Unstable blast shocks in dilute granular flows

Internal and surface waves in vibrofluidized granular materials: Role of cohesion

Wave phenomena in vibrofluidized dry and partially wet granular materials confined in a quasi-two-dimensional geometry are investigated with numerical simulations considering individual particles as hard spheres. Short-ranged cohesive interactions arising from the formation of liquid bridges between adjacent particles are modeled by changing the velocity-dependent coefficient of restitution. Such a change effectively suppresses the formation of surface waves, in agreement with previous experimental observations. The difference in pattern creation arises from the suppressed momentum transfer due to wetting and it can be quantitatively understood from an analysis of binary impacts.

Blast Dynamics in a Dissipative Gas

The blast caused by an intense explosion has been extensively studied in conservative fluids, where the Taylor-von Neumann-Sedov hydrodynamic solution is a prototypical example of self-similarity driven by conservation laws. In dissipative media, however, energy conservation is violated, yet a distinctive self-similar solution appears. It hinges on the decoupling of random and coherent motion permitted by a broad class of dissipative mechanisms. This enforces a peculiar layered structure in the shock, for which we derive the full hydrodynamic solution, validated by a microscopic approach based on molecular dynamics simulations. We predict and evidence a succession of temporal regimes, as well as a long-time corrugation instability, also self-similar, which disrupts the blast boundary. These generic results may apply from astrophysical systems to granular gases, and invite further cross-fertilization between microscopic and hydrodynamic approaches of shock waves.

Self-organized shocks in the sedimentation of a granular gas

A granular gas in gravity heated from below develops a certain stationary density profile. When the heating is switched off, the granular gas collapses. We investigate the process of sedimentation using computational hydrodynamics, based on the Jenkins-Richman theory, and find that the process is significantly more complex than generally acknowledged. In particular, during its evolution, the system passes several stages which reveal distinct spatial regions of inertial (supersonic) and diffusive (subsonic) dynamics. During the supersonic stages, characterized by Mach>1, the system develops supersonic shocks which are followed by a steep front of the hydrodynamic fields of temperature and density, traveling upward.

Evolution and stability of shock waves in dissipative gases characterized by activated inelastic collisions

Previous experiments have revealed that shock waves driven through dissipative gases may become unstable, for example, in granular gases and in molecular gases undergoing strong relaxation effects. The mechanisms controlling these instabilities are not well understood. We successfully isolated and investigated this instability in the canonical problem of piston-driven shock waves propagating into a medium characterized by inelastic collision processes. We treat the standard model of granular gases, where particle collisions are taken as inelastic, with a constant coefficient of restitution. The inelasticity is activated for sufficiently strong collisions. Molecular dynamic simulations were performed for 30,000 particles. We find that all shock waves investigated become unstable, with density nonuniformities forming in the relaxation region. The wavelength of these fingers is found to be comparable to the characteristic relaxation thickness. Shock Hugoniot curves for both elastic and inelastic collisions were obtained analytically and numerically. Analysis of these curves indicates that the instability is not of the Bethe-Zeldovich-Thompson or D'yakov-Kontorovich type. Analysis of the shock relaxation rates and rates for clustering in a convected fluid element with the same thermodynamic history ruled out the clustering instability of a homogeneous granular gas. Instead, wave reconstruction of the early transient evolution indicates that the onset of instability occurs during repressurization of the gas following the initial relaxation of the medium behind the lead shock. This repressurization gives rise to internal pressure waves in the presence of strong density gradients. This indicates that the mechanism of instability is more likely of the vorticity-generating Richtmyer-Meshkov type, relying on the action of the inner pressure wave development during the transient relaxation.