Towards a theoretical picture of dense granular flows down inclines

Quantitative Understanding of the Onset of Dense Granular Flows

The question of when and how dense granular materials start to flow under stress, despite many industrial and geophysical applications, remains largely unresolved. We develop and test a simple equation for the onset of quasistatic flows of granular materials which is based on the frictional aging of the granular packing. The result is a nonmonotonic stress-strain relation which-akin to classical friction-is independent of the shear rate. This relation suffices to understand the quasistatic deformations of aging granular media, and its solid-to-liquid transition. Our results also elucidate the (flow) history dependence of the mechanical properties, and the sensitivity to the initial preparation of granular media.

The Study of Three-Dimensional Granular Stream Flowing through the Test Hopper-Shaped Target

The experiments are carried out in a three-dimensional channel with a screw conveyor, which plays the role of granular drives for the granular flow system and determines the injection of granular in the test target section. The jam-to-dense transition of granular flow is studied with the different inclination angle. The results show that, with a fixed diameter of hopper orifice and initial filling position, there is a change from jam to dense when the inclination angle larger than 22°. Variation of the flow rate with elevated frequency of the screw conveyor is further studied. The flow pattern is changed from dilute to dense with increasing rotation frequency of the screw rod. When the rotation frequency is larger than 5 Hz, the flow is dense. The dynamic balance of the interface between dilute to dense granular is observed in the main target section. We further research the dynamic interface by measuring the highest and lowest location with time and also simulate the gravity flow rate and screw conveyor flow rate with EDEM. From the results, we find that the interface between dilute flow and dense flow is influenced by the combined action of crew conveyor flow and dense gravity flow.

Force fluctuations at the transition from quasi-static to inertial granular flow

We analyse the rheology of gravity-driven, dry granular flows in experiments where individual forces within the flow bulk are measured. We release photoelastic discs at the top of an incline to create a quasi-static erodible bed over which flows a steady 2D avalanche. The flowing layers we produce are dense (φ ≈ 0.8), thin (h ≈ 10d), and in the slow to intermediate flow regime (I = 0.1 to 1). Using particle tracking and photoelastic force measurements we report coarse-grained profiles for packing fraction, velocity, shear rate, inertial number, and stress tensor components. In addition, we define a quantitative measure for the rate of generation of new force chain networks and we observe that fluctuations extend below the boundary between dense flow and quasi-static layers. Finally, we evaluate several existing definitions for granular fluidity, and make comparisons among them and the behaviour of our experimentally-measured stress tensor components. Our measurements of the non-dimensional stress ratio μ show that our experiments lie within the local rheological regime, yet we observe rearrangements of the force network extending into the quasi-static layer where shear rates vanish. This elucidates why non-local rheological models rely on the notion of stress diffusion, and we thus propose non-local effects may in fact be dependent on the local force network fluctuation rate.

Inclined granular flow in a narrow chute

In this paper we presents a detailed description of granular flow down a flat, narrow chute using discrete element method simulations, with emphasis on the influence of sidewalls on the flow. The overall phase diagram is provided and it is found that there are four flow regimes (no flow, bulk flow, surface flow, and gas flow). The H̃_stop curve is very complicated and quite different from that in the case without sidewalls. The effective friction coefficient [Formula: see text] increases with pile height H̃ and a surface flow occurs when the inclination angle [Formula: see text] exceeds a critical value. The profile of [Formula: see text] shows that the [Formula: see text] rheology is valid in boundary layers. Furthermore, [Formula: see text] increases with the velocity of particles and there is a saturation to a nonzero value in static heap. For small H̃, the static heap vanishes and there is a bulk flow. A similarity between basal particles and sidewall particles indicates a universal role of the boundaries. In this bulk flow, there is a transition of the velocity profile with wall friction [Formula: see text]. When [Formula: see text] is large, the velocity is linear and decreases with increasing height. With small [Formula: see text], the velocity is nonlinear and the flow rate is roughly proportional to H̃^3/2.

