ULTRAFILTRATION OF COLLOIDAL DISPERSIONS - A THEORETICAL-MODEL OF THECONCENTRATION POLARIZATION PHENOMENA

A general thermodynamic model of the concentration polarization phenom ena of colloidal particles at a membrane surface is presented. The mod el is based on the balance between a thermodynamic force, due to the o smotic pressure gradient, and a frictional force, due to the fluid flo w around each particle. A cell model description is used to model the concentration dependence of the thermodynamic force as well as the how properties in the concentrated colloidal solution. Equilibrium thermo dynamics of the colloidal system can be used in the cell calculations since local equilibrium is assumed in the neighborhood of each colloid al particle (i.e., in each cell). This means that the concentration de pendence of the osmotic pressure can be obtained, either from an exper imental determination or from a theoretical model of the bulk properti es of the colloidal system. To exemplify the usefulness of the model w hen establishing the influence of different operating parameters, such as the transmembrane pressure, the fluid shear, or different solution properties, such as concentration, particle size, pH, and ionic stren gth, a model system of charged spherical colloidal particles is used. The interaction between the particles is in the presented examples ass umed to be a combination of electrostatic interactions, calculated fro m the Poisson-Boltzmann equation, dispersion forces, calculated as add itive 1/r(6) interactions, and a hard sphere interaction calculated fr om the Carnahan-Starling equation. (C) 1996 Academic Press, Inc.