Kinetics of Fragmenting Freely Evolving Granular Gases

Ignacio Pagonabarraga, Emmanuel Trizac

Published 2003-03-03Version 1

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.