Multicomponent diffusion—A brief review

• Brief historical summary of the theory of diffusion in multicomponent systems.
• Development of an expression for the driving forces for diffusion in mixtures.
• Driving force includes concentration, thermal, pressure, and forced diffusion.
• Merk’s method for relating generalized Fick and Maxwell diffusivities in mixtures.
• The role of activity vs. concentration data in interpreting multicomponent diffusion.

After a brief summary of previous work on multicomponent diffusion theory, we review how the thermodynamics of irreversible processes leads us to an expression for the generalized driving force for diffusion. We then give the generalized Fick’s law expression containing the diffusivities DαγDαγ; then we show how this may be turned “wrong-side out” using Merk’s method to give the generalized Maxwell–Stefan equations containing the diffusivities Ð12≡x1x2/C12Ð12≡x1x2/C12. Finally, we show how the latter are related to the diffusivities D12D12 that are usually reported in the literature. All results are applicable to gases or liquids. This review is restricted to presenting the basic theory in a consistent notation, and not to the applications of the theory.