  We consider a model of a third grade viscous Korteweg--type fluid in three
space dimensions, and apply the extended Liu procedure in order to explicitly
solve the constraints imposed by the entropy principle on the non--local
constitutive relations. We detail the algorithm we use, and are able to
characterize the material functions involved in the constitutive equations. In
a natural way, the application of the extended Liu procedure allows us to
recover an extra term in the entropy flux, preserving all the features of third
grade viscous Korteweg--type fluids. Moreover, a further constraint, in order
to avoid that at equilibrium only very special phase boundaries are admissible,
is investigated.
