  The high-friction limit in Euler-Korteweg equations for fluid mixtures is
analyzed. The convergence of the solutions towards the zeroth-order limiting
system and the first-order correction is shown, assuming suitable uniform
bounds. Three results are proved: The first-order correction system is shown to
be of Maxwell-Stefan type and its diffusive part is parabolic in the sense of
Petrovskii. The high-friction limit towards the first-order Chapman-Enskog
approximate system is proved in the weak-strong solution context for general
Euler-Korteweg systems. Finally, the limit towards the zeroth-order system is
shown for smooth solutions in the isentropic case and for weak-strong solutions
in the Euler-Korteweg case. These results include the case of constant
capillarities and multicomponent quantum hydrodynamic models.
