Shock propagation in granular flow subjected to an external impact

Abstract

We analyze a recent experiment [Boudet, Cassagne, and Kellay, Phys. Rev. Lett. 103, 224501 (2009)] in which the shock created by the impact of a steel ball on a flowing monolayer of glass beads is studied quantitatively. We argue that radial momentum is conserved in the process and hence show that in two dimensions the shock radius increases in time t as a power law t{1/3}. This is confirmed in event driven simulations of an inelastic hard sphere system. The experimental data are compared with the theoretical prediction and are shown to compare well at intermediate times. At long times the experimental data exhibit a crossover to a different scaling behavior. We attribute this to the problem becoming effectively three dimensional due to the accumulation of particles at the shock front and propose a simple hard sphere model that incorporates this effect. Simulations of this model capture the crossover seen in the experimental data.

Microscopic origin of self-similarity in granular blast waves

“…Numerical studies of the granular blast 19,35,36 have remarked that the shape of the shock boundary is preserved: contrary to the conservative case where central pressure pushes particles outward isotropically, the dissipative blast region does not tend to evolve toward central symmetry with a clear circular (or spherical) boundary. Instead, it retains any anisotropy it had at the start of the self-similar regime, as a result of random collisions during the transient phase, see Fig.…”

“…Finally, the granular blast itself has recently started to attract studies, both experimental 17,18,34 and numerical 19,35,36 . These papers have been focusing on global scaling laws, revealing clear self-similarity in a MCS regime (see previous section) in Molecular Dynamics simulations…”

Self-organized shocks in the sedimentation of a granular gas

“…Later, Tan and Goldhirsch [4] showed that supersonic behavior is not an exotic state but dynamical granular systems are nearly always supersonic, that is, it is a typical state of granular matter. There is much recent progress regarding the supersonic properties of granular matter, including shocks, theoretically [5][6][7][8][9], numerically [10][11][12][13][14][15][16][17], and experimentally [7][8][9][18][19][20][21][22][23][24]; however, surprisingly little is known about the spatiotemporal relation between the field of Mach number influenced by temperature and density and the dynamics of supersonic shocks in granular systems [25][26][27].…”

Shock propagation in locally driven granular systems

“…Numerical simulations of the elastic system are consistent with the TvNS exponents [38,39]. In the inelastic system, the disturbance is concentrated in dense bands that move radially outward, and the relevant exponents may be obtained through scaling arguments based on the conservation of radial momentum [18,39,40]. The variation of physical quantities inside the dense band may be obtained through a hydrodynamic description [41,42].…”