Granular flow down an inclined plane: Bagnold scaling and rheology

Shear flow of dense granular materials near smooth walls. I. Shear localization and constitutive laws in the boundary region

We report on a numerical study of the shear flow of a simple two-dimensional model of a granular material under controlled normal stress between two parallel smooth frictional walls moving with opposite velocities ± V. Discrete simulations, which are carried out with the contact dynamics method in dense assemblies of disks, reveal that, unlike rough walls made of strands of particles, smooth ones can lead to shear strain localization in the boundary layer. Specifically, we observe, for decreasing V, first a fluidlike regime (A), in which the whole granular layer is sheared, with a homogeneous strain rate except near the walls, then (B) a symmetric velocity profile with a solid block in the middle and strain localized near the walls, and finally (C) a state with broken symmetry in which the shear rate is confined to one boundary layer, while the bulk of the material moves together with the opposite wall. Both transitions are independent of system size and occur for specific values of V. Transient times are discussed. We show that the first transition, between regimes A and B, can be deduced from constitutive laws identified for the bulk material and the boundary layer, while the second one could be associated with an instability in the behavior of the boundary layer. The boundary zone constitutive law, however, is observed to depend on the state of the bulk material nearby.

Entangled granular media

We study the geometrically induced cohesion of ensembles of granular "u particles" that mechanically entangle through particle interpenetration. We vary the length-to-width ratio l/w of the u particles and form them into freestanding vertical columns. In a laboratory experiment, we monitor the response of the columns to sinusoidal vibration (with peak acceleration Γ). Column collapse occurs in a characteristic time τ which follows the relation τ∝exp(Γ/Δ). Δ resembles an activation energy and is maximal at intermediate l/w. A simulation reveals that optimal strength results from competition between packing and entanglement.

Nonlocal constitutive relation for steady granular flow

Extending recent modeling efforts for emulsions, we propose a nonlocal fluidity relation for flowing granular materials, capturing several known finite-size effects observed in steady flow. We express the local Bagnold-type granular flow law in terms of a fluidity ratio and then extend it with a particular Laplacian term that is scaled by the grain size. The resulting model is calibrated against a sequence of existing discrete element method data sets for two-dimensional annular shear, where it is shown that the model correctly describes the divergence from a local rheology due to the grain size as well as the rate-independence phenomenon commonly observed in slowly flowing zones. The same law is then applied in two additional inhomogeneous flow geometries, and the predicted velocity profiles are compared against corresponding discrete element method simulations utilizing the same grain composition as before, yielding favorable agreement in each case.

Relevance of numerical simulations to booming sand

We have performed a simulation study of three-dimensional cohesionless granular flows down an inclined chute. We find that the oscillations observed in [L. E. Silbert, Phys. Rev. Lett. 94, 098002 (2005)] near the angle of repose are harmonic vibrations of the lowest normal mode. Their frequencies depend on the contact stiffness as well as on the depth of the flow. Could these oscillations account for the phenomena of "booming sand"? We estimate an effective contact stiffness from the Hertz law, but this leads to frequencies that are several times higher than observed. However, the Hertz law also predicts interpenetrations of a few nanometers, indicating that the oscillations frequencies are governed by the surface stiffness, which can be much lower than the bulk one. This is in agreement with previous studies ascribing the ability to sing to the presence of a soft coating on the grain surface.

Lift force on an asymmetrical obstacle immersed in a dilute granular flow

This paper investigates the lift force exerted on an elliptical obstacle immersed in a granular flow through analytical calculations and computer simulations. The results are shown as a function of the obstacle size, orientation with respect to the flow direction (tilt angle), the restitution coefficient and ellipse eccentricity. The theoretical argument, based on the force exerted on the obstacle due to inelastic, frictionless collisions of a very dilute flow, captures the qualitative features of the lift, but fails to reproduce the data quantitatively. The reason behind this disagreement is that the dilute flow assumption on which this argument is built breaks down as a granular shock wave forms in front of the obstacle. More specifically, the shock wave changes the grains impact velocity at the obstacle, decreasing the overall net lift obtained from a very dilute flow.

