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

Henri Gouin (1) , Tommaso Ruggeri (2)

1 IUSTI - Institut universitaire des systèmes thermiques industriels
2 CIRAM - Department of Mathematics and Research Center of Applied Mathematics

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.

Mots clés: Multitemperature mixture of fluids; Dynamical pressure; Diffusion; Nonequilibrium thermodynamics

Domaines: Mécanique des fluides [physics.class-ph]; Thermique [physics.class-ph]; Physique mathématique [math-ph]

Henri Gouin, Tommaso Ruggeri. Identification of an average temperature and a dynamical pressure in a multitemperature mixture of fluids. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 78 (1), pp.016303. ⟨10.1103/PhysRevE.78.016303⟩. ⟨hal-00299294⟩