Diffusing uphill with James Clerk Maxwell and Josef Stefan

The primary objective of this article is to highlight a number of situations of importance in chemical engineering in which one of the components in a mixture is transported uphill of its own composition gradient. The proper appreciation and modeling of uphill diffusion requires the use of chemical potential gradients as driving forces. Furthermore, due account needs to be taken of coupling effects, that is, the influence of the driving force of any component in the mixture on the transport fluxes of all partner species in the mixture. The Maxwell-Stefan formulation, that has its roots in theory of irreversible thermodynamics, affords the most general, and convenient, approach for modeling diffusion in fluid mixtures, electrolytes, alloys, glasses, and porous adsorbents.