Dynamic X-ray radiography reveals particle size and shape orientation fields during granular flow

When granular materials flow, the constituent particles segregate by size and align by shape. The impacts of these changes in fabric on the flow itself are not well understood, and thus novel non-invasive means are needed to observe the interior of the material. Here, we propose a new experimental technique using dynamic X-ray radiography to make such measurements possible. The technique is based on Fourier transformation to extract spatiotemporal fields of internal particle size and shape orientation distributions during flow, in addition to complementary measurements of velocity fields through image correlation. We show X-ray radiography captures the bulk flow properties, in contrast to optical methods which typically measure flow within boundary layers, as these are adjacent to any walls. Our results reveal the rich dynamic alignment of particles with respect to streamlines in the bulk during silo discharge, the understanding of which is critical to preventing destructive instabilities and undesirable clogging. The ideas developed in this paper are directly applicable to many other open questions in granular and soft matter systems, such as the evolution of size and shape distributions in foams and biological materials.

Micromechanical Origin of Particle Size Segregation

We computationally study the micromechanics of shear-induced size segregation and propose distinct migration mechanisms for individual large and small particles. While small particles percolate through voids without enduring contacts, large particles climb under shear through their crowded neighborhoods with anisotropic contact network. Particle rotation associated with shear is necessary for the upward migration of large particles. Segregation of large particles can be suppressed with inadequate friction, or with no rotation; increasing interparticle friction promotes the migration of large particles, but has little effect on the percolation of small particles.

Unified rheology of vibro-fluidized dry granular media: From slow dense flows to fast gas-like regimes

Granular media take on great importance in industry and geophysics, posing a severe challenge to materials science. Their response properties elude known soft rheological models, even when the yield-stress discontinuity is blurred by vibro-fluidization. Here we propose a broad rheological scenario where average stress sums up a frictional contribution, generalizing conventional μ(I)-rheology, and a kinetic collisional term dominating at fast fluidization. Our conjecture fairly describes a wide series of experiments in a vibrofluidized vane setup, whose phenomenology includes velocity weakening, shear thinning, a discontinuous thinning transition, and gaseous shear thickening. The employed setup gives access to dynamic fluctuations, which exhibit a broad range of timescales. In the slow dense regime the frequency of cage-opening increases with stress and enhances, with respect to μ(I)-rheology, the decrease of viscosity. Diffusivity is exponential in the shear stress in both thinning and thickening regimes, with a huge growth near the transition.

Characterization of base roughness for granular chute flows

Base roughness plays an important role in the dynamics of granular flows but is still poorly understood due to the difficulty of its quantification. For a bumpy base made of spheres, at least two factors should be considered in order to characterize its geometric roughness, namely, the size ratio of flow to base particles and the packing arrangement of base particles. In this paper, we propose an alternative definition of base roughness, R_{a}, as a function of both the size ratio and the distribution of base particles. This definition is generalized for random and regular packings of multilayered spheres. The range of possible values of R_{a} is presented, and optimal arrangements for maximizing base roughness are studied. Our definition is applied to granular chute flows in both two- and three-dimensional configurations, and is shown to successfully predict whether slip occurs at the base. A transition is observed from slip to nonslip conditions as R_{a} increases. Critical values of R_{a} are identified for the construction of a nonslip base at various angles of inclination.

Dissipation of Energy by Dry Granular Matter in a Rotating Cylinder

We study experimentally the dissipation of energy in a rotating cylinder which is partially filled by granular material. We consider the range of angular velocity corresponding to continous and stationary flow of the granulate. In this regime, the stationary state depends on the angular velocity and on the filling mass. For a wide interval of filling levels we find a universal behavior of the driving torque required to sustain the stationary state as a function of the angular velocity. The result may be of relevance to industrial applications, e.g. to understand the power consumption of ball mills or rotary kilns and also for damping applications where mechanical energy has to be dissipated in a controlled way.

