A total salt balance model for concentration polarization in crossflow reverse osmosis channels with shear flow

A new model in determining concentration polarization in reverse osmosis (RO) channel was developed, upon previous works on the retained salt for the transverse distribution and the total salt balance (TSB) along the longitudinal direction in the RO channel. Shear flow was employed in the new formulation of concentration polarization in the RO channel so that the result of the model could be compared to the analytical solution of Song-Elimelech model for the membrane channels where the changes in hydraulic conditions were negligible. When applied to long-narrow RO channels, the difference in concentration polarization caused by employment of plug or shear flows was shown to be small, indicating the applicability of relatively simple formulation based on plug flow in determining concentration polarization of practical RO processes. Finally, comparisons of the mass transfer method and Song-Elimelech model with the new model indicated that the former two methods could only be used with precautions in the predicting polarization modulus and permeate velocity under certain conditions.