Non-equilibrium thermodynamics of concentration polarization.

Ultrafiltration is a membrane separation process with many applications, including the treatment of industrial wastes and the processing of milk and juices. 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 is not yet fully understood, and is related to a decline in the efficiency, is the concentration polarization layer, which develops as the macromolecules retained by the membrane form a highly concentrated layer that attempts to diffuse back toward the bulk of the solution. Using the postulates of classical non-equilibrium thermodynamics, a complete model, which accounts for the fact that a concentration polarization layer may have properties of both a porous medium and a region undergoing Brownian diffusion, has been derived and applied to several systems from the literature.