A modified Donnan–steric-pore model for predicting flux and rejection of dye/NaCl mixture in nanofiltration membranes

Abstract

This paper presents a modified Donnan–steric-pore model (DSPM) to predict the rejection of mixture of salts/charged organic in nanofiltration (NF) membranes, based on the extended Nernst–Planck equation with the incorporation of charge and steric effects for the transport of ions inside the membrane, and incorporation of concentration polarization effect for a mixture of charged ions/solutes. With this approach, the permeate flux can be calculated based on the concentration of ions/charged solutes at the membrane surface. The membrane performance was modeled using three parameters, namely: effective pore radius, r p; effective ratio of membrane thickness to porosity, Δx/A k; and the effective charge density, X d. Comparison of the calculation based on the model with published experimental data shows that the model can predict the tendencies and patterns of rejection and flux reduction behavior reasonably well for systems containing NaCl–dye–H2O. Effects on fluxes and NaCl rejections of system variables such as mass transfer film thickness, dye valence, dye diffusivity, and dye/salt concentration ratio were studied using this model. This model can be used as a preliminary tool to assess the rejection capability as well as the flux behavior of NF membranes towards binary solution and mixtures.