Many systems can develop a yield stress while in an amorphous state. For example, a supercooled liquid, when cooled sufficiently, forms a glass - an amorphous solid with a yield stress. Another common example is a granular material which will remain solid and not move even under the influence of moderate stresses. This accounts for why piles of grain or sand can exist with a non-zero slope even though gravity is acting to flatten out the upper surface. The solidity in that case is due to the system having become jammed. Similar jamming often inhibits flow out of a hopper or in conduits transporting material across a factory floor. Jamming is a ubiquitous phenomenon occurring in many different systems such as colloidal suspensions, foams and, of course, traffic. We tend to think of the jamming transition as being stress-induced. A “fluid” at constant density (or under a confining pressure) flows if the stress is above the yield stress but becomes stuck in an amorphous configuration if the stress is too low. The idea of temperature, per se, does not seem to be crucial to the transition. This makes it seems quite different from the formation of a glass out of a supercooled liquid by lowering the temperature. However, there are similarities between these two types of transitions, aside from the obvious fact that they both have to do with the complete arrest of dynamics and flow. An exploration of these similarities was the subject of a program at the Institute for Theoretical Physics in Santa Barbara held in the Autumn of 1997. A synopsis of this program was published that details some of the interesting ideas now current in that field.[1]

Experimental measurements of discharge rate and observations of flow pattern were made for spherical, monosized particles in a liquid- filled, hourglass shaped container. Different combinations of fluid properties, solid properties and vessel geometry exhibited a range of flow patterns that are described as lubricated, fluidized, oscillatory, or localized channeling discharges. A Bagnold number is used to present the discharge rate and flow regime results.

In many industrial applications involving granular media, knowledge about the structural transformations suffered during the industrial process is desirable. Optical techniques are noninvasive, fast, and versatile tools for monitoring such transformations. We have recently introduced optical path-length spectroscopy as a new technique for random media investigation. The principle of the method is to use a partially coherent source in a Michelson interferometer, where the fields from a reference mirror and the sample are combined to obtain an interference signal. When the system under investigation is a multiple-scattering medium, by tuning the optical length of the reference arm, the optical path-length probability density of light backscattered from the sample is obtained. This distribution carries information about the structural details of the medium. In the present paper, we apply the technique of optical path-length spectroscopy to investigate inhomogeneous distributions of particulate dielectrics such as ceramics and powders. The experiments are performed on suspensions of systems with different solid loads, as well as on powders and suspensions of particles with different sizes. We show that the methodology is highly sensitive to changes in volume concentration and particle size and, therefore, it can be successfully used for real-time monitoring. In addition, the technique is fiber optic-based and has all the advantages associated with the inherent versatility.

The slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

We probe the transitions between solid-like and fluid-like granular states in the presence of shaking in the horizontal and vertical directions. These transitions are fundamental to other aspects of granular flow such as avalanche flow, in which there is a free surface. Key control parameters include accelerations in the vertical and horizontal directions, Γi = Aiω2i/g, for shaking of the form si = Ai cos(ωit + φi), i = h, v. Here, g is the acceleration of gravity. Also important is the relative phase between the two modes of shaking. We focus on low to moderate dimensionless accelerations, 0 < Γv,h < 1.6. We consider first the case Γv = 0, i.e. pure horizontal shaking. In this case, there is a hysteretic transition between solid and fluid states, where the fluid state consists of a sloshing layer of material of height H plus additional transverse flow. The hysteresis is lifted in the presence of a modest amount of fluidization by gas flow, or if a slight overburden is provided. We also identify a time scale, τ, for the transition between the phases that diverges inversely as the distance ε = (Γh–Γhc)/Γhc, from the appropriate transition points, i.e. as τ α ε-1. We identify a new convective mechanism, associated with horizontal shearing at the walls, as the mechanism that drives the transverse convective flow. For combined horizontal and vertical shaking, there exist a related set of novel dynamics and stability properties. These include the spontaneous formation of a static heap and a transition to flow, similar to the flow state under horizontal shaking, when the vertical acceleration Γv < 1. A simple friction model provides a good description of the steady states and a reasonably good description of the transition to flow. Horizontal and vertical shaking frequencies that differ by a small amount can lead to a novel switching state, as the relative phase, φh—φv, shifts over time.

First, a non linear incremental modelling is proposed to describe rheological behaviour of granular material under different simple (i.e. triaxial-, oedometric-, undrained-) stress-strain paths. Validity of isotropic-response assumption is demonstrated whatever the stress ratio as far as deformation range remains small (ε1<5%). This contradicts some recent hypothesis made on the evolution of contact distribution during anisotropic loading.

