The concept that the total mass flow was the sum of a diffusional flux and a translation was applied to the general case of diffusional transport in an r-component compound (defined as interdiffusion in a 1-dimensional mixture). The equations of local mass conservation (continuity equations), appropriate expressions for describing the fluxes (drift and diffusional), and the momentum conservation equation (equation of motion) permitted a complete quantitative description to be given for the diffusional transport process (in a 1-dimensional mixture with constant concentration). Equations were derived which described the interdiffusion process (mixing) in the general case where the component diffusivities varied as a function of composition. When certain regularity assumptions and quantitative conditions (such as the diffusion coefficients having to lead to a parabolic-type final equation) were fulfilled, there was an unique solution to the interdiffusion problem. A good agreement between numerical solutions (obtained using the Faedo-Galerkin method) and experimental data was demonstrated. An algebraic criterion permitted the detection of a parabolic nature for a given problem. The required condition for so-called up-hill diffusion in a 3-component mixture was given, and a universal example of such an effect was demonstrated. The results extended the usual Darken approach. The phenomenology permitted quantitative data on the dynamics of processes to be obtained within an interdiffusion zone.

K.Holly, M.Danielewski: Physical Review B, 1994, 50[18], 13336-46