On a model of mixtures with internal variables: extended Liu procedure for the exploitation of the entropy principle

The exploitation of second law of thermodynamics for a mixture of two fluids with a scalar internal variable and a first order nonlocal state space is achieved by using the extended Liu approach. This method requires to insert as constraints in the entropy inequality either the field equations or their gradient extensions. Consequently, the thermodynamic restrictions imposed by the entropy principle are derived without introducing extra terms neither in the energy balance equation nor in the entropy inequality.