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

TL;DR

This paper develops a classical thermodynamic framework for multitemperature fluid mixtures, introducing an average temperature and a dynamical pressure related to temperature differences, with implications for cosmology.

Contribution

It proposes a new classical approach incorporating an average temperature and dynamical pressure in multitemperature fluid mixtures, aligning with recent thermodynamics results.

Findings

Introduction of an average temperature for multicomponent fluids

Derivation of a dynamical pressure linked to temperature differences

Potential relevance of dynamical pressure in cosmological models

Abstract

We present a classical approach of 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 Maxwellian iteration procedure in extended thermodynamics theory of multitemperature mixtures. The differences of temperatures between the constituents imply the existence of a new 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 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.