Permeability of media composed of impenetrable cylinders covered with porous layer

The liquid flow through a set of nonuniform porous cylinders with a impenetrable core are studied by the Happel—Brenner cell method. Different orientations of cylinders relative to the liquid flow, such as transverse, longitudinal, and random, are considered. Brinkman equations are used to describe the flow of liquid in the porous layer. All known boundary conditions on the cell surface (Happel, Kuwabara, Kvashnin, and Cunningham conditions) are considered. The models proposed can be used to describe the processes of reverse osmosis, as well as nano-and ultrafiltration.