The continuum mechanical theory of multicomponent diffusion in fluid mixtures

The continuum mechanical approach for deriving the generalized equations of multicomponent diffusion in fluids is described here in detail, which is based on application of the principle of linear momentum balance to a species in a mixture, resulting in the complete set of diffusion driving forces. When combined with the usual constitutive equations including the continuum friction treatment of diffusion, the result is a very complete and clear exposition of multicomponent diffusion that unifies previous work and includes all of the various possible driving forces as well as the generalized Maxwell–Stefan form of the constitutive equations, with reciprocal diffusion coefficients resulting from Newton’s third law applied to individual molecular encounters. This intuitively appealing and rigorous approach, first proposed over 50 years ago, has been virtually ignored in the chemical engineering literature, although it has a considerable following in the mechanical engineering literature, where the focus, naturally, has been physical properties of multiphase fluid and solid mixtures. The described approach has the advantages of transparency over the conventional approach of non-equilibrium thermodynamics and of simplicity over those based on statistical mechanical or kinetic theory of gases or liquids. We provide the general derivation along with some new results in order to call attention of chemical engineers to this comprehensive, attractive, and accessible theory of multicomponent diffusion in fluids.