Granular fountains: Convection cascade in a compartmentalized granular gas

This paper extends the two-compartment granular fountain [D. van der Meer, P. Reimann, K. van der Weele, and D. Lohse, Phys. Rev. Lett. 92, 184301 (2004)] to an arbitrary number of compartments: The tendency of a granular gas to form clusters is exploited to generate spontaneous convective currents, with particles going down in the well-filled compartments and going up in the diluted ones. We focus upon the bifurcation diagram of the general K-compartment system, which is constructed using a dynamical flux model and which proves to agree quantitatively with results from molecular dynamics simulations

Transient granular shock waves and upstream motion on a staircase

A granular cluster, placed on a staircase setup, is brought into motion by vertical shaking. Molecular dynamics simulations show that the system goes through three phases. After a rapid initial breakdown of the cluster, the particle stream organizes itself in the form of a shock wave moving down the steps of the staircase. As this wave becomes diluted, it transforms into a more symmetric flow, in which the particles move not only downwards but also toward the top of the staircase. This series of events is accurately reproduced by a dynamical model in which the particle flow from step to step is modeled by a flux function. To explain the observed scaling behavior during the three stages, we study the continuum version of this model (a nonlinear partial differential equation) in three successive limiting cases. (i) The first limit gives the correct t−1/3 decay law during the rapid initial phase, (ii) the second limit reveals that the transient shock wave is of the Burgers type, with the density of the wave front decreasing as t−1/2, and (iii) the third limit shows that the eventual symmetric flow is a slow diffusive process for which the density falls off as t−1/3 again. For any finite number of compartments, the system finally reaches an equilibrium distribution with a bias toward the lower compartments. For an unbounded staircase, however, the t−1/3 decay goes on forever and the distribution becomes increasingly more symmetric as the dilution progresses

Competitive Clustering in a Bi-disperse Granular Gas

A bi-disperse granular gas in a compartmentalized system is experimentally found to cluster competitively: Depending on the shaking strength, the clustering can be directed either towards the compartment initially containing mainly small particles, or to the one containing mainly large particles. The experimental observations are quantitatively explained within a flux model.Comment: 4 pages, 4 figures, Phys. Rev. Lett., in pres

Interplay of air and sand: Faraday heaping unravelled

We report on numerical simulations of a vibrated granular bed including the effect of the ambient air, generating the famous Faraday heaps known from experiment. A detailed analysis of the forces shows that the heaps are formed and stabilized by the airflow through the bed while the gap between bed and vibrating bottom is growing, confirming the pressure gradient mechanism found experimentally by Thomas and Squires [Phys. Rev. Lett. 81, 574 (1998)], with the addition that the airflow is partly generated by isobars running parallel to the surface of the granular bed. Importantly, the simulations also explain the heaping instability of the initially flat surface and the experimentally observed coarsening of a number of small heaps into a larger one

Phase Diagram of Vertically Shaken Granular Matter

A shallow, vertically shaken granular bed in a quasi 2-D container is studied experimentally yielding a wider variety of phenomena than in any previous study: (1) bouncing bed, (2) undulations, (3) granular Leidenfrost effect, (4) convection rolls, and (5) granular gas. These phenomena and the transitions between them are characterized by dimensionless control parameters and combined in a full experimental phase diagram.Comment: 11 pages, 14 figures, submitted to "Physics of Fluids

Small-number statistics near the clustering transition in a compartementalized granular gas

Statistical fluctuations are observed to profoundly influence the clustering behavior of granular material in a vibrated system consisting of two connected compartments. When the number of particles N is sufficiently large sN<300 is sufficientd, the clustering follows the lines of a standard second-order phase transition and a mean-field description works. For smaller N, however, the enhanced influence of statistical fluctuations breaks the mean-field behavior. We quantitatively describe the competition between fluctuations and mean-field behavior sas a function of Nd using a dynamical flux model and molecular dynamics simulations

Spontaneous Ratchet Effect in a Granular Gas

The spontaneous clustering of a vibrofluidized granular gas is employed to generate directed transport in two different compartmentalized systems: a "granular fountain" in which the transport takes the form of convection rolls, and a "granular ratchet" with a spontaneous particle current perpendicular to the direction of energy input. In both instances, transport is not due to any system-intrinsic anisotropy, but arises as a spontaneous collective symmetry breaking effect of many interacting granular particles. The experimental and numerical results are quantitatively accounted for within a flux model.Comment: 4 pages, 5 figures; Fig. 4 has been reduced in size and qualit

Bifurcation Diagram for Compartmentalized Granular Gases

The bifurcation diagram for a vibro-fluidized granular gas in N connected compartments is constructed and discussed. At vigorous driving, the uniform distribution (in which the gas is equi-partitioned over the compartments) is stable. But when the driving intensity is decreased this uniform distribution becomes unstable and gives way to a clustered state. For the simplest case, N=2, this transition takes place via a pitchfork bifurcation but for all N>2 the transition involves saddle-node bifurcations. The associated hysteresis becomes more and more pronounced for growing N. In the bifurcation diagram, apart from the uniform and the one-peaked distributions, also a number of multi-peaked solutions occur. These are transient states. Their physical relevance is discussed in the context of a stability analysis.Comment: Phys. Rev. E, in press. Figure quality has been reduced in order to decrease file-siz