The separation of mixed-electrolyte solutions with nanofiltration membranes was investigated by the combination of the extended Nernst-Planck equation, Donnan equilibrium model and the Poisson-Boltzmann equation. The nanofiltration membrane pores were modeled as slitlike pores characterized by the fixed pore size, pure water permeability and surface electrical potential. The ions in mixed-electrolyte solutions were represented as charged hard-spheres with the hydrodynamic diameters and diffusion coefficients at infinite dilution. The membrane parameters for three commercial nanofiltration membranes (ESNA1-LF, ESNA1 and LES90) were determined from the experimental ion fluxes and rejections of the electrolyte solutions through the corresponding membranes. The theoretical predictions show that diffusion and electro-migration are the main mechanisms of ion transport, and the steric and electrostatic effects are dominant for the ion rejections in nanofiltration (NF) membranes. From comparisons of the predicted ion rejections with the experiment data, it is suggested that the theory should give satisfactory results at low concentration for the mixed-electrolyte solutions containing monovalent ions, while deviations were found at a high concentration or for divalent ions.

Key words: membrane separation, nanofiltration, mixed electrolyte solution, extended Nernst-Planck equation, Poisson-Boltzmann theory