Granular Motor in the Non-Brownian Limit

In this work we experimentally study a granular rotor which is similar to the famous Smoluchowski-Feynman device and which consists of a rotor with four vanes immersed in a granular gas. Each side of the vanes can be composed of two different materials, creating a rotational asymmetry and turning the rotor into a ratchet. When the granular temperature is high, the rotor is in movement all the time, and its angular velocity distribution is well described by the Brownian Limit discussed in previous works. When the granular temperature is lowered considerably we enter the so-called Single Kick Limit, where collisions occur rarely and the unavoidable external friction causes the rotor to be at rest for most of the time. We find that the existing models are not capable of adequately describing the experimentally observed distribution in this limit. We trace back this discrepancy to the non-constancy of the deceleration due to external friction and show that incorporating this effect into the existing models leads to full agreement with our experiments. Subsequently, we extend this model to describe the angular velocity distribution of the rotor for any temperature of the gas, and obtain a very good agreement between the model and experimental data

Linear stability analysis of a time-divergent slamming flow

When a liquid slams into a solid, the intermediate gas is squeezed out at a speed that diverges when approaching the moment of impact. Although there is mounting experimental evidence that instabilities form on the liquid interface during such an event, understanding of the nature of these instabilities is limited. This study therefore addresses the stability of a liquid-gas interface with surface tension, subject to a diverging flow in the gas phase, where the liquid and the gas phase are both represented as potential fluids. We perform a Kelvin-Helmholtz-type linear modal stability analysis of the surface to obtain an amplitude equation that is subsequently analysed in detail and applied to two cases of interest for impact problems, namely, the parallel impact of a wave onto a vertical wall, and the impact of a horizontal plate onto a liquid surface. In both cases we find that long wavelengths are stabilised considerably in comparison to what may be expected based upon classical knowledge of the stability of interfaces subject to a constant gas flow. In the former case, this leads to the prediction of a marginally stable wavelength that is completely absent in the classical analysis. For the latter we find much resemblance to the classical case, with the connotation that the instability is suppressed for smaller disk sizes. The study ends with a discussion of the influence of gas viscosity and gas compressibility on the respective stability diagrams.Comment: 37 pages, 10 figure

Impact on Granular Beds

The impact of an object on a granular solid is an ubiquitous phenomenon in nature, the scale of which ranges from the impact of a raindrop onto sand all the way to that of a large asteroid on a planet. Despite the obvious relevance of these impact events, the study of the underlying physics mechanisms that guide them is relatively young, with most work concentrated in the past decade. Upon impact, an object starts to interact with a granular bed and experiences a drag force from the sand. This ultimately leads to phenomena such as crater formation and the creation of a transient cavity that upon collapse may cause a jet to appear from above the surface of the sand. This review provides an overview of research that targets these phenomena, from the perspective of the analogous but markedly different impact of an object on a liquid. It successively addresses the drag an object experiences inside a granular bed, the expansion and collapse of the cavity created by the object leading to the formation of a jet, and the remarkable role played by the air that resides within the pores between the grains

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

Experiments and characterization of low-frequency oscillations in a granular column

The behaviour of a vertically vibrated granular bed is reminiscent of a liquid in that it exhibits many phenomena such as convection and Faraday-like surface waves. However, when the lateral dimensions of the bed are confined such that a quasi-one-dimensional geometry is formed, the only phenomena that remain are bouncing bed and the granular Leidenfrost effect. This permits the observation of the granular Leidenfrost state for a wide range of energy injection parameters, and more specifically allows for a thorough characterisation of the low-frequency oscillation (LFO) that is present in this state. In both experiments and particle simulations we determine the LFO frequency from the power spectral density of the centre of mass signal of the grains, varying the amplitude and frequency of the driving, the particle diameter and the number of layers in the system. We thus find that (i) the LFO frequency is inversely proportional to the fast inertial time scale and (ii) decorrelates with a typical decay time proportional to the slow dissipative time scale in the system. The latter is consistent with the view that the LFO is driven by the inherent noise that is present in the granular Leidenfrost state with a low number of particles

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