Kinetics of Fragmenting Freely Evolving Granular Gases

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.Comment: 22 pages, 8 figure

Driven Granular Gases

“…Freely cooling systems -mainly examined numerically and theoretically -are almost impossible to realize experimentally. Only in the last years, laboratory experiments were performed, where clustering could be examined in driven systems [14][15][16][17][18][19][20], where also kinetic theory approaches [21][22][23][24][25][26][27][28][29][30][31][32] complemented by numerical simulations have proven to be successful [12,25,[33][34][35][36][37][38][39].…”

Fragmenting granular gases

“…( 1). Its specific form depends on energy injection, and ψ = 0 for a freely evolving granular gas [21]. Subsequently, we discuss results corresponding to a steady state, where heating and collision frequencies are proportional to each other, i.e.…”

“…The increase in grain number as a result of fragmentation requires an equivalent increase in the frequency of energy injection to sustain a steady state. For (Ff (v, σ, t) = 0), we recover a freely evolving fragmenting granular gas [21].…”

“…where the first term accounts for energy dissipation due to inelasticity, with b c the dimensionless collisional average [22] and ω the collision frequency [21,22]. The second contribution describes the energy input and corresponds to the last term in eq.…”

Coarse-grained dynamics of the freely cooling granular gas in one dimension

“…We note that, in the above, fragmentation is an emergent process, not defined apriori in the microscopic dynamics, unlike some other models of granular gas where fragmentation occurs on collision [23,24]. We study the model by means of event driven molecular dynamics simulations [25].…”