MODELING MULTIION TRANSPORT IN HYPERFILTRATION MEMBRANES WITH FIXED CHARGES

A new model for the pressure driven transport of ionic solutes across hyperfiltration membranes containing fixed charges is presented in terms of membrane thickness and charge density, flux, ion concentrations in the feed solution and ion diffusivities in the membrane. The model envisages the transport of the ions from the feed solution to the permeate solution as passing through three defined regions: a transition region between the feed and the core of the membrane, the core of the membrane and another transition region between the core of the membrane and the permeate. The transport equations are the extended Nerst Planck (ENP) equations coupled with the one-dimensional Poisson equation in the two equations regions and the ENP equation coupled with the electroneutrality condition in the core of the membrane. Thus, the model hypothesizes that the electric field in the core of the membrane is zero. It predicts an increase in rejection with increasing membrane fixed charge density, flux and thickness and a decrease with increasing feed concentration. In an application with a solution containing mixed coions, H+ and K+, it predicted a large difference in rejection of the coions, approaching the experimental values using parameters appropriate for the membrane. The direct dependence of rejection on membrane thickness has not been given significance until now and is an important result of the model.