Experimental compaction of anisotropic granular media

We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic and weakly confined granular material, using high-resolution -ray adsorption. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical solicitations evolve to a dense state. We find that the packing fraction evolution is slowed by the grain anisotropy but, as for spherically shaped grains, can be well fitted by a stretched exponential. For a given type of grains, the characteristic times of relaxation and of convection are found to be of the same order of magnitude. On the contrary, compaction mechanisms in the media strongly depend on the grain anisotropy.     

Short-time dynamics of a packing of polyhedral grains under horizontal vibrations

We analyze the dynamics of a 3D granular packing composed of particles of irregular polyhedral shape confined inside a rectangular box with a retaining wall subjected to horizontal harmonic forcing. The simulations are performed by means of the contact dynamics method for a broad set of loading parameters. We explore the vibrational dynamics of the packing, the evolution of solid fraction and the scaling of dynamics with the loading parameters. We show that the motion of the retaining wall is strongly anharmonic as a result of jamming and grain rearrangements. It is found that the mean particle displacement scales with inverse square of frequency, the inverse of the force amplitude and the square of gravity. The short-time compaction rate grows in proportion to frequency up to a characteristic frequency, corresponding to collective particle rearrangements between equilibrium states, and then it declines in inverse proportion to frequency.     

Upward penetration of grains through a granular medium

We study experimentally the creeping penetration of guest (percolating) grains through densely packed granular media in two dimensions. The evolution of the system of the guest grains during the penetration is studied by image analysis. To quantify the changes in the internal structure of the packing, we use Voronoï tessellation and a certain shape factor which is a clear indicator of the presence of different underlying substructures (domains). We first consider the impact of the effective gravitational acceleration on upward penetration of grains. It is found that the higher effective gravity increases the resistance to upward penetration and enhances structural organization in the system of the percolating grains. We also focus our attention on the dependence of the structural rearrangements of percolating grains on some parameters like polydispersity and the initial packing fraction of the host granular system. It is found that the anisotropy of penetration is larger in the monodisperse case than in the bidisperse one, for the same value of the packing fraction of the host medium. Compaction of initial host granular packing also increases anisotropy of penetration of guest grains. When a binary mixture of large and small guest grains is penetrated into the host granular medium, we observe size segregation patterns.     

Compaction of a granular material under cyclic shear

In this paper we present experimental results concerning the compaction of a granular assembly of spheres under periodic shear deformation. The dynamics of the system is slow and continuous when the amplitude of the shear is constant, but exhibits rapid evolution of the volume fraction when a sudden change in shear amplitude is imposed. This rapid response is shown to be uncorrelated with the slow compaction process. Received 31 March 2000     

Improving mixture of grains by using bi-dimensional Galton boards

This paper presents an experimental and numerical study that deals with the problem of mixing grains falling down through a bi-dimensional Galton board (BGB). The special issue addressed here is the influence of the presence of lateral walls in the BGB. Disks of equal diameters but different species are launched from the top of the device. During the fall, disks collide with obstacles (arranged to form a triangular lattice) and with the lateral walls. The exit distribution of particles at the bottom of the board is determined and the incidence of the presence of walls in the mixing quality is studied as a function of W the relative separation between lateral walls. Two types of indexes are evaluated to characterize the efficiency in the obtained mixture. The presence of walls has proven to be crucial to enhance the quality of the mixture of particles.     

Initiation and evolution of current ripples on a flat sand bed under turbulent water flow

We investigate the formation and dynamics of sand ripples under a turbulent water flow. Our experiments were conducted in an open flume with spherical glass beads between 100 and 500μm in diameter. The flow Reynolds number is of the order of 10 000 and the particle Reynolds number of the order of 1 to 10. We study the development of ripples by measuring their wavelength and amplitude in course of time and investigate the influence of the grain size and the flow properties. In particular, we demonstrate two different regimes according to the grain size. For fine grains, a slow coarsening process (i.e., a logarithmic increase of the wavelength and amplitude) takes place, while for coarser grains, this process occurs at a much faster rate (i.e., with a linear growth) and stops after a finite time. In the later case, a stable pattern is eventually observed. Besides, we carefully analyze the wavelength of ripples in the first stages of the instability as a function of the grain size and the shear velocity of the flow, and compare our results with other available experimental data and with theoretical predictions based on linear stability analyses.     

Delayed transitions between fluid-like and solid-like granular states

Analysis of granular flows has been a significant theoretical challenge over the past several decades. These flows are difficult to analyze largely because they exhibit both solid-like and fluid-like behaviors side-by-side in single experiments. In this paper, we examine two experiments in which the co-existence between these states is especially marked and leads to unique patterns that may serve as signatures for underlying granular dynamics deserving of further scrutiny. In these experiments, we find that when fluidization of grains is prolonged — as can be expected to occur for example under reduced gravity environments or under conditions of strong kinetic forcing (e.g. during earthquakes) — grains can produce residual depositional patterns that are difficult to distinguish from fluvial deposits. This suggests that geological landforms under low gravity (for example on Mars) or influenced by strong forcing (for example during earthquakes) may behave in a fluid-like manner despite being entirely dry.     

