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 J_r, 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.