The central Darken problem was considered from the point of view of the choice of the coordinate axes for diffusion. That is, the definition of this mode of motion and of the method of diffusion displacement, was defined and measured. The Euler and Liouville theorems were used extensively in the analysis. The formula was derived for volume density conservation (volume continuity equation). This fundamental formula defined a volume-fixed frame of reference in the multicomponent solid, gas and liquid solutions. The volume-fixed frame of reference was self-consistent with the foundations of linear irreversible thermodynamics; except that it recognised the need to add volume density to the usual list of extensive physical properties undergoing transport in every continuum. The proposed modifications were consistent with literature dating back to Onsager, the experiments of Kirkendall, their interpretation by Darken and recent generalized formulations. It was shown that the method could be applied to mechano-chemistry and electro-mechano-chemistry.

Diffusion, Drift and their Interrelation through Volume Density. M.Danielewski, B.Wierzba: Philosophical Magazine, 2009, 89[4], 331-48