A Cell Model of a Membrane with Allowance for Variable Viscosity of Liquid in Porous Shells of Spherical Grains

Abstract

The Happel–Brenner cell method has been employed to calculate the hydrodynamic permeability of a porous medium (membrane) composed of a set of partially porous spherical particles with solid impermeable cores. This representation is used to describe the globular structure of membranes containing soluble grains. The apparent viscosity of a liquid is suggested to increase as a power function of the depth of the porous shell from the viscosity of the pure liquid at the porous medium–liquid shell interface to some larger value at the boundary with the impermeable core. All known boundary conditions used for the cell surface, i.e., those proposed by Happel, Kuwabara, Kvashnin, and Cunningham, have been considered. Important limiting cases have been analyzed.