Concentration polarization in cross-flow reverse osmosis

A dimensionless governing equation was formulated for a cross-flow RO process in which the local variation of concentration polarization was rigorously considered. It was shown in this formulation that the cross-flow RO process could be fully characterized with a single dimensionless parameter. The coupling between permeate flux and concentration polarization was properly solved and a closed-form analytical solution was obtained. This analytical solution enabled us to conveniently investigate concentration polarization in the RO process. The significance of local variation of concentration polarization was demonstrated, and the operations of RO under various conditions were simulated and investigated with the newly developed model.

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