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.