Granular flows on a dissipative base

We study inclined channel flows of sand over a sensor-enabled composite geotextile fabric base that dissipates granular fluctuation energy. We record strain of the fabric along the flow direction with imbedded fiber-optic Bragg gratings, flow velocity on the surface by correlating grain position in successive images, flow thickness with the streamwise shift of an oblique laser light sheet, velocity depth profile through a transparent side wall using a high-speed camera, and overall discharge rate. These independent measurements at inclinations between 33∘ and 37∘ above the angle of repose at 32.1±0.8∘ are consistent with a mass flow rate scaling as the 3/2 power of the flow depth, which is markedly different than flows on a rigid bumpy boundary. However, this power changes to 5/2 when flows are forced on the sand bed below its angle of repose. Strain measurements imply that the mean solid volume fraction in the flowing layer above the angle of repose is 0.268±0.033, independent of discharge rate or inclination.

Arrest stress of uniformly sheared wet granular matter

We conduct extensive independent numerical experiments considering frictionless disks without internal degrees of freedom (rotation, etc.) in two dimensions. We report here that for a large range of the packing fractions below random-close packing, all components of the stress tensor of wet granular materials remain finite in the limit of zero shear rate. This is direct evidence for a fluid-to-solid arrest transition. The offset value of the shear stress characterizes plastic deformation of the arrested state which corresponds to dynamic yield stress of the system. Based on an analytical line of argument, we propose that the mean number of capillary bridges per particle, ν, follows a nontrivial dependence on the packing fraction, ϕ, and the capillary energy, ɛ. Most noticeably, we show that ν is a generic and universal quantity which does not depend on the driving protocol. Using this universal quantity, we calculate the arrest stress, σ(a), analytically based on a balance of the energy injection rate due to the external force driving the flow and the dissipation rate accounting for the rupture of capillary bridges. The resulting prediction of σ(a) is a nonlinear function of the packing fraction, ϕ, and the capillary energy, ɛ. This formula provides an excellent, parameter-free prediction of the numerical data. Corrections to the theory for small and large packing fractions are connected to the emergence of shear bands and of contributions to the stress from repulsive particle interactions, respectively.

On granular elasticity

Mesoscopic structures form in dense granular materials due to the self-organisation of the constituent particles. These structures have internal structural degrees of freedom in addition to the translational degree of freedom. The resultant granular elasticity, which exhibits intrinsic variations and inevitable relaxation, is a key quantity that accounts for macroscopic solid- or fluid-like properties and the transitions between them. In this work, we propose a potential energy landscape (PEL) with local stable basins and low elastic energy barriers to analyse the nature of granular elasticity. A function for the elastic energy density is proposed for stable states and is further calibrated with ultrasonic measurements. Fluctuations in the elastic energy due to the evolution of internal structures are proposed to describe a so-called configuration temperature T(c) as a counterpart of the classical kinetic granular temperature T(k) that is attributed to the translational degrees of freedom. The two granular temperatures are chosen as the state variables, and a fundamental equation is established to develop non-equilibrium thermodynamics for granular materials. Due to the relatively low elastic energy barrier in the PEL, granular elasticity relaxes more under common mechanical loadings, and a simple model based on mean-field theory is developed to account for this behaviour.

Nonlocal effects in sand flows on an inclined plane

The flow of sand on a rough inclined plane is investigated experimentally. We directly show that a jammed layer of grains spontaneously forms below the avalanche. Its properties and its relation with the rheology of the flowing layer of grains are presented and discussed. In a second part, we study the dynamics of erosion and deposition solitary waves in the domain where they are transversally stable. We characterize their shapes and velocity profiles. We relate their translational velocity to the stopping height and to the mass trapped in the avalanche. Finally, we use the velocity profile to get insight into the rheology very close to the jamming limit.

Phase transition and flow-rate behavior of merging granular flows

Merging of granular flows is ubiquitous in industrial, mining, and geological processes. However, its behavior remains poorly understood. This paper studies the phase transition and flow-rate behavior of two granular flows merging into one channel. When the main channel is wider than the side channel, the system shows a remarkable two-sudden-drops phenomenon in the outflow rate when gradually increasing the main inflow. When gradually decreasing the main inflow, the system shows obvious hysteresis phenomenon. We study the flow-rate-drop phenomenon by measuring the area fraction and the mean velocity at the merging point. The phase diagram of the system is also presented to understand the occurrence of the phenomenon. We find that the dilute-to-dense transition occurs when the area fraction of particles at the joint point exceeds a critical value ϕ(c)=0.65±0.03.

