Kinetics of Fragmenting Freely Evolving Granular Gases

TL;DR

This paper studies how fragmentation affects the cooling and evolution of granular gases, revealing a scaling regime and potential finite-time divergence linked to a shattering transition.

Contribution

It introduces a kinetic model combining inelastic collisions and fragmentation, analyzing the resulting size and velocity distributions with theoretical and simulation methods.

Findings

Identification of a scaling regime with a single collisional average.

Observation of a possible finite-time divergence in particle number.

Detection of a shattering transition with a delta singularity at small grains.

Abstract

We investigate the effect of fragmentation on the homogeneous free cooling of inelastic hard spheres, using Boltzmann kinetic theory and Direct Monte Carlo simulations. We analyze in detail a model where dissipative collisions may subsequently lead to a break-up of the grains. With a given probability, two off-springs are then created from one of the two colliding partners, with conservation of mass, momentum and kinetic energy. We observe a scaling regime characterized by a single collisional average, that quantifies the deviations from Gaussian behaviour for the joint size and velocity distribution function. We also discuss the possibility of a catastrophe whereby the number of particles diverges in a finite time. This phenomenon appears correlated to a ``shattering'' transition marked by a delta singularity at vanishingly small grains for the rescaled size distribution.