  This work is devoted to the consistent modeling of a three-phase mixture of a
gas, a liquid and its vapor. Since the gas and the vapor are mis-cible, the
mixture is subjected to a non-symmetric constraint on the volume. Adopting the
Gibbs formalism, the study of the extensive equilibrium entropy of the system
allows to recover the Dalton's law between the two gaseous phases. In addition,
we distinguish whether phase transition occurs or not between the liquid and
its vapor. The thermodynamical equilibria are described both in extensive and
intensive variables. In the latter case, we focus on the geometrical properties
of equilibrium entropy. The consistent characterization of the thermodynamics
of the three-phase mixture is used to introduce two Homogeneous Equilibrium
Models (HEM) depending on mass transfer is taking into account or not.
Hyperbolicity is investigated while analyzing the entropy structure of the
systems. Finally we propose two Homogeneous Relaxation Models (HRM) for the
three-phase mixtures with and without phase transition. Supplementary equations
on mass, volume and energy fractions are considered with appropriate source
terms which model the relaxation towards the thermodynamical equilibrium, in
agreement with entropy growth criterion.
