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Transport coefficients for relativistic gas mixtures of hard-sphere particles

Author

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  • Kremer, Gilberto M.
  • Moratto, Valdemar

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.

Suggested Citation

  • Kremer, Gilberto M. & Moratto, Valdemar, 2017. "Transport coefficients for relativistic gas mixtures of hard-sphere particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 44-58.
    • Handle: RePEc:eee:phsmap:v:471:y:2017:i:c:p:44-58
    DOI: 10.1016/j.physa.2016.12.004
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    References listed on IDEAS

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    1. Kox, A.J. & Van Leeuwen, W.A. & De Groot, S.R., 1976. "On relativistic kinetic gas theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(1), pages 165-174.
    2. Kremer, Gilberto M., 2014. "Diffusion of relativistic gas mixtures in gravitational fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 76-85.
    3. Kox, A.J., 1976. "On relativistic kinetic gas theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(3), pages 603-612.
    4. Kox, A.J. & De Groot, S.R. & Van Leeuwen, W.A., 1976. "On relativistic kinetic gas theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(1), pages 155-164.
    5. Van Leeuwen, W.A. & Kox, A.J. & de Groot, S.R., 1975. "On relativistic kinetic gas theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 79(2), pages 233-255.
    6. Kremer, G.M., 2007. "Note on the relativistic reaction rate coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 61-65.
    7. van Leeuwen, W.A., 1975. "On relativistic kinetic gas theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 81(2), pages 249-275.
    8. De Groot, S.R. & Kox, A.J. & Van Leeuwen, W.A., 1976. "On relativistic kinetic gas theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(3), pages 613-619.
    9. Anderson, J.L., 1976. "Variational principles for calculation of transport coefficients of relativistic multi-component systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 85(2), pages 287-309.
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