Breakdown of the Sonine expansion for the velocity distribution of Granular Gases

Abstract

The velocity distribution of a granular gas is analyzed in terms of the Sonine polynomials expansion. We derive an analytical expression for the third Sonine coefficient a_3. In contrast to frequently used assumptions this coefficient is of the same order of magnitude as the second Sonine coefficient a_2. For small inelasticity the theoretical result is in good agreement with numerical simulations. The next-order Sonine coefficients a_4, a_5 and a_6 are determined numerically. While these coefficients are negligible for small dissipation, their magnitude grows rapidly with increasing inelasticity for 0< epsilon < 0.6. We conclude that this behavior of the Sonine coefficients manifests the break down of the Sonine polynomial expansion caused by the increasing impact of the overpopulated high-energy tail of the distribution function.

arXiv comment7 pages, 3 figures

References in corpus (5)

• The Granular Phase Diagram
• Computer simulation of uniformly heated granular fluids
• Velocity distribution in granular gases of viscoelastic particles
• Deviation from Maxwell Distribution in Granular Gases with Constant Restitution Coefficient
• Velocity Distribution of Inelastic Granular Gas in Homogeneous Cooling State

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