Jamming phase diagram for frictional particles

We investigate the jamming transition of frictional particulate systems via discrete element simulations, reporting the existence of new regimes, which are conveniently described in a jamming phase diagram with axes density, shear stress, and friction coefficient. The resulting jammed states are characterized by different mechanical and structural properties and appear not to be "fragile" as speculated. In particular, we find a regime, characterized by extremely long processes, with a diverging time scale, whereby a suspension first flows but then suddenly jams. We link this sudden jamming transition to the presence of impeded dilatancy.

Automatic target recognition based on cross-plot

Automatic target recognition that relies on rapid feature extraction of real-time target from photo-realistic imaging will enable efficient identification of target patterns. To achieve this objective, Cross-plots of binary patterns are explored as potential signatures for the observed target by high-speed capture of the crucial spatial features using minimal computational resources. Target recognition was implemented based on the proposed pattern recognition concept and tested rigorously for its precision and recall performance. We conclude that Cross-plotting is able to produce a digital fingerprint of a target that correlates efficiently and effectively to signatures of patterns having its identity in a target repository.

Numerical simulation of the sedimentation of a sphere in a sheared granular fluid: a granular Stokes experiment

We study, computationally, the sedimentation of a sphere of higher mass in a steady, gravity-driven granular flow of otherwise identical spheres, on a rough inclined plane. Taking a hydrodynamic approach at the scale of the particle, we find the drag force to be given by a modified Stokes law and the buoyancy force by the Archimedes principle, with excluded volume effects taken into account. We also find significant differences between the hydrodynamic case and the granular case, which are highlighted.

Constitutive relations for steady, dense granular flows

This work focuses on the mechanical response of dry granular materials under steady, simple shear conditions. In particular, the goal is to obtain a complete rheology able to describe the material behavior within the entire range of concentrations for which the flow can be considered dense. The total stress is assumed to be the linear sum of a frictional and a kinetic component. The frictional and the kinetic contributions are modeled in the context of the critical state theory and the kinetic theory of dense granular gases, respectively; in the latter, the correlated motion among the particles, which is likely to occur at high concentration, is also included. In accordance with recent findings on disordered granular packings, the frictional component of stresses is assumed to vanish when the concentration is below the random loose packing. According to this approach, four nondimensional quantities govern steady, simple shear flows: the concentration, the shear to normal stress ratio, the ratio of the time scales associated with the motion perpendicular and parallel to the flow, and the ratio between the particle stiffness and the normal stress. The present theory allows us to reproduce, in a notable way, both numerical simulations on simple shear flows of disks and physical experiments on incline flows of glass spheres taken from the literature.

Undulatory swimming in sand: experimental and simulation studies of a robotic sandfish

A previous study of a sand-swimming lizard, the sandfish, revealed that it swims within granular media at speeds up to 0.4 body-lengths/cycle using body undulations (approximately a single period sinusoidal traveling wave) without limb use. Inspired by the organism, we develop a numerical model of a robot swimming in a simulated granular medium to guide the design of a physical device. Both in simulation and experiment the robot swims limblessly subsurface at speeds up to 0.3 body-lengths/cycle and, like the animal, increases its speed by increasing its oscillation frequency. The performance of the robot measured in terms of its wave efficiency η, the ratio of its forward speed to wave speed, is 0.34 ± 0.02 , within 8% of the simulation prediction. Both in simulation and experiment, η increases with increasing particle—particle friction but decreases with increasing body—particle friction. On a flat, rigid surface the robot fails to move forward, as expected, due to the frictional isotropy between the interacting surfaces. However, the surface and subsurface performance of the robot on low friction particles are comparable. Our work provides a validated simulation tool and the design of a robot that can move on or within yielding terrestrial substrates.

Gradient Monte Carlo simulations: hard spheres in spatially varying temperature and gravitational fields

There are many physical situations where particles experience external fields or are in a nonisothermal environment. Monte Carlo (MC) simulations can be useful to understand such experimental systems at steady state. Within this context, we formulate a general framework to study these systems via inhomogeneous MC simulations incorporating spatially varying temperature and gravitational fields. Using this approach we study granular materials consisting of hard spheres in an external field with either uniform or nonuniform temperature. We present comprehensive results from our MC simulations and compare these with theoretical results based on the Carnahan-Starling equation of state.

