The rejections of electrolyte solution in the nanofiltration membranes are very important for the desalination of sea water and the removal of heavy metal ions from water. In this work the nanofiltration membrane pores were modeled as slit-like pores with fixed pore size and surface electrical potential. The extended Nernst-Planck equation was used for the calculation of the ion fluxes through the membrane pores, in which the local concentrations of electrolyte ions on the membrane surfaces were evaluated from the Donnan equi-librium model and the charge densities on the membrane surfaces were predicted from the Gouy-Chapman theory. The parameters characterizing the nanofiltration membranes are the pure water permeability, pore width and membrane surface electrical potential, which are regressed from the experimental ion fluxes and rejections of single-electrolyte solutions in the nanofiltration membranes using Levenberg-Marquardt non-linear parameter estimation method. The rejections of 1∶1 (NaCl, KCl, LiCl), 2∶1 (K₂SO₄) and 2∶2 (MgSO₄) in the two commerical nanofiltration membranes (NF45 and SU200) are calculated using the developed model and compared with the ex-perimental data. Good agreements between theoretical and experimental results are achieved. The calculated results show that diffusion and electro-migration are the main mechanisms of ion transport. The steric and electrostatic effects are dominant for the ion rejections in nanofiltraiton (NF) membranes. Comparisons of the calculated ion rejections with the experimental data indicate that the model gave satisfactory results at low concentration for single-electrolyte solutions, while deviations are found at high concentration.

Key words: membrane separation, nanofiltration, electrolyte solution, extended Nernst-Planck equation, Gouy-Chapman theory