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This article discusses the theoretical description of transport of large molecules through membranes with narrow pores. An overview of commonly used model descriptions of membrane filtration processes is given; it is shown that these descriptions are special cases of the generalised Maxwell–Stefan description. The work on Maxwell–Stefan descriptions of Mason and others is expanded and connected to the hydrodynamic theory of Bungay, Brenner and Deen. Two different forms of the Maxwell–Stefan equations for porous media are considered, defined as the structured approach and the overall approach. In the structured approach, the membrane is taken to be a structure with defined pores. In this description, diffusive and viscous transport are considered separately. In the overall approach, the membrane and permeants are considered to form one, pseudo-homogeneous phase. This description does not distinguish between diffusive and viscous transport, instead it combines these mechanisms in one overall transport velocity. It is important to distinguish between the approaches in order to correctly connect the generalised Maxwell–Stefan equations to the hydrodynamic theory. In this article, this connection has been made and relations for the friction coefficients and the viscous selectivity have been derived for use in the generalised Maxwell–Stefan equations. The description thus developed is compared to data on falling spheres through cylindrical tubes, diffusion of uncharged solutes through membrane pores and pressure-driven transport of these solutes through membranes. |
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