We develop the statistical-mechanical theory that delivers the fundamental equations of stress equilibrium for static arrays of rigid grains. The random geometry of static granular packing composed of rigid cohesionless particles can be visualised as a network of intergranular contacts. The contact network and external loading determine the network of intergranular forces. In general, the contact network can have an arbitrary coordination number varying within the system. It follows then that the network of intergranular forces is indeterminate i.e. the number of unknown forces is larger than the number of Newton's equations of mechanical equilibrium. Thus, in order for the network of intergranular forces to be determined, the number of equations must equal the number of unknowns. We argue that this determines the contact network with a certain fixed coordination number. The complete system of equations for the stress tensor is derived from the equations of intergranular force and torque balance, given the geometric specification of the packing. The granular material fabric gives rise to corrections to the Euler-Cauchy equation that become significant at mesoscopic lengthscales. The stress-geometry equation establishes the relation between various components of the stress tensor, and depends on the topology of the granular array.

Nonlinear acoustic impulses travel as weakly dispersive bundles of energy through 3-D, dry, granular assemblies. Such impulses can therefore be exploited to probe for buried objects in 3-D granular assemblies. In this article, we shall discuss the details of propagation of an impulse generated at the surface of a granular bed. The role of polydispersity will be briefly addressed. The calculations suggest that backscattered data, as received at predetermined locations at the surface, may be helpful in reconstructing an approximate image of the buried inclusion, as viewed from above.

Heat transfer in granular materials impacts a variety of industrial applications, such as calcination, drying kilns, packed bed and multiphase reactors, etc. and may yield insight into the thermal response of some porous materials (in combustion synthesis or sintering, for example). In a dense bed of granular material, conduction occurs almost exclusively through the particle-particle contacts over a wide range of conditions. We have developed a novel Thermal Particle Dynamics (TPD) Simulation technique which incorporates both contact mechanics and contact conductance theories in order to model the dynamics of flow and heat conduction through granular materials. This model is uniquely suited to studying the effects of microstructure and flow on the dynamics of heat conduction in particulate materials. In this paper, we present experimental as well as numerical results of transient heat conduction through a bed of cylinders.

This paper describes recent computer simulation studies into the rheological behavior of granular materials in the regime that lies between the quasistatic and rapid-flow regime. This investigation was prompted by studies of landslides, hopper flows and the “phase change” (i.e. the change between solidlike and fluid-like behavior) all of which indicated that the shear-to-normal stress ratio (the effective friction coefficient for the material) increased with shear rate. The results presented herein do demonstrate that the stress ratio varies with a dimensionless parameter created by scaling the shear rate with the stiffness of the interparticle contacts. In dense regimes, the stresses themselves scale with the stiffness indicating that they are generated by the elastic response of particle networks. Such speculation is supported by studies that show that the normal stresses are strongly dependent on the interparticle friction coefficient which affects the ability of internal elastic particle structures to support load and by the time variation of stress, which shows a spiky behavior as the structures form and break. However, analyses also indicate that these observations cannot explain the hopper, landslide and phase-change as these systems operate in regimes different from those in which the effect was observed. Finally, the effects of non-linear contacts are investigated and an appropriate scaling that takes the non-linearity into account is proposed.

Magnetic Resonance Imaging (MRI) technique was used to study the mixing and segregation processes of granular materials in a sophisticated tumbling blender (Turbula® mixer) using binary mixtures of sugar beads of different diameters d. Its motion generates mixtures with complex patterns. Effects of some parameters (beads diameter ratio, rotation speed, mixing time) were checked on segregation and mixing processes. We report in this paper, a qualitative and quantitative analysis of these phenomena. A segregation index S was defined to study the homogeneity and the kinetics of the mixing/segregation processes. When the ratio of bead diameters dmax/dmin is approximately 1, mixing process is observed but segregation occurs as soon as dmax/dmin is greater than 1.1.

Experiments were performed under accurately-controlled humidity conditions in order to quantify effects induced by humidity on granular materials. Measurements of the maximal stability angle of a pile made of small glass beads are reported as a function of the relative vapor pressure in the cell, up to close to saturation. The comparison of the results obtained with fluids differing in their molecular interactions with glass, namely water and heptane, shows that the wetting properties of the interstitial liquid on the grains have a strong influence on the cohesion of the non-saturated granular medium. This suggests that gravimetric experiments which could indirectly give information on the size of the capillary bridges that form between grains should be useful to understand the close connection that exists, through interparticle forces, between microscopic properties such as wetting properties and surface roughness of the grains, and global-scale properties of the pile, as its stability and flowability.

We present a numerical study of a surface instability occurring in a bidimensional vibrated granular layer. The driving mechanism for the formation of stationary waves is closely followed. Two regimes of wavelength selection are identified : a dispersive regime and a saturation regime. For the saturation regime, a connection is established between the pattern formation and an intrinsic instability occurring spontaneously in dissipative gases. We also address the importance of the detailed dissipation laws determining the wavelength values.

The vertical granular chain changes the elastic property of the medium due to gravity. Therefore, the solitary propagating mode in the horizontal chain disperses and damps in the vertical chain. We show that there are two different types of propagating modes, i.e., quasi-solitary and oscillatory, depending on the strength of impulse and the dispersion and damping of the signal follow power-laws. The power-law behavior in the linear oscillatory regime is explained analytically. The nonlinear solitary regime in which soliton damps and disperses due to gravity is discussed briefly.

