  The applicability of theories describing the kinetic evolution of fluid
mixtures depends on the underlying physical assumptions. The Maxwell-Stefan
equations, widely used for miscible fluids, express forces depending on coupled
fluxes. They need to be inverted to recover a Fickian form which is generally
impossible analytically. Moreover, the concentration dependence of the
diffusivities has to be modelled, e.g. by the multicomponent Darken equation.
Cahn-Hilliard type equations are preferred for immiscible mixtures, whereby
different assumptions on the coupling of fluxes lead to the slow-mode and
fast-mode theories. For two components, these were derived from the
Maxwell-Stefan theory in the past. Here, we prove that the fast-mode theory and
the generalized Maxwell-Stefan theory together with the multicomponent Darken
equation are strictly equivalent even for multicomponent systems with very
different molecular sizes. Our findings allow to reduce the choice of a
suitable theory to the most efficient algorithm for solving the underlying
equations.
