within a cell is evaluated. The hydrodynamic permeability of the membrane built by the porous particles is also investigated. For different values of parameters, the variation of drag force and the hydrodynamic permeability are presented graphically and discussed.

Keywords

• Cell models; Brinkman equation; Modified Bessel’s functions; Hydrodynamic permeability.