  Multi-component Baer-Nunziato-type models for isothermal and isentropic
fluids are investigated. These are given by balance equations for volume
fractions, density and momentum for each component accounting for the
relaxation to equilibrium by means of relaxation terms. Mathematical properties
of the models are derived such as hyperbolicity and symmetrization. The fields
are characterized and corresponding Riemann invariants are determined.
Appropriate entropy-entropy flux pairs are derived taking into account the
phasic energy equations including the heat flux. Physically meaningful
constraints are presented that ensure the entropy inequality to hold.
Instantaneous relaxation to equilibrium is investigated and appropriate
algorithms are presented. Numerical results for the isothermal Baer-Nunziato
model are compared to an isothermal Euler model and to an isothermal
phase-field model.
