Non-equilibrium thermodynamics of concentration polarization

Ultrafiltration is a membrane separation process with many applications, in cluding the treatment of industrial wastes and the processing of milk and j uices. Academics are also interested in ultrafiltration as a possible tool for measuring empirical coefficients such as the diffusion coefficient and the permeability. One particular region of an ultrafiltration system that i s not yet fully understood, and is related to a decline in the efficiency, is the concentration polarization layer, which develops as the macromolecul es retained by the membrane form a highly concentrated layer that attempts to diffuse back toward the bulk of the solution. Using the postulates of cl assical non-equilibrium thermodynamics, a complete model, which accounts fo r the fact that a concentration polarization layer may have properties of b oth a porous medium and a region undergoing Brownian diffusion, has been de rived and applied to several systems from the literature. (C) 2001 Elsevier Science B.V. All rights reserved.