  A complete thermodynamical analysis for a non-reacting binary mixture
exhibiting the features of a third grade fluid is analyzed. The constitutive
functions are allowed to depend on the mass density of the mixture and the
concentration of one of the constituents, together with their first and second
order gradients, on the specific internal energy of the mixture with its first
order gradient, as well as on the symmetric part of the gradient of barycentric
velocity. Compatibility with second law of thermodynamics is investigated by
applying the extended Liu procedure. An explicit solution of the set of
thermodynamic restrictions is obtained by postulating a suitable form of the
constitutive relations for the diffusional mass flux, the heat flux and the
Cauchy stress tensor. Taking a first order expansion in the gradients of the
specific entropy, the expression of the entropy flux is determined. It includes
an additional contribution due to non-local effects.