Droplet and cluster formation in freely falling granular streams

Particle beams are important tools for probing atomic and molecular interactions. Here we demonstrate that particle beams also offer a unique opportunity to investigate interactions in macroscopic systems, such as granular media. Motivated by recent experiments on streams of grains that exhibit liquid-like breakup into droplets, we use molecular dynamics simulations to investigate the evolution of a dense stream of macroscopic spheres accelerating out of an opening at the bottom of a reservoir. We show how nanoscale details associated with energy dissipation during collisions modify the stream's macroscopic behavior. We find that inelastic collisions collimate the stream, while the presence of short-range attractive interactions drives structure formation. Parameterizing the collision dynamics by the coefficient of restitution (i.e., the ratio of relative velocities before and after impact) and the strength of the cohesive interaction, we map out a spectrum of behaviors that ranges from gaslike jets in which all grains drift apart to liquid-like streams that break into large droplets containing hundreds of grains. We also find a new, intermediate regime in which small aggregates form by capture from the gas phase, similar to what can be observed in molecular beams. Our results show that nearly all aspects of stream behavior are closely related to the velocity gradient associated with vertical free fall. Led by this observation, we propose a simple energy balance model to explain the droplet formation process. The qualitative as well as many quantitative features of the simulations and the model compare well with available experimental data and provide a first quantitative measure of the role of attractions in freely cooling granular streams.

Hysteresis in a hydrodynamic model of dense granular flows

A hydrodynamic model for dense granular flows, previously developed for confined flows, has been extended to address free surface flow down an inclined chute. Results show that the model can predict the existence of two critical inclination angles, namely, the avalanche starting angle θ(start) above which the granular bed begins flowing from an initially jammed configuration, and an avalanche stopping angle θ(stop), which is the minimum to maintain flowing conditions, in agreement with experiments and numerical simulations available from the literature. The dependence of these critical angles on the bed depth is also analytically formulated, reflecting the expected qualitative behavior. Such a hysteretic behavior is specific of granular flow and its prediction provides indications of consistence of the modeling approach. The improved model also captures the scaling of the velocity profiles down the bed depth.

Bubbling in vibrated granular films

With the help of experiments, computer simulations, and a theoretical investigation, a general model is developed of the flow dynamics of dense granular media immersed in air in an intermediate regime where both collisional and frictional interactions may affect the flow behavior. The model is tested using the example of a system in which bubbles and solid structures are produced in granular films shaken vertically. Both experiments and large-scale, three-dimensional simulations of this system are performed. The experimental results are compared with the results of the simulation to verify the validity of the model. The data indicate evidence of formation of bubbles when peak acceleration relative to gravity exceeds a critical value Γ(b). The air-grain interfaces of bubblelike structures are found to exhibit fractal structure with dimension D=1.7±0.05.

Shallow granular flows

Many processes in geophysical and industrial settings involve the flow of granular materials down a slope. In order to investigate the granular dynamics, we report a series of laboratory experiments conducted by releasing grains at a steady rate from a localized source on a rough inclined plane. Different types of dense granular flow are observed by varying the flow rate at the source and the slope of the inclined plane. The two cases of steady flow confined by levees and the flow of avalanches down the plane are examined. The width of the steady flow increases linearly with the prescribed flow rate, which does not appreciably affect the characteristic depth or surface velocity of the bulk flow. When the flow rate is just below that required for sustaining the steady flow, avalanches are triggered at regular intervals. The avalanches maintain their shape, size, and speed down the inclined plane. We propose a simple model of steady flow that is consistent with our observations and discuss the challenges associated with the theoretical treatment of avalanche dynamics.

Stochastic transitions and jamming in granular pipe flow

We study a model granular suspension driven down a channel by an embedding fluid via computer simulations. We characterize the different system flow regimes and the stochastic nature of the transitions between them. For packing fractions below a threshold ϕ{m}, granular flow is disordered and exhibits an Ostwald-de Waele-type power-law shear-stress constitutive relation. Above ϕ{m}, two asymptotic states exist; disordered flow can persist indefinitely, yet, in a fraction of samples, the system self-organizes in an ordered form of flow where grains move in parallel ordered layers. In the latter regime, the Ostwald-de Waele relationship breaks down and a nearly solid plug appears in the center, with linear shear regions at the boundaries. Above a higher threshold ϕ{g}, an abrupt jamming transition is observed if ordering is avoided.

