Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases

Abstract

A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It is found that disks typically present a stronger rotational-translational nonequipartition but a weaker component-component nonequipartition than spheres. A noteworthy "mimicry" effect is unveiled, according to which a polydisperse gas of disks having common values of the coefficient of restitution and of the reduced moment of inertia can be made indistinguishable from a monodisperse gas in what concerns the degree of rotational-translational energy nonequipartition. This effect requires the mass of a disk of component $i$ to be approximately proportional to $2{\sigma }_i+⟨\sigma ⟩$, where ${\sigma }_i$ is the diameter of the disk and $⟨\sigma ⟩$ is the mean diameter.

17 pages, 8 figures; v2: slight change of title plus other minor changes

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Cited by in corpus (7)

• Driven and undriven states of multicomponent granular gases of inelastic and rough hard disks or spheres
• Granular gas of inelastic and rough Maxwell particles
• Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients
• Intruders in disguise: Mimicry effect in granular gases
• Mean-squared displacements of rough particles in polydisperse granular gases
• Translational and rotational non-Gaussianities in homogeneous freely evolving granular gases
• Mpemba-like effect protocol for granular gases of inelastic and rough hard disks