Partitioning of energy in highly polydisperse granular gases

Abstract

A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes, a, giving rise to a corresponding continuous temperature profile, T(a), which we compute approximately, generalizing previous results for binary or multicomponent mixtures. If the system is driven, it evolves towards a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haff's law. The analytical results are supported by event driven simulations for a large, but discrete number of species.

10 pages; 5 figures

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Cited by in corpus (8)

• Mpemba effect in driven granular Maxwell gases
• Sonine approximation for collisional moments of granular gases of inelastic rough spheres
• The Glass Transition in Driven Granular Fluids: A Mode-Coupling Approach
• Universality of temperature distribution in granular gas mixtures with a steep particle size distribution
• Driven and undriven states of multicomponent granular gases of inelastic and rough hard disks or spheres
• Diffusion in multicomponent granular mixtures
• Asymptotic velocity distribution of a driven one dimensional binary granular Maxwell gas
• Mean-squared displacements of rough particles in polydisperse granular gases