Spherical shock-wave propagation in three-dimensional granular packings

We investigate numerically the spherical shock-wave propagation in an open dense granular packing perturbed by the sudden expansion of a spherical intruder in the interior of the pack, focusing on the correlation between geometrical fabrics and propagating properties. The measurements of the temporal and spatial variations in a variety of propagating properties define a consistent serrated wave substructure with characteristic length on the orders of particle diameters. Further inspection of particle packing reveals a well-defined particle layering that persists several particle diameters away from the intruder, although its dominant effects are only within one to two diameters. This interface-induced layering not only exactly coincides with the serrated wave profile, but also highlights the competition between two energy transmission mechanisms involving distinct transport speeds. The alternating dominances between these two mechanisms contribute to the nonlinear wave propagation on the particle scale. Moreover, the proliferation of intricate three-dimensional contact force networks suggests the anisotropic stress transmission, which is found to also arise from the localized packing structure in the vicinity of the intruder.

Transit time during the interparticle percolation process

A numerical investigation of jamming effect during the spontaneous interparticle percolation process of small beads through an unconsolidated porous media has been performed. The size ratio between the moving beads and the ones building up the porous medium was chosen larger than the geometrical trapping threshold: ξ(c)=(2/√3]-1)(-1)=6.464.... In this paper, we used the discrete element method algorithm to study the rebounds of particles on the top of the porous medium and the transit times of an assembly of particles through it. Several parameters such as the number of injected particles, the size ratio between beads, and the energy restitution coefficient are investigated. This study leads to give some important results of the evolution of the transit time versus the contiguous volume occupied by the percolating particles.

Time-varying force from dense granular avalanches on a wall

We studied avalanches of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. This paper focuses on the transient time-varying mean force exerted by the granular stream on the obstacle at various slope inclinations. A nearly triangular dead zone is formed upstream of the obstacle. It largely contributes to the overall force signal at low slope inclinations. It also drives the residual force corresponding to the avalanche tail until its standstill whatever the slope inclination. An analytical hydrodynamic model based on depth-averaged momentum conservation was successfully developed for steady-flow conditions to predict the steady-state force computed from discrete numerical simulations [T. Faug, R. Beguin, and B. Chanut, Phys. Rev. E 80, 021305 (2009)]. The basic equations of the model are briefly reviewed and adapted to transient time-varying flows. The modified hydrodynamic model quite accurately represents the force peak produced by the granular avalanche flows computed from discrete numerical simulations reported in previous studies. A fitting procedure is needed to represent the decrease of the force after the force peak, thus quantifying the different contributions to the mean force on the wall. We show that the weight of each contribution is largely dependent on the slope inclination.

Janssen effect and the stability of quasi-two-dimensional sandpiles

We present the results of three-dimensional discrete element simulations of global normal stresses in quasi-two-dimensional sandpiles formed by pouring monodispersed cohesionless spherical grains into a vertical granular Hele-Shaw cell. We observe the Janssen effect which is the phenomenon of pressure saturation at the bottom of the container. Simulation of cells with different thicknesses shows that the Janssen coefficient κ is a function of the cell thickness. Dependence of global normal stresses as well as κ on the friction coefficients between the grains (μ(p)) and with walls (μ(w)) are also studied. The results show that in the range of our simulations κ usually increases with the wall-grain friction coefficient. Meanwhile by increasing μ(p) while the other system parameters are fixed, we witness a gradual increase in κ to a parameter dependent maximal value.

Constitutive relations in dense granular flows

We use simulations to investigate constitutive relations in dry granular flow. Our system is comprised of polydisperse sets of spherical grains falling down a vertical chute under the influence of gravity. Three phases or states of granular matter are observed: a free-fall dilute granular gas region at the top of the chute, a granular fluid in the middle and then a glassy region at the bottom. We examine a complete closed set of constitutive relations capable of describing the local stresses, heat flow, and dissipation in the different regions. While the pressure can be reasonably described by hard sphere gas models, the transport coefficients cannot. Transport coefficients such as viscosity and heat conductivity increase with decreasing temperature in the fluid and glassy phases. The glass exhibits signs of a finite yield stress and we show that the static sand pile is a limit of our glassy state.