Effective temperature and jamming transition in dense, gently sheared granular assemblies

We present extensive computational results for the effective temperature, defined by the fluctuation-dissipation relation between the mean square displacement and the average displacement of grains, under the action of a weak, external perturbation, of a sheared, bi-disperse granular packing of compressible spheres. We study the dependence of this parameter on the shear rate and volume fractions, the type of particle and the observable in the fluctuation-dissipation relation. We find the same temperature for different tracer particles in the system. The temperature becomes independent on the shear rate for slow enough shear suggesting that it is the effective temperature of the jammed packing. However, we also show that the agreement of the effective temperature for different observables is only approximate, for very long times, suggesting that this defintion may not capture the full thermodynamics of the system. On the other hand, we find good agreement between the dynamical effective temperature and a compactivity calculated assuming that all jammed states are equiprobable. Therefore, this definition of temperature may capture an instance of the ergodic hypothesis for granular materials as proposed by theoretical formalisms for jamming. Finally, our simulations indicate that the average shear stress and apparent shear viscosity follow the usual relation with the shear rate for complex fluids. Our results show that the application of shear induces jamming in packings whose particles interact by tangential forces.     

Density inversion in rapid granular flows: the supported regime

This paper presents numerical findings on rapid 2D and 3D granular flows on a bumpy base. In the supported regime studied here, a strongly sheared, dilute and agitated layer spontaneously appears at the base of the flow and supports a compact packing of grains moving as a whole. In this regime, the flow behaves like a sliding block on the bumpy base. In particular, for flows on a horizontal base, the average velocity decreases linearly in time and the average kinetic energy decreases linearly with the travelled distance, those features being characteristic of solid-like friction. This allows us to define and measure an effective friction coefficient, which is independent of the mass and velocity of the flow. This coefficient only loosely depends on the value of the micromechanical friction coefficient whereas the infuence of the bumpiness of the base is strong. We give evidence that this dilute and agitated layer does not result in significantly less friction. Finally, we show that a steady regime of supported flows can exist on inclines whose angle is carefully chosen.     

Dispersive flow of disks through a two-dimensional Galton board

We report here an experimental and numerical study of the flow properties of disks driven by gravity through a hexagonal lattice of obstacles, i.e. a Galton board. During the fall, particles experience dissipative collisions that scatter them in random directions. A driven-diffusion regime can be achieved under certain conditions. A characteristic length of the motion and its dependence on geometrical parameters of the system is analyzed in the steady regime. The influence of collective effects on the dispersion process is investigated by comparison between single- and many-particle flows. The characterization of the dynamics and the diffusive properties of the flow in a system like a Galton board can be expanded to other granular systems, particularly static solid particle mixers and will give some insight in understanding granular mixing.     

A model of binary assemblies of spheres

We propose a theoretical model of random binary assemblies of spheres at any packing fraction. We use the notion of geometrical neighborhood between grains that is defined through two generalizations of the Vorono? tessellation: the radical (or Laguerre) tessellation and the navigation map. The model is tested on different numerical packings. We find a weak local segregation for high packing fraction. We also find that the higher the size ratio of the particles, the more important the segregation. Received 19 February 2001 and Received in final form 27 June 2001     

Compaction of cereal grain

Abstract

We report on simple shaking experiments to measure the compaction of a column of Firth oat grain. Such grains are elongated anisotropic particles with a bimodal polydispersity. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical shaking evolve to a dense state with evidence of nematic-like structure at the surface of the confining tube. This is accompanied by an increase in the packing fraction of the grain.     

Monodisperse dry granular flows on inclined planes: Role of roughness

Recent studies have pointed out the importance of the basal friction on the dynamics of granular flows. We present experimental results on the influence of the roughness of the inclined plane on the dynamics of a monodisperse dry granular flow. We found experimentally that there exists a maximum of the friction for a given relative roughness. This maximum is shown to be independent of the slope angle. This behavior is observed for four planes with different bump sizes (given by the size of the beads glued on the plane) from 200 m to 2 mm. The relative roughness corresponding to the maximum of the friction can be predicted with a geometrical model of stability of one single bead on the plane. The main parameters are the size of the bumps and the size of the flowing beads. In order to obtain a higher precision, the model also takes into account the spacing between the bumps of the rough plane. Experimental results and model are in good agreement for all the planes we studied. Other parameters, like the sphericity of the beads, or irregularities in the thickness of the layer of glued particles, are shown to be of influence on the friction.     

Experimental study of granular compaction dynamics at different scales: grain mobility, hexagonal domains, and packing fraction

We present an original experimental study of the compaction dynamics for two-dimensional granular systems. Compaction dynamics is measured at three different scales: the macroscopic scale through the normalized packing fraction rho, the mesoscopic scale through the normalized fraction phi of hexagonal domains in the system, and the microscopic scale through the grain mobility mu. Moreover, the hexagonal domains are found to obey a growth process dominated by the displacement of domain boundaries. A global picture of compaction dynamics relevant at each scale is proposed.     

