Transport coefficients for relativistic gas mixtures of hard-sphere particles

TL;DR

This paper calculates the transport coefficients for a relativistic binary gas mixture of hard-sphere particles within a gravitational field, analyzing their temperature dependence and limits to single gases.

Contribution

It provides new integral expressions for transport coefficients considering relativistic effects and gravitational influence, with numerical evaluations for hard-sphere interactions.

Findings

Transport coefficients depend on temperature and gravitational field.

Results recover non-relativistic and ultra-relativistic limits.

Transport coefficients vary with particle mass and diameter differences.

Abstract

In the present work, we calculate the transport coefficients for a relativistic binary mixture of diluted gases of hard-sphere particles. The gas mixture under consideration is studied within the relativistic Boltzmann equation in the presence of a gravitational field described by the isotropic Schwarzschild metric. We obtain the linear constitutive equations for the thermodynamic fluxes. The driving forces for the fluxes of particles and heat will appear with terms proportional to the gradient of gravitational potential. We discuss the consequences of the gravitational dependence on the driving forces. We obtain general integral expressions for the transport coefficients and evaluate them by assuming a hard-sphere interaction amongst the particles when they collide and not very disparate masses and diameters of the particles of each species. The obtained results are expressed in terms of their temperature dependence through the relativistic parameter which gives the ratio of the rest energy of the particles and the thermal energy of the gas mixture. Plots are given to analyze the behavior of the transport coefficients with respect to the temperature when small variations in masses and diameters of the particles of the species are present. We also analyze for each coefficient the corresponding limits to a single gas so the non-relativistic and ultra-relativistic limiting cases are recovered as well. Furthermore, we show that the transport coefficients have a dependence on the gravitational field.