Identification of an average temperature and a dynamical pressure in a multitemperature mixture of fluids

We present a classical approach to a mixture of compressible fluids when each constituent has its own temperature. The introduction of an average temperature together with the entropy principle dictates the classical Fick law for diffusion and also novel constitutive equations associated with the difference of temperatures between the components. The constitutive equations fit with results recently obtained through a Maxwellian iteration procedure in extended thermodynamics theory of multitemperature mixtures. The differences of temperatures between the constituents imply the existence of a dynamical pressure even if the fluids have a zero bulk viscosity. The nonequilibrium dynamical pressure can be measured and may be convenient in several physical situations, such as, for example, in cosmological circumstances where—as many authors assert—a dynamical pressure played a major role in the evolution of the early universe.