Hyperfiltration in charged membranes: the fixed charge model

Salt rejection, R, in charged membranes was evaluated according to the fixed charge model as described by Teorell-Meyer-Sievers. Taking into account the concentration dependence of the transport coefficients, it was found that R at given Jr, is a function of the ratio between membrane charge and salt concentration, the mobilities of the ions, and the effective thickness of the membrane. The limiting salt rejection at high flow rates, R∞, is given by the reflection coefficient corresponding to the salt concentration in the feed solution R∞ = σ . Concentration profiles at high flow rates confirm this conclusion. The reflection coefficient,σ , is completely determined by the ratio between membrane charge and feed concentration, the valencies of the ions and the transport number of the counter-ion in free solution. R∞ was calculated for a wide region of relative charge densities, and several transport numbers corresponding to some common electrolytes. High transport number of the co-ion decreases R∞. For divalent counter-ions salt rejection is lower, as a consequence of the different ion distribution. Negative values for R∞ are obtained in a considerable part of the region. High salt rejection is obtained for divalent co-ions.