Hydrodynamic permeability of aggregates of porous particles with an impermeable core

A hydrodynamic permeability of membranes built up by porous cylindrical or spherical particles with impermeable core is investigated. Different versions of a cell method are used to calculate the hydrodynamic permeability of the membranes. Four known boundary conditions, namely, Happel's, Kuwabara's, Kvashnin's and Cunningham/Mehta-Morse's, are considered on the outer surface of the cell. Comparison of the resulting hydrodynamic permeability is undertaken. A possible jump of a shear stress at the fluid-membrane interface, its impact on the hydrodynamic permeability is also investigated. New results related to the calculated hydrodynamic permeability and the theoretical values of Kozeny constant are reported. Both transversal and normal flows of liquid with respect to the cylindrical fibers that compose the membrane are studied. The deduced theoretical results can be applied for the investigation of the hydrodynamic permeability of colloidal cake layers on the membrane surface, the hydrodynamic permeability of woven materials.