Continuum simulations of shocks and patterns in vertically oscillated granular layers

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.

Unstable blast shocks in dilute granular flows

Shocks and blasts can be readily obtained in granular flows be they dense or dilute. Here, by examining the propagation of a blast shock in a dilute granular flow, we show that such a front is unstable with respect to transverse variations of the density of grains. This instability has a well-defined wavelength which depends on the density of the medium and has an amplitude which grows as an exponential of the distance traveled. These features can be understood using a simple model for the shock front, including dissipation which is inherent to granular flows. While this instability bears much resemblance to that anticipated in gases, it is distinct and has special features we discuss here.

Time dependence and density inversion in simulations of vertically oscillated granular layers

We study a layer of grains atop a plate which oscillates sinusoidally in the direction of gravity, using three-dimensional, time-dependent numerical solutions of continuum equations to Navier-Stokes order as well as hard-sphere molecular dynamics simulations. For high accelerational amplitudes of the plate, the layer exhibits a steady-state "density inversion" in which a high-density portion of the layer is supported by a lower-density portion. At low accelerational amplitudes, the layer exhibits oscillatory time dependence that is strongly correlated to the motion of the plate. We show that continuum simulations yield results consistent with molecular dynamics results in both regimes.

Separation patterns between Brazilian nut and reversed Brazilian nut of a binary granular system

This paper studies the segregation behavior of binary granular particles with diameters at approximately 10:1 in a vertically vibrated container. An array of transitional separation patterns between reversed Brazilian nut (RBN) and Brazilian nut (BN) separations are observed, with their geometrical features carefully measured. The binary particle system develops into either a stable separation pattern when f and Γ are relatively low or an oscillating pattern when f and Γ are relatively high. We regard these patterns as different phases, in which the stable patterns can be divided into phases of RBN, RBN transitional (RBNT), BNT, and BN. A phase parameter λ between-1 and 1 is defined to describe the separation patterns based on the mass center height difference in large and small particles. By drawing f-Γ-λ phase diagrams, the system's tendency toward BN separation was found to increase with f and decrease with Γ. Furthermore, the range of the tendency toward BN separation expands when the size of small particles rises. As the total mass of the small particles increases, the system's tendency toward RBN separation is enhanced. Abnormal points are also observed in the stable phase regions, and the oscillating phase shifts among the four stable phases with time. These stable phases can be explained via an analysis of the distribution of the dissipation energy, whereas the mechanism of the oscillating phase remains to be discovered.