Concentration polarization affects numerous systems of membrane separation, and combined with osmosis, it can cause substantial reductions in permeation. We establish an exact solution to the conservation law of a solute advected by Berman flow. This flow is characteristic of reverse osmosis or nanofiltration. The resulting concentration polarization is then combined with the osmosis (counter-) effect. For large Peclet number of permeation, it yields a rigorous support to the semi-empirical "film" model, and accounts for the limit flux phenomenon. The main results are summarized in a simple diagram that relates three different Peclet numbers, and show that polarization combined with osmosis can withstand operating pressure almost totally. (C) 2010 Elsevier Ltd. All rights reserved.