Mathematical modeling of the hydrodynamic permeability of a membrane built up from porous particles with a permeable shell

The authors review their investigations of the hydrodynamic permeability of porous membranes built up from completely porous particles or particles with a porous shell. During a filtration process, the particles or fibers, which form the membrane, may change their surface structure due to dissolution and/or an adsorption of polymers. Both processes result in a formation of a porous layer of the surface of particles or fibers. The presence of the porous layer influences the total permeability of the membrane. The influence of the porous shell on the total permeability is investigated. The cell method is used along with special boundary conditions on the cell surface. For the description of the fluid flow inside a porous layer or a completely porous particle, the Brinkman equations are applied. It is shown that the fluid flow penetrates only on a finite depth inside the porous shell of the particles. Different limiting cases are investigated.