Concentration Polarization of Interacting Solute Particles in Cross-Flow Membrane Filtration

Abstract

A theoretical approach for predicting the influence of interparticle interactions on concentration polarization and the ensuing permeate flux decline during cross-flow membrane filtration of charged solute particles is presented. The Ornstein–Zernike integral equation is solved using appropriate closures corresponding to hard-spherical and long-range solute–solute interactions to predict the radial distribution function of the solute particles in a concentrated solution (dispersion). Two properties of the solution, namely the osmotic pressure and the diffusion coefficient, are determined on the basis of the radial distribution function at different solute concentrations. Incorporation of the concentration dependence of these two properties in the concentration polarization model comprising the convective-diffusion equation and the osmotic-pressure governed permeate flux equation leads to the coupled prediction of the solute concentration profile and the local permeate flux. The approach leads to a direct quantitative incorporation of solute–solute interactions in the framework of a standard theory of concentration polarization. The developed model is used to study the effects of ionic strength and electrostatic potential on the variations of solute diffusivity and osmotic pressure. Finally, the combined influence of these two properties on the permeate flux decline behavior during cross-flow membrane filtration of charged solute particles is predicted.