Granular Leidenfrost effect: experiment and theory of floating particle clusters

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 epsilon. 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.     

竖直振动颗粒床中的倍周期运动

实验研究了竖直振动颗粒床中颗粒对容器底部的压力随振动强度的变化情况.发现压力随振动加速度的增加经历倍周期分岔，典型的分岔序列为：2P，4P，混沌，3P，6P，混沌，4P，8P，混沌.观察表明，伴随倍周期分岔现象，在颗粒床底部出现颗粒的聚集态.聚集态内颗粒密堆积在一起并作整体的上下运动.采用完全非弹性蹦球模型分析了颗粒对容器底的冲击力，并给出了倍周期分岔现象的一种解释. 关键词： 颗粒物质 混沌 倍周期分岔 非弹性碰撞     

竖直振动颗粒物厚层中冲击力分岔现象

实验研究了竖直振动颗粒物厚层中颗粒对容器底部的压力. 发现这种压力是脉冲式的，并表现出受振动加速度控制的倍周期分岔现象. 在颗粒层底部观察到颗粒密堆积在一起的聚集态. 聚集态内颗粒的自由程较小，并像一个整体一样运动. 关键词： 颗粒物质 混沌 倍周期分岔 非弹性碰撞     

Granular dynamics of a vibrated bed of dumbbells

A two-dimensional vibrated bed of dumbbells was investigated using experiment and numerical simulation. Experimentally, high speed photography in combination with image analysis and tracking software was used to determine the location of the centre of mass and the locations and direction of motion of the component particles of the dumbbells. Numerically, a geometry analogous to that used experimentally was employed and the equations of motion for each of the particles were solved using the distinct element method. It was found that, despite some differences, the numerical simulations agreed reasonably well with the experimental results. Subsequently, the simulation method was used to explore the behaviour of the bed over a range of densities. The moments of the velocity distributions were determined as a function of height for a range of numbers of particles, and it was found that a normal distribution of velocities is a good approximation, except close to the vibrating base where there were suggestions that the distribution of the vertical component of the velocities is a composite of two sets of particles, one pre-collision with the base, and the other post-collision.     

On the occurrence of polygon-shaped patterns in vibrated cylindrical granular beds

We report experimental observations of polygon-shaped patterns formed in a vertically vibrated bed of circular cross-section. A phase map is determined, showing that the polygon pattern is established for ?? = A(2??f)²/g ? 10 . The sensitivity of the polygon structure to bed parameters was tested by studying beds of different particle sizes and fill levels. It was hypothesized that the polygon pattern observed in cylindrical beds is the corresponding pattern to the formation of arches in square-shaped beds. The close relationship between these two patterns was demonstrated by two observations: i) the radii of the arches of a corresponding square bed and the inner radius of the cylindrical bed were found to be very similar and ii) the boundary lengths of the two patterns were in good agreement.      

Discrete element modeling of triboelectric charging of insulating materials in vibrated granular beds

The triboelectric charging of granular insulating materials is very difficult to predict because of the complex physical mechanism involved in this process. The aim of this paper is to describe in detail the implementation of a numerical model of the tribocharging process taking place in vertically-vibrated beds of granular plastics. The charge exchanged in granule-to-granule and granule-to-wall collisions is computed by taking into account some electrical properties of the respective materials, their area of contact and the effect of the electric field generated by a system of high-voltage electrodes and by the charges of the granules themselves. The electrical model is coupled with the Discrete Element Method (DEM) which undertakes the whole granular dynamics and allows to compute accurately the contact surface of two colliding particles which is involved in the triboelectric charging model.Beside the numerical simulations an experiment has been conducted with mixtures of mm-size polyamide and polycarbonate granules in a laboratory vibrated bed to validate the model. The numerical results have been found to be in good agreement with the experimental ones.     

器壁滑动摩擦力对受振颗粒体系中冲击力倍周期分岔过程的影响

颗粒物质由离散的固体颗粒组成, 受到周期性振动时可以表现出复杂的动力学行为. 这些行为往往受众多因素的影响, 如空气阻力和器壁摩擦力等. 针对受振颗粒体系中冲击力的倍周期分岔现象, 通过抽真空或将容器底镂空消除空气阻力, 单独研究器壁滑动摩擦力的影响. 结果表明在仅有器壁摩擦力作用的情况下, 倍周期分岔过程仅受约化振动加速度的控制, 与颗粒的尺寸、颗粒层数及振动频率无关. 将器壁摩擦力处理成一个大小恒定、方向与颗粒和器壁相对速度反向的阻力, 并包含到完全非弹性蹦球模型中, 能够对所观察到的现象给出很好的解释. 通过对倍周期分岔点测量平均值的拟合, 得到器壁滑动摩擦力的大小约为颗粒总重量的10%. 关键词： 颗粒物质 器壁摩擦力 倍周期分岔 冲击力     

Developable modes in vibrated thin plates

We investigate the normal modes of a developable cone singularity as observed in a circular sheet supported by a rigid circular frame and pushed at its center. When the center of the sheet is in addition submitted to a sinusoidal forcing, two types of bending modes, named here rolling and tilt modes, are parametrically excited. The rolling mode is an angular oscillation of the concave sector of the developable cone structure. If the amplitude of vibration is high enough, the rolling mode amplitude increases dramatically giving rise to both a continuous rotation of the concave sector and a material angular displacement of the sheet, similar to that produced by a moving wrinkle in a carpet.     

