Coupled model of concentration polarization and pore transport in crossflow nanofiltration

A coupled model of concentration polarization and pore transport of multicomponent salt mixtures in crossflow nanofiltration rigorously predicts local variations of ionic concentrations, flux and individual ion rejections along a rectangular crossflow filtration channel by a coupled solution of the convective-diffusion and extended Nernst-planck equations. Coupling the pore transport model with the multicomponent convective-diffusion equation in the concentration polarization layer provides a comprehensive understanding of the interplay between concentration polarization and salt rejection. The coupled model is used to predict the local variations of ion rejection, permeate flux and mixture composition in a rectangular crossflow filtration channel for three-component salt mixtures. The total membrane surface concentration of the ions and the ratio of different ions in the mixture (salt ratio) can change considerably along a crossflow filtration channel, and, consequently, cause remarkable variations in intrinsic ion rejections with axial position in the channel.