Dissipative Two-Fluid Models
  From Hamilton's principle of stationary action, we derive governing equations of two-fluid mixtures and extend the model to the dissipative case without chemical reactions. For both conservative and dissipative cases, an algebraic identity connecting equations of momentum, mass, energy and entropy is obtained by extending the Gibbs identity in dynamics. The obtained system is hyperbolic for small relative velocity of the phases. 
Henri Gouin (MSNMGP, LMMT), Sergey Gavrilyuk