Stability limit of a granular monolayer

A granular monolayer is composed by spherical grains on a horizontal plate. The plate is then tilted until the monolayer breaks down. This critical angle has been measured for different widths and heights of the rectangular monolayer. The highest critical angles are found when one of these two characteristic lengths is less than about 30 bead diameters. When the polydispersity is less than one percent, the monolayer may be stable till angles close to 90^°. Arches induce large critical angles. On the other hand, for a large and high monolayer, the critical angle saturates towards a lower value. This angle is related to the static friction of a grain on the plate. A model based on the block dynamics is proposed to describe the behavior of the avalanche angle as a function of the size of the monolayer and the polydispersity of the beads.-1     

Bidisperse granular avalanches on inclined planes: A rich variety of behaviors

Experiments were performed to provide insight into the flow behavior and structure of bimodal mixtures of grains in gravity-driven, free-surface flows. Unsteady unconfined flows were produced by releasing instantaneously a dry granular mass, composed of two particle sizes, over a rough inclined plane. As a result of size segregation, the small particles are found at the bottom of the flow and final deposit, the large particles are found at the free surface, but also on the lateral borders and at the front of the flow. The lateral and vertical inhomogeneous repartitions of particles lead to two main effects that are completely absent in monodispersed flows. The outline effect results from the accumulation of large beads on the periphery of the flow depending on the value of the relative friction of each particle species on the plane. This effect in turn causes a narrowing of the flow and/or an increase of length of the final deposit. The interface effect results of the interaction between layers of different size particles and causes the modification of the thickness of the deposit. These effects occur simultaneously and their combination leads to a great variety of behaviors. In this investigation, evidence of the diversity of behaviors is presented as the size ratio, relative friction and concentration of each particle species are varied.     

Fragmentation dynamics within shear bands--a model for aging tectonic faults?

A numerical model for packing of fragmenting blocks in a shear band is introduced, and its dynamics is compared with that of a tectonic fault. The shear band undergoes a slow aging process in which the blocks are being grinded by the shear motion and the compression. The dynamics of the model have the same statistical characteristics as the seismic activity in faults. The characteristic magnitude distribution of earthquakes appears to result from frictional slips at small and medium magnitudes, and from fragmentation of blocks at the largest magnitudes. Aftershocks to large-magnitude earthquakes are local recombinations of the fragments before they reach a new quasi-static equilibrium. The aftershocks satisfy Omori's law. Local precursor activity at a few times the normal background level appears at a short time before a major earthquake. Seismic gaps appear as a natural consequence of the aging process of a fault. Explanation of the heat flux and principal stress direction anomalies at the faults both involve the value of fracture stress of the blocks in the gouge. The final form of a tectonic fault is predicted to involve a gouge dominated by fine-grained and rather rounded blocks so that it cannot withstand large shear stresses. Received 26 July 2000     

Dynamical diversity and metastability in a hindered granular column near jamming

Granular media jam into a panoply of metastable states. The way in which these states are achieved depends on the nature of local and global constraints on grains; here we investigate this issue by means of a non-equilibrium stochastic model of a hindered granular column near its jamming limit. Grains feel the constraints of grains above and below them differently, depending on their position. A rich phase diagram with four dynamical phases (ballistic, activated, logarithmic and glassy) is revealed. The statistics of the jamming time and of the metastable states reached as attractors of the zero-temperature dynamics is investigated in each of these phases. Of particular interest is the glassy phase, where intermittency and a strong deviation from Edwards' flatness are manifest.     

Well defined transition to gel–like aggregates of attractive athermal particles

In an attempt to extend the range of model jamming transitions, we simulate systems of athermal particles which attract when slightly overlapping. Following from recent work on purely repulsive systems, dynamics are neglected and relaxation performed via a potential energy minimisation algorithm. Our central finding is of a transition to a low-density tensile solid which is sharp in the limit of infinite system size. The critical density depends on the range of the attractive regime in the pair-potential. Furthermore, solidity is shown to be related to the coordination number of the packing according to the approximate constraint-counting scheme known as Maxwell counting, although more corrections need to be considered than with the repulsive-only case, as explained. We finish by discussing how the numerical difficulties encountered in this work could be overcome in future studies.     

Shear- and vibration-induced order-disorder transitions in granular media

By molecular dynamics simulations we investigate the order-disorder transitions induced in granular media by an applied drive combining vibrations and shear. As the steady state is attained, the pack is found in disordered configurations for comparatively high intensities of the drive; conversely, ordering and packing fractions exceeding the random close packing are found when vibrations and shear are weak. As forcing amplitudes get smaller, we find diverging time scales in the dynamics, as the system enters a jamming region. Under this perspective, our picture supports the intuition that externally applied forcing has, in driven granular media, a role similar to temperature in thermal systems.