Steady flow of smooth, inelastic particles on a bumpy inclined plane: hard and soft particle simulations

We study smooth, slightly inelastic particles flowing under gravity on a bumpy inclined plane using event-driven and discrete-element simulations. Shallow layers (ten particle diameters) are used to enable simulation using the event-driven method within reasonable computational times. Steady flows are obtained in a narrow range of angles (13 degrees-14.5 degrees); lower angles result in stopping of the flow and higher angles in continuous acceleration. The flow is relatively dense with the solid volume fraction, nu approximately 0.5 , and significant layering of particles is observed. We derive expressions for the stress, heat flux, and dissipation for the hard and soft particle models from first principles. The computed mean velocity, temperature, stress, dissipation, and heat flux profiles of hard particles are compared to soft particle results for different values of stiffness constant (k). The value of stiffness constant for which results for hard and soft particles are identical is found to be k>or=2x10(6) mg/d, where m is the mass of a particle, g is the acceleration due to gravity, and d is the particle diameter. We compare the simulation results to constitutive relations obtained from the kinetic theory of Jenkins and Richman [J. T. Jenkins and M. W. Richman, Arch. Ration. Mech. Anal. 87, 355 (1985)] for pressure, dissipation, viscosity, and thermal conductivity. We find that all the quantities are very well predicted by kinetic theory for volume fractions nu<0.5. At higher densities, obtained for thicker layers (H=15d and H=20d), the kinetic theory does not give accurate prediction. Deviations of the kinetic theory predictions from simulation results are relatively small for dissipation and heat flux and most significant deviations are observed for shear viscosity and pressure. The results indicate the range of applicability of soft particle simulations and kinetic theory for dense flows.

A non-local rheology for dense granular flows

A non-local theory is proposed to model dense granular flows. The idea is to describe the rearrangements occurring when a granular material is sheared as a self-activated process. A rearrangement at one position is triggered by the stress fluctuations induced by rearrangements elsewhere in the material. Within this framework, the constitutive law, which gives the relation between the shear rate and the stress distribution, is written as an integral over the entire flow. Taking into account the finite time of local rearrangements, the model is applicable from the quasi-static regime up to the inertial regime. We have checked the prediction of the model in two different configurations, namely granular flows down inclined planes and plane shear under gravity, and we show that many of the experimental observations are predicted within the self-activated model.

Dynamical fluctuations in dense granular flows

We have made measurements of force and velocity fluctuations in a variety of dense, gravity-driven granular flows under flow conditions close to the threshold of jamming. The measurements reveal a microscopic state that evolves rapidly from entirely collisional to largely frictional, as the system is taken close to jamming. On coarse-grained time scales, some descriptors of the dynamics-such as the probability distribution of force fluctuations, or the mean friction angle-do not reflect this profound change in the micromechanics of the flow. Other quantities, such as the frequency spectrum of force fluctuations, change significantly, developing low-frequency structure in the fluctuations as jamming is approached. We also show evidence of spatial structure, with force fluctuations being organized into local collision chains. These local structures propagate rapidly in the flow, with consequences far away from their origin, leading to long-range correlations in velocity fluctuations.

Jamming at zero temperature, zero friction, and finite applied shear stress

Shear stress, as temperature, induces particle motion, and affects the jamming transition from a fluid to a disordered solid state. Here, we show that at finite shear stress, the jamming transition is characterized by the presence of hysteresis, as in a given range of control parameters a flowing or a jammed state can be found, depending on whether the system is prepared coming from the fluid or the jammed phase. At small shear stress, where the hysteresis is negligible, the jamming transition has a mixed first-order second-order character close to that found at the glass transition of thermal systems, with discontinuities in the asymptotic values of two time quantities such as the self-intermediate scattering function.

Patterns in flowing sand: understanding the physics of granular flow

Dense granular flows are often unstable and form inhomogeneous structures. Although significant advances have been recently made in understanding simple flows, instabilities of such flows are often not understood. We present experimental and numerical results that show the formation of longitudinal stripes that arise from instability of the uniform flowing state of granular media on a rough inclined plane. The form of the stripes depends critically on the mean density of the flow with a robust form of stripes at high density that consists of fast sliding pluglike regions (stripes) on top of highly agitated boiling material--a configuration reminiscent of the Leidenfrost effect when a droplet of liquid lifted by its vapor is hovering above a hot surface.

