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.     

The influence of grain shape,friction and cohesion on granular compaction dynamics

This article is a review of our recent and new experimental works on granular compaction. The effects of various microscopic parameters on the compaction dynamics are addressed, in particular the influence of the grain shape, the friction and the cohesion between the grains. Two dimensionnal and three dimensionnal systems are analysed. And the role of dimensionality will be emphasized. Theoretical and numerical investigations provide additional informations about that phenomenon. Indeed numerical models permit us to study the influence of some parameters not easily accessible experimentally. Our results show that the above mentioned parameters have a deep impact on the compaction dynamics. Anisotropic grains lead to two different compaction regimes separated by a “burst" of the packing fraction. Friction is observed to modify how the grains are arranged in the pile. This is confirmed by numerical simulations. Cohesive forces between particles inhibit compaction and lead to extremely low values of the packing fraction.     

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.     

On the existence of stationary states during granular compaction

When submitted to gentle mechanical taps a granular packing slowly compacts until it reaches a stationary state that depends on the tap characteristics. The properties of such stationary states are experimentally investigated. The influence of the initial state, taps properties and tapping protocol are studied. The compactivity of the packings is determinated. Our results strongly support the idea that the stationary states are genuine thermodynamic states.     

Interrupted shear of granular media

The response of a granular material during a stop-and-go shear experiment is investigated using an annular shear cell and silicagel powders of different particle sizes. The experimental results are examined on the basis of the Dieterich-Rice-Ruina model for solid friction. In addition to making this analogy with solid friction, we describe a new instability that is observed when restarting shear, where the powder bed is found to slip and compact for short hold times but only dilates for long hold times. The minimum hold time to restore a non-slip behaviour has been investigated for different size particles and normal loadings. The observed dependencies show analogies between this behaviour and the sliding rearrangements seen above the stick-slip threshold.     

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.     

Strength and failure of cemented granular matter

Cemented granular materials (CGMs) consist of densely packed solid particles and a pore-filling solid matrix sticking to the particles. We use a sub-particle lattice discretization method to investigate the particle-scale origins of strength and failure properties of CGMs. We show that jamming of the particles leads to highly inhomogeneous stress fields. The stress probability density functions are increasingly wider for a decreasing matrix volume fraction, the stresses being more and more concentrated in the interparticle contact zones with an exponential distribution as in cohesionless granular media. Under uniaxial loading, pronounced asymmetry can occur between tension and compression both in strength and in the initial stiffness as a result of the presence of bare contacts (with no matrix interposed) between the particles. Damage growth is analyzed by considering the evolution of stiffness degradation and the number of broken bonds in the particle phase. A brutal degradation appears in tension as a consequence of brittle fracture in contrast to the more progressive nature of damage growth in compression. We also carry out a detailed parametric study in order to assess the combined influence of the matrix volume fraction and particle-matrix adherence. Three regimes of crack propagation can be distinguished corresponding to no particle damage, particle abrasion and particle fragmentation, respectively. We find that particle damage scales well with the relative toughness of the particle-matrix interface with respect to the particle toughness. This relative toughness is a function of both matrix volume fraction and particle-matrix adherence and it appears therefore to be the unique control parameter governing transition from soft to hard behavior.     

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.     

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     

Correlations and aggregate statistics in granular packs

We study how the aggregate statistical properties for density fluctuations in granular aggregates scale with the sample size and how such a scaling is associated with the correlations between grains. Correlations are studied both between grain positions and between Vorono? cell volumes, showing distinct behaviors and properties. A non-linear scaling in the aggregate volume fluctuations as function of the sample size is discovered and the connection between such anomalous scaling and correlations is explained. It emerges that volume fluctuations might be described by means of a single universal equation for all samples at all cluster sizes.     

