Concentration polarization of interacting solute particles in cross-flow membrane filtration

A theoretical approach for predicting the influence of interparticle intera ctions on concentration polarization and the ensuing permeate flux decline during cross-flow membrane filtration of charged solute particles is presen ted. The Ornstein-Zernike integral equation is solved using appropriate clo sures corresponding to hard-spherical and long-range solute-solute interact ions to predict the radial distribution function of the solute particles in a concentrated solution (dispersion). Two properties of the solution, name ly the osmotic pressure and the diffusion coefficient, are determined on th e basis of the radial distribution function at different solute concentrati ons. 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 p ermeate flux. The approach leads to a direct quantitative incorporation of solute-solute interactions in the framework of a standard theory of concent ration polarization. The developed model is used to study the effects of io nic strength and electrostatic potential on the variations of solute diffus ivity and osmotic pressure. Finally, the combined influence of these two pr operties on the permeate flux decline behavior during cross-flow membrane f iltration of charged solute particles is predicted.(C) 1999 Academic Press.