The Maxwell–Stefan description of binary diffusion

Abstract

The paper deals with interdiffusion in a two-component fluid (also called binary or mutual diffusion) near isothermal equilibrium. The historical approach of Maxwell and Stefan, developed in an ideal gaseous mixture, is updated by introducing the chemical potentials of the components subsequently devised by Gibbs, which enable one to implement the Maxwell–Stefan picture of interdiffusion in an arbitrary fluid mixture. The pattern of the interdiffusion law reduces to Fick's in the high-dilution limit, but care should be taken of the reference frame in which the laws of diffusion are written. For a third-year university student, the assets of the modern Maxwell–Stefan description, besides its simplicity and inborn connection with thermodynamics, are (i) manifest Galilean invariance (the principle of relativity of motion); (ii) straightforward compatibility with fluid dynamics; and (iii) simple generalization to a multicomponent fluid in future, graduate-level studies. The value of the mutual-diffusion coefficient, which is not given by the macroscopic description, was calculated by Stefan in an ideal gaseous mixture and found to be independent of the composition. That independence is often observed in real mixtures and is taken as evidence against the mean-free-path account of diffusion. Yet a mixture of components of disparate masses shows a dependence of the mutual-diffusion coefficient on its composition, and we examine why Stefan's calculation can be invalid for this mixture.