Nanofiltration Theory:  Good Co-Ion Exclusion Approximation for Single Salts

We applied an approximate analytic method, the good co-ion exclusion (GCE) approximation, to the hindered electrotransport theory describing salt and solution transport across charged nanofiltration membranes. This approximation, which should be valid at sufficiently low feed electrolyte concentration, leads to a considerable simplification of the exact parametrized equations obtained previously for single salt nanofiltration parameters (salt rejection, electric filtration potential, and volume flux density) and therefore provides further insight into ion transfer in nanoporous membranes. We also established the domain of validity of the GCE approximation as a function of the salt type for 1:1, 2:1, 1:2, and 2:2 salts. Our results for the volume flux density, obtained within an extended GCE approximation, confirm that the global osmotic reflection coefficient in the solution flux equation is not equal to the limiting salt rejection.