Hamilton's Principle and Rankine-Hugoniot Conditions for General Motions of Mixtures

In previous papers, we have presented hyperbolic governing equations and jump conditions for barotropic fluid mixtures. Now we extend our results to the most general case of two-fluid conservative mixtures taking into account the entropies of components. We obtain governing equations for each component of the medium. This is not a system of conservation laws. Nevertheless, using Hamilton's principle we are able to obtain a complete set of Rankine-Hugoniot conditions. In particular, for the gas dynamics they coincide with classical jump conditions of conservation of momentum and energy. For the two-fluid case, the jump relations do not involve the conservation of the total momentum and the total energy.