Multicomponent diffusion in highly asymmetric systems. An extended Maxwell-Stefan model for starkly different-sized, segment-accessible chain molecules

An extended version of the Maxwell-Stefan (EMS) equation is proposed to describe transport in multicomponent solutions of molecules that are starkly different in size and whose segments are all accessible for mutual frictional interactions. The proposed modification corrects the friction factor between the colliding molecules by replacing the molar species concentration by the molar segment concentration, or equivalently, by the volume fraction of the component. The new expression for the friction factor is consistent with the kinetic theory of Curtiss and Bird for polymer solutions in the limit of linear isotropic systems. When the classical generalized Maxwell-Stefan equation is applied to diffusion in a membrane-solvent system, the (unknown) molecular weight of the membrane must be specified. In EMS, however, such a specification is not required. Further, in contrast to a previous equation for polymer solutions proposed by Heintz and Stephan (J. Membr. Sci. 1994, 89, 153), EMS is consistent with restrictions given by the Gibbs-Duhem equation and by Onsager's reciprocity relations. The multicomponent diffusion equation proposed here is appropriate for modeling mass transfer in a variety of technologies, including membrane-separation operations, polymer drying and coating, and multicomponent transport in biological membranes, cells, and drug-delivery systems.