Force fluctuations in a vertically pushed granular column

We present series of experiments on the resistance force encountered by a bottom piston pushing a vertical granular column confined in a two-dimensional cell. We show that, due to the presence of friction at the boundaries and between the grains, the signal shows many complex features. At slow driving velocities, we observe a transition to a stick-slip dynamic instability. Depending on the granular material used, the elementary stick-slip events may either be well characterized or largely distributed. We present a statistical study on the waiting time between events and the distribution of energy release as a function of the spring stiffness and the driving velocity. Received 5 August 1998 and Received in final form 22 October 1998     

Cluster formation, pressure and density measurements in a granular medium fluidized by vibrations

We report experimental results on the behavior of an ensemble of inelastically colliding particles, excited by a vibrated piston in a vertical cylinder. When the particle number is increased, we observe a transition from a regime where the particles have erratic motions (“granular gas”) to a collective behavior where all the particles bounce like a nearly solid body. In the gas-like regime, we measure the density of particles as a function of the altitude and the pressure as a function of the number N of particles. The atmosphere is found to be exponential far enough from the piston, and the “granular temperature”, T, dependence on the piston velocity, V, is of the form , where is a decreasing function of N. This may explain previous conflicting numerical results. Received 1 February 1999     

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.     

Shocks in non-loaded bead chains with impurities

We numerically investigate the problem of the propagation of a shock in an horizontal non-loaded granular chain with a bead interaction force exponent varying from unity to large values. When is close to unity we observed a cross-over between a nonlinearity-dominated regime and a solitonic one, the latest being the final steady state of the propagating wave. In the case of large values of the deformation field given by the numerical simulations is completely different from the one obtained by analytical calculation. In the following we studied the interaction of these shock waves with a mass impurity placed in the bead chain. Two different physical pictures emerge whether we consider a light or a heavy impurity mass. The scatter of the shock wave with a light impurity yields damped oscillations of the impurity which then behave as a solitary wave source. Differently an heavy impurity is just shifted by the shock and the transmitted wave loses its solitonic character being fragmented into waves of decreasing amplitudes. Received 23 June 1999     

Gas-driven subharmonic waves in a vibrated two-phase granular material

Vibrated powders exhibit striking phenomena: subharmonic waves, oscillons, convection, heaping, and even bubbling. We demonstrate novel rectangular profile subharmonic waves for vibrated granular material, that occur uniquely in the two-phase case of grains, and a fluid, such as air. These waves differ substantially from those for the gas-free case, exhibit different dispersion relations, and occur for specific shaking parameters and air pressure, understandable with gas-particle flow models. These waves occur when the gas diffusively penetrates the granular layer in a time comparable to the shaker period. As the pressure is lowered towards P =0, the granular-gas system exhibits a Knudsen regime. This instability provides an opportunity to quantitatively test models of two-phase flow.     

A quasi-elastic regime for vibrated granular gases

Using simple scaling arguments and two-dimensional numerical simulations of a granular gas excited by vibrating one of the container boundaries, we study a double limit of small 1-r and large L, where r is the restitution coefficient and L the size of the container. We show that if the particle density n₀ and (1-r²)(n₀ Ld) where d is the particle diameter, are kept constant and small enough, the granular temperature, i.e. the mean value of the kinetic energy per particle, 〈E 〉/N, tends to a constant whereas the mean dissipated power per particle, 〈D 〉/N, decreases like when N increases, provided that (1-r²)(n₀ Ld)² < 1. The relative fluctuations of E, D and the power injected by the moving boundary, I, have simple properties in that regime. In addition, the granular temperature can be determined from the fluctuations of the power I(t) injected by the moving boundary.     

Self-organized branching process for a one-dimensional rice-pile model

A self-organized branching process is introduced to describe one-dimensional rice-pile model with stochastic topplings. Although the branching processes are generally expected to describe well high-dimensional systems, our modification highlights some of the peculiarities present in one dimension. We find analytically that the crossover behavior from the trivial one-dimensional BTW behaviour to self-organized criticality is characterised by a power-law distribution of avalanches. The finite-size effects, which are crucial to the crossover, are calculated. Received 21 June 2001 and Received in final form 14 November 2001     

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.     

Phenomenology and theory of horizontally oscillated granular mixtures

We overview the physics of a granular mixture subject to horizontal oscillations, recently investigated via experiments and molecular dynamics simulations. First we discuss the rich phenomenology exhibited by this system, which encompasses both segregation and dynamical instabilities. Then we show that the phenomenology can be explained via an effective interaction approach, by which the driven, non-thermal, granular mixture in mapped into a monodispersed thermal system of particles interacting via an effective potential. After determining the effective interaction we discuss its microscopic origin and investigate how it induces the observed phenomenology. Finally, as much as in thermal fluids, from the effective interaction we derive a Cahn-Hilliard dynamics equation, which appears to capture the essential characteristics of the dynamics of the granular mixture.