On the Slow Viscous Flow through a Swarm of Solid Spherical Particles Covered by Porous Shells

Abstract

This paper concerns the slow viscous flow through a swarm of concentric clusters of porous spherical parti- cles. An aggregate of clusters of porous spherical particles is considered as a hydro-dynamically equivalent to a porous spherical shell enclosing a solid spherical core. The Brinkman equation inside and the Stokes equation outside the porous spherical shell in their stream function formulations are used. As boundary conditions, continuity of velocity, continuity of normal stress and stress-jump condition at the porous and fluid interface, the continuity of velocity components on the solid spherical core are employed. On the hypothetical surface, uniform velocity and Happel boundary conditions are used. The drag force experienced by each porous spherical shell in a cell is evaluated. As a particular case, the drag force experienced by a porous sphere in a cell with jump is also investigated. The earlier results reported for the drag force by Davis and Stone(5) for the drag force experienced by a porous sphere in a cell without jump, Happel(2) for a solid sphere in a cell and Qin and Kaloni(4) for a porous sphere in an unbounded medium have been then deduced. Representative results are pre- sented in graphical form and discussed.