Long-wavelength structural anomalies in jammed systems

The structural properties of static, jammed packings of monodisperse spheres in the vicinity of the jamming transition are investigated using large-scale computer simulations. At small wave number k , we argue that the anomalous behavior in the static structure factor, S(k) approximately k , is consequential of an excess of low-frequency, collective excitations seen in the vibrational spectrum. This anomalous feature becomes more pronounced closest to the jamming transition, such that S(0)-->0 at the transition point. We introduce an appropriate dispersion relation that accounts for these phenomena that leads us to relate these structural features to characteristic length scales associated with the low-frequency vibrational modes of these systems. When the particles are frictional, this anomalous behavior is suppressed providing yet more evidence that the jamming transitions for frictional spheres lie at lower packing fractions than for frictionless spheres. These results suggest that the mechanical properties of jammed and glassy media may therefore be inferred from measurements of both the static and dynamical structure factors.

Effect of noise on solid-to-liquid transition in small granular systems under shear

The effect of noise on the solid-to-liquid transition of a dense granular assembly under planar shear is studied numerically using soft-particle molecular dynamics simulations in two dimensions. We focus on small systems in a thin planar Couette cell, examining the bistable region while increasing shear, with varying amounts of random noise, and determine statistics of the shear required for fluidization. In the absence of noise, the threshold value of the shear stress depends on the preparation of the system and has a broad distribution. However, adding force fluctuations both lowers the mean threshold value of the shear stress and decreases its variability. This behavior is interpreted as thermoactivated escape through a fluctuating barrier.

Physical test of a particle simulation model in a sheared granular system

We report a detailed comparison of a slow gravity-driven sheared granular flow with a discrete-element simulation performed in the same geometry. In the experiments, grains flow inside a silo with a rectangular cross section and are sheared by a rough boundary on one side and smooth boundaries on the other sides. Individual grain position and motion are measured using a particle index-matching imaging technique where a fluorescent dye is added to the interstitial liquid which has the same refractive index as the glass beads. The simulations use a Cundall-Strack contact model between the grains using contact parameters that have been used in many other previous studies and ignore the hydrodynamic effects of the interstitial liquid. Computations are performed to understand the effect of particle coefficient of friction, elasticity, contact model, and polydispersity on mean flow properties. We then perform a detailed comparison of the particle fluctuation properties as measured by the displacement probability distribution function and the mean square displacement. All in all, our study suggests a high level of quantitative agreement between the simulations and experiments.

Structure and dynamics of two-dimensional sheared granular flows

The structure and dynamics of the two-dimensional linear shear flow of inelastic disks at high area fractions are analyzed. The event-driven simulation technique is used in the hard-particle limit, where the particles interact through instantaneous collisions. The structure (relative arrangement of particles) is analyzed using the bond-orientational order parameter. It is found that the shear flow reduces the order in the system, and the order parameter in a shear flow is lower than that in a collection of elastic hard disks at equilibrium. The distribution of relative velocities between colliding particles is analyzed. The relative velocity distribution undergoes a transition from a Gaussian distribution for nearly elastic particles, to an exponential distribution at low coefficients of restitution. However, the single-particle distribution function is close to a Gaussian in the dense limit, indicating that correlations between colliding particles have a strong influence on the relative velocity distribution. This results in a much lower dissipation rate than that predicted using the molecular chaos assumption, where the velocities of colliding particles are considered to be uncorrelated.

Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows

We studied free-surface gravity-driven recirculating flows of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. We performed two-dimensional spherical particle discrete element simulations using a linear damped spring law between particles with a Coulomb failure criterion. High-frequency force fluctuations were observed. This paper focuses on the mean steady force exerted by the flow on the obstacle versus the macroscopic inertial number of the incoming flow, where the inertial number measures the ratio between a macroscopic deformation time scale and an inertial time scale. A triangular stagnant zone is formed upstream of the obstacle and sharply increases the mean force at low incoming inertial numbers. A simple hydrodynamic model based on depth-averaged momentum conservation is proposed. This analytical model predicts the numerical data fairly well and allows us to quantify the different contributions to the mean force on the wall. Beyond this model, our study provides an example of the ability of simple hydrodynamic approaches to describe the macroscopic behavior of an assembly of discrete particles not only in terms of kinematics but also in terms of forces.

