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.

Granular material is vertically vibrated in a 2D container: above a critical shaking strength, and for a sufficient number of beads, a crystalline cluster is elevated and supported by a dilute gaseous layer of fast beads underneath. We call this phenomenon the granular Leidenfrost effect. The experimental observations are explained by a hydrodynamic model featuring three dimensionless control parameters: the energy input S, the number of particle layers F, and the inelasticity of the particle collisions ". The S; F phase diagram, in which the Leidenfrost state lies between the purely solid and gas phases, shows accurate agreement between experiment and theory. DOI: 10.1103/PhysRevLett.95.258001 PACS numbers: 45.70.ÿn, 05.65.+b Vertically shaken granular matter typically exhibits a region of reduced density just above the vibrating bottom [1][2][3][4][5]. An exceptionally strong form of this so-called density inversion was recently encountered in a theoretical study by Meerson et al. [6]: for sufficiently strong shaking a dense cluster of particles, showing a hexagonal packing, was observed to be elevated and supported by a dilute layer of fast particles underneath.Here we present the first experimental observation of this phenomenon, which we will call the granular Leidenfrost effect. It is analogous to the original Leidenfrost effect of a water droplet hovering over a hot plate [7,8]: when the temperature of the plate exceeds the Leidenfrost temperature T L 220 C (equivalent to the critical shaking strength in the granular system), the bottom layer of the drop vaporizes instantly and prevents direct heat transfer from the plate to the drop, causing the droplet to hover and survive for a long time.We also give a theoretical explanation in the spirit of Meerson et al. [6,9,10]. These authors focused on the point where the density at the bottom first becomes inverted, which is a precursor to the granular Leidenfrost effect (not yet the actual phase separation). We study the subsequent transition from this density-inverted state to the Leidenfrost state in which the solid and gas phases coexist. A major challenge in granular research today is to achieve a hydrodynamiclike continuum description [11][12][13][14][15][16], which, however, in many cases breaks down due to the tendency of the particles to cluster together [17,18]. We show that the Leidenfrost effect (despite the clustered phase) is well described by a hydrodynamic model.Our experimental setup (Fig. 1) consists of a quasi-2D container (10 0:45 14 cm) [19] filled with glass beads of diameter d 4:0 mm, density 2:5 g=cm 3 , and coefficient of normal restitution e 0:95. The setup is mounted on a shaker with tunable frequency f and amplitude a. The Leidenfrost effect, see Fig. 1, is stably reproduced for given, sufficiently large values of the shaking strength and the number of particle layers.The four natural dimensionless control parameters to analyze the experiment are (i) the shaking acceleration (with g the gravitational acceleration):(ii) the number ...

We construct a ratchet of the Smoluchowski-Feynman type, consisting of four vanes that are allowed to rotate freely in a vibrofluidized granular gas. The necessary out-of-equilibrium environment is provided by the inelastically colliding grains, and the equally crucial symmetry breaking by applying a soft coating to one side of each vane. The onset of the ratchet effect occurs at a critical shaking strength via a smooth, continuous phase transition. For very strong shaking the vanes interact actively with the gas and a convection roll develops, sustaining the rotation of the vanes. Introduction.-Throughout the ages scientists and laymen alike have tried to find a way to circumvent the second law of thermodynamics and create work out of thermal noise. In 1912, Marian Smoluchowski devised an especially appealing thought experiment [1], which consisted of four vanes and an asymmetrically toothed wheel with a pawl, submerged in a molecular heat bath [ Fig. 1(a)]. At first glance it seems that the wheel can turn in one direction only, in violation of the second law. However, Richard Feynman unambiguously showed that this type of device does not produce work at thermal equilibrium [2]: Since not only the vanes but also the pawl are subject to collisions with the gas molecules, the pawl bounces off the toothed wheel and causes the system to rotate randomly in either direction.In contrast, systems outside of thermal equilibrium are very well capable of creating work (directed motion) out of a noisy environment by means of the ratchet effect [3]. In fact, ratchet type devices have been proposed as the paradigmatic way in which motors operate at Brownian scales [4], and during the last decade scientists have realized (over a limited rotation range) a molecular version of Smoluchowski's device [5]. Here-on a macroscopic level-we construct a fully operational rotational ratchet of the Smoluchowski-Feynman type, capable of any uninterrupted number of revolutions. It consists of four vanes that are allowed to rotate freely in a granular gas. The necessary out-of-equilibrium environment-to bypass the second law of thermodynamics which prohibits the extraction of work from a system at thermal equilibrium-is provided by the granular gas. This is by its very nature out of equilibrium since in order to sustain the gaseous state it requires an external energy input to balance the energy dissipation caused by the inelastically colliding particles. The equally essential second ingredient, the symmetry breaking that must be present in order to rectify the stochastic motion due to the noisy environment, is provided by the fact that the two sides of each vane are coated differently. Although similar devices have been

Strongly vertically shaken granular matter can display a density inversion: A high-density cluster of beads is elevated by a dilute gaslike layer of fast beads underneath ("granular Leidenfrost effect"). For even stronger shaking the granular Leidenfrost state becomes unstable and granular convection rolls emerge. This transition resembles the classical onset of convection in fluid heated from below at some critical Rayleigh number. The same transition is seen in molecular dynamics (MD) simulations of the shaken granular material. The critical shaking strength for the onset of granular convection can be calculated from a linear stability analysis of a hydrodynamiclike model of the granular flow. Experiment, MD simulations, and theory quantitatively agree.

Using high-speed video and magnetic resonance imaging (MRI) we study the motion of a large sphere in a vertically vibrated bed of smaller grains. As previously reported we find a non-monotonic density dependence of the rise and sink time of the large sphere. We show that air drag causes relative motion between the intruder and the bed during the shaking cycle and is ultimately responsible for the observed density dependence of the rise time. We investigate in detail how the motion of the intruder sphere is influenced by size of the background particles, initial vertical position in the bed, ambient pressure and convection. We explain our results in the framework of a simple model and find quantitative agreement in key aspects with numerical simulations to the model equations.