Correlation of permeability and solute uptake in membranes of arbitrary pore morphology

Membrane fouling is a phenomenon that plagues practically all ultrafiltration processes, and involves a buildup of solute molecules or particles on the external and internal pore surface of the asymmetric membrane. As a result, the effective pore size and porosity of the membrane decrease, with a concomitant decline in the solvent flux and an alteration of the sieving coefficient. There have been a number of attempts, generally based on the assumption of straight cylindrical pores, to qualitatively correlate the solute uptake with the decline in permeability. It is useful to develop a physically more appealing model that provides a quantitative correlation between adsorbed solute surface coverage and hydraulic permeability. This work develops such a model without recourse to a specific pore geometry, but rather in terms of independently measurable quantities: pore surface area and volume. Theoretical results are compared with previously published experimental results for protein uptake and hydraulic permeabilities (Robertson and Zydney, 1990) in ultrafiltration membranes.