Permeability of complex porous media

Hydrodynamic permeability of membrane composed of a set of porous spherical particles with rigid impenetrable cores is calculated. The cell method proposed by Happel and Brenner is used in calculations. All known boundary conditions on the cell surface, such as the Happel, Kuwabara, Kvashnin, and Cunningham (Mehta-Morse) models, are considered. The flow of liquid is described by the Brinkman equations. The problem of flow around a single spherical particle covered with porous layer by the uniform flow of viscous incompressible liquid is solved. Theoretical and empirical results are compared. Different limiting cases for which the derived formulas lead to results known from published literature are considered.