Isolating segregation mechanisms in a split-bottom cell

We study the segregation of mixtures of particles in a split-bottom cell to isolate three possible driving mechanisms for segregation of densely sheared granular mixtures: gravity, porosity, and velocity gradients. We find that gravity alone does not drive segregation associated with particle size without a sufficiently large porosity or porosity gradient. A velocity gradient, however, appears to be capable of driving segregation associated with both particle size and material density. In all cases, the final segregation state is approached exponentially.     

Steady-State Properties of Driven Polydisperse Granular Mixtures

We represent a two-dimensional model of polydisperse granular mixtures with a power-law size distribution. The model consists of smooth hard disks in a rectangular box with inelastic collisions, driven by a homogeneous heat bath at zero gravity. The width of particle size distribution is characterized by the only
parameter, namely, the fractal dimension D. The energy dissipation of the mixture is increased as D increases or as e decreases. Furthermore, it is found that the steady-state properties of the mixture such as the collision rate, granular temperature, kinetic pressure and velocity distribution depend sensitively on size distribution parameter D.     

Arch generated shear bands in granular systems

We propose an arch based model, on cubic and square lattices, to simulate the internal mobility of grains, in a dense granular system under shear. In this model, the role of the arches in granular transport presents a non-linear dependence on the local values of the stress components that can be modeled geometrically. This non-linearity is very important since a linear dependence on the stress will make the models behave similarly to viscous fluids, which will not reproduce highly interesting properties of the sheared systems such as shear bands. In particular, we study a modified Couette flow and find the appearance of shear bands in accordance with the literature.     

Creep motion in a granular pile exhibiting steady surface flow

We investigate experimentally granular piles exhibiting steady surface flow. Below the surface flow, it has been believed that a "frozen" bulk region exists, but our results show no such frozen bulk. We report here that even the particles in layers deep in the bulk exhibit very slow flow and that such motion can be detected at an arbitrary depth. The mean velocity of the creep motion decays exponentially with depth, and the characteristic decay length is approximately equal to the particle size and is independent of the flow rate. It is expected that the creep motion we have seen is observable in all sheared granular systems.     

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.     

Effect of interstitial air pressure and particle size on the heat storage coefficient of a two phase system

An expression for the heat storage coefficient (HSC) of loose granular systems at interstitial air pressures is developed in terms of the characteristic pressure. The dependence of the HSC on pore and particle sizes and characteristic pressure is also discussed. To test the validity of the derived expression, the experiments are performed on a number of materials with various particle sizes and interstitial air pressures. The other reported data on the HSC are also compared with predicted values. A good agreement is found between them. This study suggests that the selection of proper particle size and partial evacuation of the pore improves the insulation characteristics of the materials.     

Hydrodynamic model for particle size segregation in granular media

We present a hydrodynamic theoretical model for “Brazil nut” size segregation in granular materials. We give analytical solutions for the rise velocity of a large intruder particle immersed in a medium of monodisperse fluidized small particles. We propose a new mechanism for this particle size-segregation due to buoyant forces caused by density variations which come from differences in the local “granular temperature”. The mobility of the particles is modified by the energy dissipation due to inelastic collisions and this leads to a different behavior from what one would expect for an elastic system. Using our model we can explain the size ratio dependence of the upward velocity.     

Mixing and segregation of granular materials in chute flows

Mixing of granular solids is invariably accompanied by segregation, however, the fundamentals of the process are not well understood. We analyze density and size segregation in a chute flow of cohesionless spherical particles by means of computations and theory based on the transport equations for a mixture of nearly elastic particles. Computations for elastic particles (Monte Carlo simulations), nearly elastic particles, and inelastic, frictional particles (particle dynamics simulations) are carried out. General expressions for the segregation fluxes due to pressure gradients and temperature gradients are derived. Simplified equations are obtained for the limiting cases of low volume fractions (ideal gas limit) and equal sized particles. Theoretical predictions of equilibrium number density profiles are in good agreement with computations for mixtures of equal sized particles with different density for all solids volume fractions, and for mixtures of different sized particles at low volume fractions (nu<0.2), when the particles are elastic or nearly elastic. In the case of inelastic, frictional particles the theory gives reasonable predictions if an appropriate effective granular temperature is assumed. The relative importance of pressure diffusion and temperature diffusion for the cases considered is discussed. (c) 1999 American Institute of Physics.     