Convection in a vibrated granular layer

When a granular layer is submitted to an oscillating acceleration with a peak value larger than gravity, a large scale motion develops. This movement is in some ways similar to the one displayed by a liquid heated from below, and it is called granular convection. Different conditions beside the parameters of the forcing can affect it, such as the presence of an interstitial gas or the roughness of the walls. We have carried out an experiment to study the convective movement of a granular layer with a temporal resolution high enough to describe the motion of individual grains within one oscillating period. We also present experimental results concerning the friction that the lateral walls exert on the grains and its relevance on granular convection.     

振动条件下颗粒的分离现象

介绍并分析比较了竖直振动条件下巴西坚果效应与反巴西坚果效应形成的机制和转化条件,以及水平振动下颗粒的分离现象,提出一些意见和建议.     

Elastic convection in vibrated viscoplastic fluids

We observe a new type of behavior in a shear-thinning yield stress fluid: freestanding convection rolls driven by vertical oscillation. The convection occurs without the constraint of container boundaries, yet the diameter of the rolls is spontaneously selected for a wide range of parameters. The transition to the convecting state occurs without hysteresis when the amplitude of the plate acceleration exceeds a critical value. We find that a nondimensional stress, the stress due to the inertia of the fluid normalized by the yield stress, governs the onset of the convective motion.     

Instabilities in vertically vibrated fluid-grain systems

When a bed of fluid-immersed fine grains is exposed to vertical vibration a wealth of phenomena may be observed. At low frequencies a horizontal bed geometry is generally unstable and the bed breaks spatial symmetry, acquiring a tilt. At the same time it undergoes asymmetric granular convection. Fine binary mixtures may separate completely into layers or patterns of stripes. The separated regions may exhibit instabilities in which they undergo wave-like motion or exhibit quasi-periodic oscillations. We briefly review these and a number of related behaviours, identifying the physical mechanisms behind each. Finally, we discuss the magneto-vibratory separation of binary mixtures which results from exposing each component to a different effective gravity and describe the influence of a background fluid on this process.     

Convection in horizontally vibrated granular material

We report observations of convective motion in a container filled with granular material when it is vibrated in the horizontal direction. We find that the roughness of the boundaries and the container dimensions play an important role in determining the shape and number of the convection cells. When the container bottom and lateral walls are rough, the system typically exhibits four counter-rotating rolls stacked in two pairs on top of each other; for very low filling height, it is possible to observe a single row of rolls arranged laterally along the bottom of the container. With smooth walls, on the other hand, we find that the system typically forms only a single pair of counter-rotating convection rolls that originate in the two upper corners of the vibrated material; when the filling height is increased to a level that depends on the container width, we observe a transition to the four-roll state. (c) 1999 American Institute of Physics.     

Light trapping effect in silicon wafers with anodically etched surfaces

Received: 10 May 1996/Accepted: 19 November 1996     

Phase boundaries in vertically vibrated granular materials

A boundary structure is observed in beds of vertically vibrated granular materials separating regions of opposite phase. This structure is investigated and it is identified as giving rise to both a global kink and hexagonal patterns. A global phase diagram of surface patterns on a vibrated bed is presented.     

Energy fluctuations in vibrated and driven granular gases

We investigate the behavior of energy fluctuations in several models of granular gases maintained in a non-equilibrium steady state. In the case of a gas heated from a boundary, the inhomogeneities of the system play a predominant role. Interpreting the total kinetic energy as a sum of independent but not identically distributed random variables, it is possible to compute the probability density function (pdf) of the total energy. Neglecting correlations and using the analytical expression for the inhomogeneous temperature profile obtained from the granular hydrodynamic equations, we recover results that have previously been observed numerically and that had been attributed to the presence of correlations. In order to separate the effects of spatial inhomogeneities from those ascribable to velocity correlations, we have also considered two models of homogeneously thermostated gases: in this framework it is possible to reveal the presence of non-trivial effects due to velocity correlations between particles. Such correlations stem from the inelasticity of collisions. Moreover, the observation that the pdf of the total energy tends to a Gaussian in the large system limit suggests that they are also due to the finite size of the system.     

Self-replicating holes in a vertically vibrated dense suspension

We find self-replicating holes on the surface of a vertically vibrated potato starch suspension. Above certain acceleration, the finite-amplitude deformation of the surface grows to form a hole that penetrates the fluid layer. The circular shape of the hole is not stable, and the hole begins to replicate just like the self-replicating spots in chemical reaction-diffusion systems. At high acceleration, these holes exhibit spatiotemporal chaos. By assessing the statistical properties in a steady state, we show that fluctuation in the number of holes can be understood by a master equation.     

Knots and random walks in vibrated granular chains

We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks interacting via hard-core exclusion in one spatial dimension. In particular, the knot survival probability follows a universal scaling function which is independent of the chain length, with a corresponding diffusive characteristic time scale. Both the large-exit-time and the small-exit-time tails of the distribution are suppressed exponentially, and the corresponding decay coefficients are in excellent agreement with theoretical values.