The application of nanofiltration in industrial fields is increasing rapidly in recent years, especially in drinking water treatment. Nevertheless, the mechanism of mass transport through these membranes has not yet been fully understood. And the optimal design of nanofiltration processes still faces challenges. At first, the Donnan Steric Pore Model (DSPM) is described in this paper, which is constructed on the basis of the extended Nernst-Planck equation for the prediction of the nanofiltration process of polymeric membrane. Then the DSPM model is used to characterize three kinds of membranes (AFC40, CA30 and NTR7450) for the nanofiltration of 50 mol/m³ NaCl solution and NTR7450 membrane for the nanofiltration of NaCl and MgSO₄ solution with different concentrations. The simulated results and their comparison with experimental results show that the DSPM model can effectively predict the membrane performance. And then a description of the Pores and Polarization Transport Model (PPTM) is presented, which is developed on the basis of the DSPM model, in order for characterizing cross-flow nanofiltration. The PPTM model combines the convection-diffusion-migration transport in the nanopores with the transport through the concentration polarization layer. To improve the PPTM model in the aspect of using an empirical model to describe the velocity field of solution above the membrane, the velocity profile in solution is solved by Navier-Stokes equation and continuity equation in this paper. The cross-flow nanofiltration of polymeric membrane is simulated using the finite element method, by coupling mass transfer in the membrane with ion concentration and velocity profile in solution above the membrane. By the comparison with experimental results and traditional PPTM results, it can be found that the modified method can reflect the change tendencies of ion concentration and velocity profile in solution, and their values are more in line with the values of experiments. The improved model can provide more reliable theoretical basis for the optimal design of cross-flow nanofiltration processes of polymeric membrane.

Key words: nanofiltration membrane, concentration polarization, transport model, velocity profile, finite element simulation