Dynamic Properties of Two-Dimensional Polydisperse Granular Gases

We propose a two-dimensional model of polydisperse granular mixtures with a power-law size distribution in the presence of stochastic driving. A fractal dimension D is introduced as a measurement of the inhomogeneity of the size distribution of particles. We define the global and partial granular temperatures of the multi-component mixture. By direct simulation Monte Carlo, we investigate how the inhomogeneity of the size distribution influences the dynamic properties of the mixture, focusing on the granular temperature, dissipated energy, velocity distribution, spatial clusterization, and collision time. We get the following results： a single granular temperature does not characterize a multi-component mixture and each species attains its own ＂granular temperature＂; The velocity deviation from Gaussian distribution becomes more and more pronounced and the partial density of the assembly is more inhomogeneous with the increasing value of the fractal dimension D; The global granular temperature decreases and average dissipated energy per particle increases as the value olD augments.     

Dynamic Properties of Two-Dimensional Polydisperse Granular Gases

We propose a two-dimensional model of polydisperse granular mixtures with a power-law size distribution in the presence of stochastic driving. A fractal dimension D is introduced as a measurement of the inhomogeneity of the size distribution of particles. We define the global and partial granular temperatures of the multi-component mixture. By direct simulation Monte Carlo, we investigate how the inhomogeneity of the size distribution influences the dynamic properties of the mixture, focusing on the granular temperature, dissipated energy, velocity distribution, spatial clusterization, and collision time. We get the following results: a single granular temperature does not characterize a multi-component mixture and each species attains its own "granular temperature"; The velocity deviation from Gaussian distribution becomes more and more pronounced and the partial density of the assembly is more inhomogeneous with the increasing value of the fractal dimension D; The global granular temperature decreases and average dissipated energy per particle increases as the value of D augments.     

Diffusion and mobility in a stirred dense granular material

We describe a probe of diffusivity (D) and mobility (B) for a dense 2D granular system. We introduce random motion by stirring, and characterize D by particle tracking. To measure B we measure the force needed to push a particle through the medium at fixed velocity, v, using three sizes of tracer particle. We find simple Brownian diffusion, but B depends strongly on v because the force needed to push a tracer through a sample is nearly independent of v. Data for D/B depend on the tracer particle size.     

Protocol dependence of mechanical properties in granular systems

We study the protocol dependence of the mechanical properties of granular media by means of computer simulations. We control a protocol of realizing disk packings in a systematic manner. In 2D, by keeping material properties of the constituents identical, we carry out compaction with various strain rates. The disk packings exhibit the strain rate dependence of the critical packing fraction above which the pressure becomes non-zero. The observed behavior contrasts with the well-studied jamming transitions for frictionless disk packings. We also observe that the elastic moduli of the disk packings depend on the strain rate logarithmically. Our results suggest that there exists a time-dependent state variable to describe macroscopic material properties of disk packings, which depend on its protocol.     

Thermodiffusion of rigid particles in pure liquids

Thermodiffusion of particles suspended in a pure liquid is a thorny problem which has not yet received a solution admitted by all the different communities interested in. We approach the subject with macroscopic tools exclusively, hydrodynamics and irreversible thermodynamics. These tools have proved their relevance for molecular mixtures and the Soret effect, and we here extend them to suspensions of particles with supra-molecular size. In particular, we obtain the momentum balance of the particulate phase from which are deduced all the physical phenomena inducing a migration of the particles relative to the carrier fluid. Focussing on thermodiffusion, we show that the osmotic pressure is irrelevant and that thermodiffusion cannot have but two distinct origins : the temperature dependence of the stress associated with the distorted particle microstructure and a fluid-particle interaction force involving the temperature gradient. For deformable particles, it is well known that the origin of the fluid-particle temperature gradient force is the temperature dependence of the surface tension. For rigid particles, we suggest it stems from the temperature dependence of the small density jump, the carrier liquid displays close to the particle’s surface.     

