Membrane Swelling and Flux Coupling

Because a vacuum is applied for the removal of the solutes on the membrane downstream face, this side of the membrane is ideally dry in comparison to the more swollen (if polymeric membranes are employed) and hence more flexible membrane upstream face resulting from the solute uptake. This anisotropy of the membrane in the direction of the diffusion of the solute always exists for polymeric membranes and results in a non-uniform diffusivity of solute within the membrane. In other words, the diffusion coefficient of solute i in the membrane, will be position-dependent and not constant across the membrane. 

For the description of such interactions as well as of polymer swelling, models based on the Flory-Huggins Theory (Flory, 1953 Mulder, 1991) and UNIQUAC are often applied for mixtures in general and, for binary mixtures, also the Solubility Parameter Theory if the feed components are hydrophobic (Hildebrand and Scott, 

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