The first measurements of the mean squared fluctuation velocity, or granular temperature, of monodispersed glass spheres in gas fluidized beds were recently obtained by two independent techniques: Power Spectral analysis of wall vibrational energy excited by random particle impact or Acoustic Shot Noise (ASN), and Diffusing Wave Spectroscopy (DWS) of reflected laser light multiply scattered by random particle motion. We explore the relevance of this data to the initial stability of the uniform fluidized state and to recent fundamental models for the magnitude, gas flow, and particle diameter dependence of the steady state granular temperature.

A nonequilibrium simulation scheme is introduced to investigate the transverse diffusive motion in unbounded shear flows of smooth, monodisperse, inelastic spherical particles. A certain labeling algorithm is used in this scheme to extract a one-way particle mass flux which results a concentration gradient for the labeled particles. The self-diffusion coefficient can then be obtained from Fick's law. Using this scheme, one may find that the self-diffusion phenomenon across any layer inside the granular shear flow is analogous to the classic diffusion problem across a membrane. Under steady conditions, the current simulation results revealed that the particle diffusivity can be described by a linear law. This finding justifies the assumption of a linear law relationship in the kinetic theory type derivation of an expression for self-diffusivity. Moreover, it is shown that the results of self-diffusion coefficient obtained from the computer simulations are in agreement with the predictions of kinetic theory formulations in the range of solid volume fractions less than 0.5.

We have identified, according to the ratio of the wavelength to the grain size, two distinct types of pulsed ultrasound transmission through a dry bead packing under stress: one corresponds to coherent ballistic waves characterized by the effective medium description, the other to the waves scattered by the inhomogeneous stress field within the granular medium. Over long distances of transport, the multiply scattered waves exhibit a diffusive character. Also we investigate the dynamics of the granular medium during a compaction under cyclic loading-unloading. Both the macroscopic deformation and the microscopic rearrangement have been measured, via an ultrasonic correlation technique using the multiple acoustic scattering very sensitive to the change of the system configuration. It is found that as the packing fraction increases, there is a continuous evolution of the system in response to external loading, from an irreversible behavior towards more elastic one.

Some years ago, Bouchaud et al. introduced a phenomenological model to describe surface flows of granular materials [J. Phys. Fr. I 4, 1383 (1994)]. According to this model, one can distinguish between a static phase and a rolling phase that are able to exchange grains through an erosion/accretion mechanism. Later, Boutreux et al. [Phys. Rev. E 58, 4692 (1998)] proposed a modification of the exchange term in order to describe thicker flows where saturation effects are present. However, these two approaches assumed that the downhill convection velocity of the grains is constant inside the rolling phase, a hypothesis that is not verified experimentally. We have recently modified the above models by introducing a velocity profile in the flow, and analyzed the physical consequences of this modification in the simple situation of an avalanche in an open cell. We here emphasize the physical predictions of our model, and show, in particular, that the thickness of the avalanche depends strongly on the velocity profile.

This is a survey of recent theoretical work on shear flow instabilities of dry granular media in the Bagnold or “grain-inertia” régime. Attention is devoted to steady homogeneous unbounded simple shear, with the goal of identifying material (constitutive) instabilities arising from the coupling of stress to granular concentration and temperature fields. Such instabilities, the dissipative analogs of thermodynamic phase transitions, are familiar in numerous branches of the mechanics of materials.

The current interest is motivated in part by the “dissipative clustering” found in various particle-dynamics (“DEM”) simulations of granular systems. Since particle clustering may invalidate standard gas kinetic theory, it is pertinent to ask whether hydrodynamic models based on such theories may themselves exhibit clustering instability.

The present article is based largely on a recent review (Goddard and Alam 1999), which provides a unified linear-stability treatment for rapid granular flow, as well for slow flow of mobile particles immersed in viscous liquids. The analysis is based on a “short-memory” response of various fluxes to perturbations on steady uniform states, a feature characteristic of the most popular constitutive models for granular flow. In the absence of gravity, previous theoretical analyses reveal transverse “layering” and spanwise “corrugations” as possible forms of material instability (Alam and Nott 1998)

Based on current theoretical findings, further work is recommended, including the exploration of the effects of gravity and of stress relaxation, both of which are likely to be important in real granular flows.

To predict the motion of powders and grains is important in pharmaceutical industries. Many pharmaceutical engineers have studied granular flows related to powder mixing. In this study, DEM (Discrete Element Method) approach is presented as an industrial application to investigate the behavior of granular flows. The granular motion in a rotating cylinder was focused on the basic study of DEM for industrial application. Rotating cylinder is a fundamental system for commercial blenders widely used in many industrial process. In addition, segregation of particles in a rotating cylinder is very interesting phenomena. Not only industrial engineers but also physicists research this segregation mechanism. DEM simulation showed radial segregation of two different size particles in a rotating cylinder. From the viewpoint of calculated granular temperature, radial segregation system was analyzed. Particle migration in axial direction, which is the source for axial segregation, was also shown by DEM simulation.