Motion of packings of frictional grains

Friction plays a key role in controlling the rheology of dense granular flows. Counting the number of constraints vs the number of variables indicates that critical coordination numbers Zc=3 (in D=2) and Zc=4 (in D=3) are special, in that states in which all contacts roll without frictional sliding are naively possible at and below these average coordination numbers. We construct an explicit example of such a state in D=2 based on a honeycomb lattice. This state has surprisingly large values for the typical angular velocities of the particles. Solving for the forces in such a state, we conclude that organized shear can exist in this state only on scales l<d/I, where d is the grain diameter and I=dgamma/sqrt[P/rhog] is the dimensionless "inertia number." Above this scale the coherent shear is destabilized by the disappearance of normal forces between a significant fraction of the grains. Moving to disordered lattices, we observe that rolling regions in such lattices are characterized by an antiferromagnetic short-range ordering of the particle rotations; the frustration of this ordering links the shearing states of the grain packing to low-energy spin-glass states on the same lattice. Random lattice states are also expected to exhibit large values for the typical angular velocities and to also have regions of coherent shear limited to be smaller than l.

Dispersion of particles by spontaneous interparticle percolation through unconsolidated porous media

We have performed extensive experimental and numerical studies of spontaneous percolation of small beads through an unconsolidated porous media made with large glass beads. In this paper, an experimental setup and a fast "discrete element method" algorithm are presented to deal with large numbers of particles during our interparticle percolation phenomenon studies. In all the experimental and numerical analyses, the size ratio between the moving beads and the stable packing was chosen larger than the geometrical trapping threshold: xi_{c}=(2/sqrt[3]-1);{-1}=6.464... . We measure the longitudinal and transverse dispersion coefficients versus the height of the porous medium or the number of falling small beads. The influence of bead properties such as density, diameter, or restitution coefficients was investigated by using either steel or glass beads. The individual description of these effects and their explanations were made possible by confrontation and coupling between experimental and numerical results. Indeed, with our numerical model, individual analysis of the effects of these mechanical or geometrical parameters were made possible and carried out.

Spatial correlations in sheared isothermal liquids: from elastic particles to granular particles

Spatial correlations in sheared isothermal liquids for both elastic and granular cases are theoretically investigated. Using the generalized fluctuating hydrodynamics, correlation functions for both the microscopic scale and the macroscopic scale are obtained. We find the existence of long-range correlations obeying power laws. The validity of our theoretical predictions has been verified from molecular-dynamics simulation.

Annular shear of cohesionless granular materials: from the inertial to quasistatic regime

Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with prescribed angular velocity, while the outer one may expand or shrink and maintains a constant radial pressure. Focusing on steady state flows, we delineate in parameter space the range of applicability of the recently introduced constitutive laws for sheared granular materials (based on the inertial number). We discuss the two origins of the stronger strain rates observed near the inner boundary, the vicinity of the wall and the heteregeneous stress field in a Couette cell. Above a certain velocity, an inertial region develops near the inner wall, to which the known constitutive laws apply, with suitable corrections due to wall slip, for small enough stress gradients. Away from the inner wall, slow, apparently unbounded creep takes place in the nominally solid material, although its density and shear to normal stress ratio are on the jammed side of the critical values. In addition to rheological characterizations, our simulations provide microscopic information on the contact network and velocity fluctuations that is potentially useful to assess theoretical approaches.

Effects of cohesion on the surface angle and velocity profiles of granular material in a rotating drum

Large scale, discrete element simulations are performed to study the dynamics of a rotating drum partially filled with cohesive granular particles. The continuous avalanche regime is explored using a simple model for interparticle cohesion in order to simulate the effects of granular media in the presence of a wetting fluid. The shape of the free surface for cohesionless particles ranges from flat to a concave S shape depending on the rotation rate and frictional properties between the grains and the drum side walls. The presence of interparticle cohesion reduces the concavity of the free surface and pushes the free surface towards a flat or even slightly convex shape. From contour plots of the velocity, we show how the position of the vortex core (the stationary spot in the laboratory frame) depends on the rotation speed and interparticle cohesion strength and how this relationship can be understood from considerations of the incompressibility condition on the mass flow.