Modeling of cadmium salts rejection through a nanofiltration membrane: relationships between solute concentration and transport parameters

Based on the model initially proposed for nanofiltration combining the modified equation of Nernst–Plank and the film theory, expressions were developed to allow accurate characterization of solute transports during nanofiltration. In nanofiltration, the solute concentration in the feed solution is one of the factors which have an effect on solute rejection. So, it was important to study the effect of solute concentration on these transport parameters. In this approach, the model transport parameters, Keff and Φ have been related to the feed solution concentration. While serving to us as the equilibrium equations of Donnan and that of Kirianov, we have established relations between these parameters of transport to the concentration of the feed aqueous solutions. Both the effective transfer coefficient and the transmittance increase when concentration increases. The relations describe our experimental results satisfactorily. They have also allowed us the determination of the order of the charge density of the membrane. It was found to be 8.57×10−4 and 49.5×10−4 equivalent mol l−1 which correspond to −33 and −191 mC m−2, respectively for a 0.4 μm membrane thickness.