  This paper revisits the modeling of multicomponent diffusion within the
framework of thermodynamics of irreversible processes. We briefly review the
two well-known main approaches, leading to the generalized Fick-Onsager
multicomponent diffusion fluxes or to the generalized Maxwell-Stefan equations.
The latter approach has the advantage that the resulting fluxes are consistent
with non-negativity of the partial mass densities for non-singular and
non-degenerate Maxwell-Stefan diffusivities. On the other hand, this approach
requires computationally expensive matrix inversions since the fluxes are only
implicitly given. We propose and discuss a novel and more direct closure which
avoids the inversion of the Maxwell-Stefan equations. It is shown that all
three closures are actually equivalent under the natural requirement of
positivity for the concentrations, thus revealing the general structure of
continuum thermodynamical diffusion fluxes. As a special case, the new closure
also gives rise to a core-diagonal diffusion model in which only those
cross-effects are present that are necessary to guarantee consistency with
total mass conservation, plus a compositional dependence of the diffusivity.
This core-diagonal closure turns out to provide a rigorous fundament for recent
extensions of the Darken equation from binary mixtures to the general
multicomponent case. As an outcome of our investigation, we also address
different questions related to the sign of multicomponent thermodynamic or
Fickian diffusion coefficients. We show rigorously that in general the second
law requires positivity properties for tensors and operators rather than for
scalar diffusivities.