Intruders in the dust: air-driven granular size separation

Using MRI and high-speed video we investigate the motion of a large intruder particle inside a vertically shaken bed of smaller particles. We find a pronounced, nonmonotonic density dependence, with both light and heavy intruders moving faster than those whose density is approximately that of the granular bed. For light intruders, we furthermore observe either rising or sinking behavior, depending on intruder starting height, boundary condition, and interstitial gas pressure. We map out the phase boundary delineating the rising and sinking regimes. A simple model can account for much of the observed behavior and shows how the two regimes are connected by considering pressure gradients across the granular bed during a shaking cycle.     

Granular layers on vibrating plates: effective bending stiffness and particle-size effects

Acoustic methods of land mine detection rely on the vibrations of the top plate of the mine in response to sound. For granular soil (e.g., sand), the particle size is expected to influence the mine response. This hypothesis is studied experimentally using a plate loaded with dry sand of various sizes from hundreds of microns to a few millimeters. For low values of sand mass, the plate resonance decreases with added mass and eventually reaches a minimum without particle size dependence. After the minimum, a frequency increase is observed with additional mass that includes a particle-size effect. Analytical nondissipative continuum models for granular media capture the observed particle-size dependence qualitatively but not quantitatively. In addition, a continuum-based finite element model (FEM) of a two-layer plate is used, with the sand layer replaced by an equivalent elastic layer for evaluation of the effective properties of the layer. Given a thickness of sand layer and corresponding experimental resonance, an inverse FEM problem is solved iteratively to give the effective Young's modulus and bending stiffness that matches the experimental frequency. It is shown that a continuum elastic model must employ a thickness-dependent elastic modulus in order to match experimental values.     

Plastic shear response of a single asperity: a discrete dislocation plasticity analysis

We investigate the plastic shear response during static friction of an asperity protruding from a large FCC single crystal. The asperity is in perfectly adhesive contact with a rigid platen and is sheared by tangentially moving the platen. Using discrete dislocation plasticity simulations, we elucidate the plastic shear behaviour of single asperities of various size and shape, in search for the length scale that controls the plastic behaviour. Since plasticity can occur also in the crystal, identification of the length scale that controls a possible size-dependent plastic behaviour is far from being trivial. It is found that scaling down the dimensions of an asperity results in a higher contact shear strength. The contact area is dominant in controlling the plastic shear response, because it determines the size of the zone, in and below the asperity, where dislocation nucleation can occur. For a specific contact area, there is still a dependence on asperity volume and shape, but this is weaker than the dependence on contact area alone.     

Dense granular flow around a penetrating object: experiment and hydrodynamic model

We present in this Letter experimental results on the bidimensional flow field around a cylinder penetrating into dense granular matter, together with drag force measurements. A hydrodynamic model based on extended kinetic theory for dense granular flow reproduces well the flow localization close to the cylinder and the corresponding scalings of the drag force, which is found to not depend on velocity, but linearly on the pressure and on the cylinder diameter and weakly on the grain size. Such a regime is found to be valid at a low enough "granular" Reynolds number.     

Suppressed compressibility at large scale in jammed packings of size-disperse spheres

We analyze the large-scale structure and fluctuations of jammed packings of size-disperse spheres, produced in a granular experiment as well as numerically. While the structure factor of the packings reveals no unusual behavior for small wave vectors, the compressibility displays an anomalous linear dependence at low wave vectors and vanishes when q→0. We show that such behavior occurs because jammed packings of size-disperse spheres have no bulk fluctuations of the volume fraction and are thus hyperuniform, a property not observed experimentally before. Our results apply to arbitrary particle size distributions. For continuous distributions, we derive a perturbative expression for the compressibility that is accurate for polydispersity up to about 30%.