Prediction of the rate of cross-flow ultrafiltration of colloids with concentration-dependent diffusion coefficient and viscosity — theory and experiment

Abstract

The influence of the physicochemical conditions on the permeation rate in cross-flow ultrafiltration of a colloidal suspension has been investigated. A numerical solution of the coupled Navier–Stokes, continuity and convective diffusion equations has been used to model the concentration polarisation and hence predict the rate of cross-flow ultrafiltration. A 2-D finite difference solution based on the Thomas algorithm and coded in FORTRAN has been developed. The model may be applied to flat sheet modules (with one or two porous walls) and is easily adapted to tubular modules. The model is versatile and can be run with constant or variable properties. The model takes into account the effects of the variation of the three key properties of osmotic pressure, diffusion coefficient and viscosity throughout the module. Determination of these three key physical properties was based on a fundamental calculation of the colloidal interactions between particles which accounts for multiparticle electrostatic interactions, dispersion forces and configurational entropic effects. These descriptions of colloidal interactions were used to develop an a priori model, with no adjustable parameters, that allows quantitative prediction of the properties of a colloidal dispersion as a function of pH (and hence colloid surface properties), colloid size, ionic strength and colloid concentration. The model results have been compared to experimentally measured data for the proteins bovine serum albumin and recombinant human lactoferrin. Good agreement between theoretical predictions and experimental cross-flow ultrafiltration data has been obtained. The results of these calculations show that, contrary to the usual assumption, the effects of variable viscosity and variable diffusion coefficient are both significant and comparable in magnitude. The numerical description of the cross-flow filtration model developed is completely general and allows for the future incorporation of any theoretical description for key solution properties.