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This paper revisits the modeling of multicomponent diffusion within theframework of thermodynamics of irreversible processes. We briefly review thetwo well-known main approaches, leading to the generalized Fick-Onsagermulticomponent diffusion fluxes or to the generalized Maxwell-Stefan equations.The latter approach has the advantage that the resulting fluxes are consistentwith non-negativity of the partial mass densities for non-singular andnon-degenerate Maxwell-Stefan diffusivities. On the other hand, this approachrequires computationally expensive matrix inversions since the fluxes are onlyimplicitly given. We propose and discuss a novel and more direct closure whichavoids the inversion of the Maxwell-Stefan equations. It is shown that allthree closures are actually equivalent under the natural requirement ofpositivity for the concentrations, thus revealing the general structure ofcontinuum thermodynamical diffusion fluxes. As a special case, the new closurealso gives rise to a core-diagonal diffusion model in which only thosecross-effects are present that are necessary to guarantee consistency withtotal mass conservation, plus a compositional dependence of the diffusivity.This core-diagonal closure turns out to provide a rigorous fundament for recentextensions of the Darken equation from binary mixtures to the generalmulticomponent case. As an outcome of our investigation, we also addressdifferent questions related to the sign of multicomponent thermodynamic orFickian diffusion coefficients. We show rigorously that in general the secondlaw requires positivity properties for tensors and operators rather than forscalar diffusivities.

On the structure of continuum thermodynamical diffusion fluxes -- A  novel closure scheme and its relation to the Maxwell-Stefan and the  Fick-Onsager approach