Theoretical analysis of pore size distribution effects on membrane transport

Abstract

The membrane selectivity can be critically affected by the pore size distribution. We examined the effect of different pore size distributions on the asymptotic membrane sieving coefficient, the hindered solute diffusivity, and the membrane hydraulic permeability by averaging the solute and solvent transport rates over specific pore size distributions. Although the calculated sieving coefficients and hindered diffusivities both increased significantly with an increase in the breadth of the distribution, the relationship between these two membrane transport parameters was relatively unaffected by the pore size distribution, allowing for reasonably accurate predictions of the hindered diffusivity from sieving data (or vice versa). These detailed calculations were also compared with predictions of a recently developed analytical model which implicitly accounts for the pore size distribution by evaluating the effective solute to pore size ratio using an expression for the solute partition coefficient in a random porous media. Model predictions were in good agreement with the detailed integral results for a membrane with a log-normal distribution with geometric standard deviation of around two, which is consistent with the observed pore size distribution for many ultrafiltration membranes. Model calculations also examined the effects of protein adsorption on membrane transport, with very different behavior seen for different adsorption mechanisms.