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Energy nonequipartition in gas mixtures of inelastic rough hard spheres: The tracer limit

Francisco Vega Reyes, Antonio Lasanta, Andrés Santos, and Vicente Garzó
Phys. Rev. E 96, 052901 – Published 6 November 2017; Erratum Phys. Rev. E 100, 049901 (2019)
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  • INTRODUCTION
  • ENERGY PRODUCTION RATES IN GENERAL…
  • TRACER LIMIT
  • COMPARISON WITH COMPUTER SIMULATIONS
  • CONCLUSIONS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    The dynamical properties of a tracer or impurity particle immersed in a host gas of inelastic and rough hard spheres in the homogeneous cooling state is studied. Specifically, the breakdown of energy equipartition as characterized by the tracer/host ratios of translational and rotational temperatures is analyzed by exploring a wide spectrum of values of the control parameters of the system (masses, moments of inertia, sizes, and coefficients of restitution). Three complementary approaches are considered. On the theoretical side, the Boltzmann and Boltzmann–Lorentz equations (both assuming the molecular chaos ansatz) are solved by means of a multitemperature Maxwellian approximation for the velocity distribution functions. This allows us to obtain explicit analytical expressions for the temperature ratios. On the computational side, two different techniques are used. First, the kinetic equations are numerically solved by the direct simulation Monte Carlo (DSMC) method. Second, molecular dynamics simulations for dilute gases are performed. Comparison between theory and simulations shows a general good agreement. This means that (i) the impact of the molecular chaos ansatz on the temperature ratios is not significant (except at high inelasticities and/or big impurities) and (ii) the simple Maxwellian approximation yields quite reliable predictions.

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    • Received 1 September 2017

    DOI:https://doi.org/10.1103/PhysRevE.96.052901

    ©2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Granular flowsKinetic theory
    1. Physical Systems
    Granular gases
    1. Techniques
    Molecular dynamicsMonte Carlo methods
    Statistical Physics & ThermodynamicsPolymers & Soft Matter

    Erratum

    Erratum: Energy nonequipartition in gas mixtures of inelastic rough hard spheres: The tracer limit [Phys. Rev. E 96, 052901 (2017)]

    Francisco Vega Reyes, Antonio Lasanta, Andrés Santos, and Vicente Garzó
    Phys. Rev. E 100, 049901 (2019)

    Authors & Affiliations

    Francisco Vega Reyes1, Antonio Lasanta2, Andrés Santos1, and Vicente Garzó1

    • 1Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, Spain
    • 2Gregorio Millán Institute of Fluid Dynamics, Nanoscience and Industrial Mathematics, Department of Materials Science and Engineering and Chemical Engineering, Universidad Carlos III de Madrid, 28911 Leganés, Spain

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    Issue

    Vol. 96, Iss. 5 — November 2017

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    Images

    • Figure 1
      Figure 1

      Plot of the temperature ratio T2rot/T2tr of the host gas versus the parameter γ2 defined in Eq. (22). The line is the theoretical prediction given by Eq. (23), while the filled and open symbols are DSMC and MD results, respectively. The symbols correspond to the cases A (squares), B (circles), C (up triangles), D (down triangles), E (left triangles), F (right triangles), and G (diamonds). The error bars in the simulation data are smaller than the size of the symbols.

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    • Figure 2
      Figure 2

      Plot of the temperature ratios T1tr/T2tr (solid lines and circles) and T1rot/T2rot (dashed lines and triangles) versus σ1/σ2 for systems (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F (see Table 2). The lines are theoretical predictions, the filled symbols are DSMC results, and the open symbols are MD results. The error bars in the simulation data are smaller than the size of the symbols. Note the vertical logarithmic scales in panels (a)–(d).

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    • Figure 3
      Figure 3

      Plot of the temperature ratios T1tr/T2tr (solid lines and circles) and T1rot/T2rot (dashed lines and triangles) versus (a) σ1/σ2 and (b) α12 for systems (a) G and (b) H (see Table 2). The lines are theoretical predictions, the filled symbols are DSMC results, and the open symbols are MD results. Except for the MD data in panel (b), the error bars in the simulation data are smaller than the size of the symbols.

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    • Figure 4
      Figure 4

      Plot of the temperature ratios T1tr/T2tr (solid lines and circles) and T1rot/T2rot (dashed lines and triangles) versus (a) β12 and (b) 32κ1 for systems (a) I and (b) J (see Table 2). The lines are theoretical predictions, the filled symbols are DSMC results, and the open symbols are MD results. The error bars in the simulation data are smaller than the size of the symbols. Note that in panel (a) the vertical scale is logarithmic for −1≤β12≤−0.5 and normal for −0.5≤β12≤1.

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