THEORY OF CONCENTRATION POLARIZATION IN CROSS-FLOW FILTRATION

A novel theory is developed for concentration polarization of non-inte racting particles in crossflow-filtration systems. This theory reveals that the extent of concentration polarization, as well as the behavio ur of the permeate flux, are characterized by an important dimensionle ss filtration number (N-F = 4 pi a(p)(3) Delta P/3kT). There is a crit ical value of the filtration number for a given suspension and operati onal conditions. When the filtration number is smaller than the critic al value, a polarization layer exists directly over the membrane surfa ce and the wall particle concentration is determined by the pressure a nd temperature. At higher filtration numbers, a cake layer of retained particles forms between the polarization layer and the membrane surfa ce. Mathematical models are constructed for both cases and analytical solutions for the permeate flux are derived. An increase in permeate f lux with increasing pressure is predicted for all operational conditio ns.