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

Nikolai V. Brilliantov·Thorsten Poeschel
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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.

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Nikolai V. Brilliantov, Thorsten Poeschel. 2005-11-19. Breakdown of the Sonine expansion for the velocity distribution of Granular Gases. https://doi.org/10.1209/epl%2Fi2005-10555-6

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