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Hydrodynamic modes for granular gases.

James W Dufty1, J Javier Brey

  • 1Department of Physics, University of Florida, Gainesville, Florida 32611, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
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This study calculates hydrodynamic modes for granular gases, confirming transport coefficients match existing solutions and demonstrating hydrodynamic behavior at long times.

Area of Science:

  • Statistical Mechanics
  • Kinetic Theory
  • Granular Materials

Background:

  • The Boltzmann equation describes granular gas dynamics.
  • Hydrodynamic modes govern long-time, long-wavelength behavior.

Purpose of the Study:

  • Calculate eigenfunctions and eigenvalues for hydrodynamic modes in inelastic hard spheres/disks.
  • Verify transport coefficients using the Chapman-Enskog method.
  • Investigate the dominance of hydrodynamic modes.

Main Methods:

  • Long wavelength limit analysis of the linearized Boltzmann equation.
  • Exact solution of a kinetic model.
  • Identification of transport coefficients.

Main Results:

Related Experiment Videos

  • Eigenfunctions and eigenvalues for d+2 hydrodynamic modes were determined.
  • Calculated transport coefficients align with Chapman-Enskog results.
  • A collisional continuum was bounded away from the hydrodynamic spectrum.

    • Conclusions:

    • Hydrodynamic description is assured at long times for granular gases.
    • The power law decay of velocity distribution relates to the hydrodynamic spectrum bound.