Slow viscous flow through a membrane built up from porous cylindrical particles with an impermeable core

Abstract

This paper concerns the slow viscous flow through an aggregate of concentric clusters of porous cylindrical particles with Happel boundary condition. An aggregate of clusters of porous cylindrical particles is considered as a hydro-dynamically equivalent to solid cylindrical core with concentric porous cylindrical shell. The Brinkman equation inside the porous cylindrical shell and the Stokes equation outside the porous cylindrical shell in their stream function formulations are used. The drag force acting on each porous cylindrical particle in a cell is evaluated. In certain limiting cases, drag force converges to pre-existing analytical results, such as, the drag on a porous circular cylinder and the drag on a solid cylinder in a Happel unit cell. Representative results are then discussed and presented in graphical forms. The hydrodynamic permeability of the membrane built up from porous particles is evaluated. The variation of hydrodynamic permeability with different parameters is graphically presented. Some new results are reported for flow pattern in the porous region. Being in resemblance with the model of colloid particles with a coating of porous layers due to adsorption phenomenon, results obtained through this model can be useful to study the membrane filtration process.