A Stefan-Maxwell Analysis of Protein Transport in Porous Membranes

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Abstract
The Stefan-Maxwell multicomponent diffusion equations were used to characterize albumin transport in ultrafiltration membranes in both an unstirred batch filtration device and a well-stirred diffusion cell. We developed a theoretical model for ultrafiltrate flux and concentration in the filtration device that explicitly incorporates the effects of protein polarization, protein osmotic pressure, and a flux-dependent sieving coefficient. Experimental data were in good agreement with model predictions, providing quantitative evidence for the predicted dependence of the apparent sieving coefficient on flux. Experimental data in the diffusion cell indicate that the effective albumin diffusivity in the 50,000 molecular weight cut-off membranes was four orders of magnitude less than the Brownian motion value. The Stefan-Maxwell diffusivities evaluated independently in the two experimental systems were in excellent agreement, indicating the general applicability of the Stefan-Maxwell approach to protein transport in ultrafiltration membranes.