Ideal limiting fluxes in ultrafiltration: comparison of various theoretical relationships

The ultrafiltration of macromolecules is characterised by a limiting flux at high transmembrane pressures. There is also some evidence that at high pressures and low crossflow velocities the flux decreases slightly with increasing pressure. It is confirmed from a theoretical viewpoint that this can only be caused by a decrease in the average mass-transfer coefficient due to concentration increases in the boundary layer. At the practical level, we propose an expression which, for a given system, enables the ideal flux to be estimated a priori as a function of the transmembrane pressure. The ideal flux is defined as that flux which would occur in the absence of fouling and gelation. The model includes the influence of both osmotic pressure and the variation in viscosity due to concentration polarisation. Thus for predictive purposes knowledge of osmotic pressure and viscosity as a function of concentration is required. The only membrane parameter that has to be experimentally determined is the membrane permeability. In the absence of adsorption (which is the ideal case) this is the permeability to the pure solvent. The model has been tested against Jonsson's data for the ultrafiltration of dextran solutions. The results are most encouraging.