A detailed discussion is presented of three well-known macroscopic theories for describing the mass transport behavior of multicomponent mixtures; these include Fick's law, the Onsager theory of irreversible thermodynamics, and the Maxwell-Stefan theory. The merits and drawbacks of these theories are discussed, together with their interrelation. These macroscopic theories and an entirely microscopic theory are applied to describe the transport of a mixture of mobile species in a microporous material obeying ideal Langmuir sorption behavior, which is an issue of considerable interest in the field of membrane technology. If a unary system, i.e., a single mobile species, is considered, the chemical diffusion coefficient appears to be independent of the concentration. In this case, mass transport can simply be described using Fick's law. For a multicomponent mixture, the chemical diffusion coefficients become a function of composition and Fick's law can no longer be used in a straightforward way. The two remaining macroscopic theories and the microscopic theory can adequately describe the mass transport behavior, assuming that mechanical interactions between the mobile species are negligible. When mechanical interactions are not negligible, only the Maxwell-Stefan theory yields a proper description. Applying the Onsager theory of irreversible thermodynamics in that case would lead to off-diagonal transport coefficients that are nonzero. Also, the microscopic theory used in this study is then no longer applicable, since it simply neglects interactions between mobile species. It is demonstrated that the use of virtual chemical potentials for the mobile species, by contrast with real chemical potentials of building units, complicates the description of mass transport.
Benes, N. E., & Verweij, H. (2000). Comparison of macro- and microscopic theories describing multicomponent mass transport in microporous media. Langmuir, 15(23), 8292-8299. https://doi.org/10.1021/la9905012