  In this paper we analyze the high friction regime for the Navier Stokes
Korteweg equations for multicomponent systems. According to the shape of the
mixing and friction terms, we shall perform two limits: the high friction limit
toward an equilibrium system for the limit densities and the barycentric
velocity, and, after an appropriate time scaling, the diffusive relaxation
toward parabolic, gradient flow equations for the limit densities. The rigorous
justification of these limits is done by means of relative entropy techniques
in the framework of weak, finite energy solutions of the relaxation models,
rewritten in the enlarged formulation in terms of the drift velocity, toward
smooth solutions of the corresponding equilibrium dynamics. Finally, since our
estimates are uniform for small viscosity, the results are also valid for the
Euler Korteweg multicomponent models, and the corresponding estimates can be
obtained by sending the viscosity to zero.
