Integral method of analysis for combined concentration polarization and pore flow model for prediction of the performance of a nanofiltration membrane

Abstract

A coupled concentration polarization and pore flow model was used to predict the transport characteristics of a monovalent salt through a nanofiltration membrane. The concentration polarization in the flow channel was modeled using an integral method under the framework of boundary layer analysis. The extended Nernst–Planck equation was used to quantify the ion transport through the membrane pores. Ion partitioning across the solution phase and in the membrane pore was modeled using the Donnan exclusion principle including the steric hindrance. The membrane pore charge density was calculated for different membranes. The contributions of convection, diffusion, and electromigration toward the solute flux within the membrane pore were estimated. The calculated permeate flux and the solute concentration in permeate were compared with the experimental data available in the literature and were found to be in good agreement, indicating validation of the developed model.