  A complete thermodynamical analysis for a binary mixture of viscous Korteweg
fluids with two velocities and two temperatures is developed. The constitutive
functions are allowed to depend on the diffusion velocity and the specific
internal energies of both constituents, together with their first gradients, on
the symmetric part of the gradient of barycentric velocity, as well as on the
mass density of the mixture and the concentration of one of the constituents,
together with their first and second gradients. Compatibility with entropy
principle is analyzed by applying the extended Liu procedure, and a complete
solution of the set of thermodynamical restrictions is recovered in three space
dimensions. Finally, the equilibrium configurations are investigated, and it is
proved that no restrictions arise on the admissible phase boundaries. The
theoretical results here provided may serve as a basis for experimental and/or
numerical investigations, in particular for determining the surface levels of
phase boundaries at equilibrium and making a comparison with experimental
profiles.

Fluid Dynamics