Characterizing the rheology of fluidized granular matter

In this study we characterize the rheology of fluidized granular matter subject to secondary forcing. Our approach consists of first fluidizing granular matter in a drum half filled with grains via simple rotation and then superimposing oscillatory shear perpendicular to the downhill flow direction. The response of the system is mostly linear, with a phase lag between the grain motion and the oscillatory forcing. The rheology of the system can be well characterized by the GDR MiDi model if the system is forced with slow oscillations. The model breaks down when the forcing time scale becomes comparable to the characteristic time for energy dissipation in the flow.

Shallow granular flows down flat frictional channels: steady flows and longitudinal vortices

Granular flows down inclined channels with smooth boundaries are common in nature and industry. Nevertheless, flat boundaries have been much less investigated than bumpy ones, which are used by most experimental and numerical studies to avoid sliding effects. Using numerical simulations of each grain and of the side walls we recover quantitatively experimental results. At larger angles we predict a rich behavior, including granular convection and inverted density profiles suggesting a Rayleigh-Bénard type of instability. In many aspects flows on a flat base can be seen as flows over an effective bumpy base made of the basal rolling layer, giving Bagnold-type profiles in the overburden. We have tested a simple viscoplastic rheological model [Nature (London) 441, 727 (2006)] in average form. The transition between the unidirectional and the convective flows is then clearly apparent as a discontinuity in the constitutive relation.

Transition dynamics and magic-number-like behavior of frictional granular clusters

Force chains, the primary load-bearing structures in dense granular materials, rearrange in response to applied stresses and strains. These self-organized grain columns rely on contacts from weakly stressed grains for lateral support to maintain and find new stable states. However, the dynamics associated with the regulation of the topology of contacts and strong versus weak forces through such contacts remains unclear. This study of local self-organization of frictional particles in a deforming dense granular material exploits a transition matrix to quantify preferred conformations and the most likely conformational transitions. It reveals that favored cluster conformations reside in distinct stability states, reminiscent of "magic numbers" for molecular clusters. To support axial loads, force chains typically reside in more stable states of the stability landscape, preferring stabilizing trusslike, three-cycle contact triangular topologies with neighboring grains. The most likely conformational transitions during force chain failure by buckling correspond to rearrangements among, or loss of, contacts which break the three-cycle topology.

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.

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.

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.

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.

Rheology of confined granular flows: scale invariance, glass transition, and friction weakening

We study fully developed, steady granular flows confined between parallel flat frictional sidewalls using numerical simulations and experiments. Above a critical rate, sidewall friction stabilizes the underlying heap at an inclination larger than the angle of repose. The shear rate is constant and independent of inclination over much of the flowing layer. In the direction normal to the free surface, the solid volume fraction increases on a scale equal to half the flowing layer depth. Beneath a critical depth at which internal friction is invariant, grains exhibit creeping and intermittent cage motion similar to that in glasses, causing gradual weakening of friction at the walls.

Nonlocal rheological properties of granular flows near a jamming limit

We study the rheology of sheared granular flows close to a jamming transition. We use the approach of partially fluidized theory (PFT) with a full set of equations extending the thin layer approximation derived previously for the description of the granular avalanches phenomenology. This theory provides a picture compatible with a local rheology at large shear rates [G. D. R. Midi, Eur. Phys. J. E 14, 341 (2004)] and it works in the vicinity of the jamming transition, where a description in terms of a simple local rheology comes short. We investigate two situations displaying important deviations from local rheology. The first one is based on a set of numerical simulations of sheared soft two-dimensional circular grains. The next case describes previous experimental results obtained on avalanches of sandy material flowing down an incline. Both cases display, close to jamming, significant deviations from the now standard Pouliquen's flow rule [O. Pouliquen, Phys. Fluids 11, 542 (1999); 11, 1956 (1999)]. This discrepancy is the hallmark of a strongly nonlocal rheology and in both cases, we relate the empirical results and the outcomes of PFT. The numerical simulations show a characteristic constitutive structure for the fluid part of the stress involving the confining pressure and the material stiffness that appear in the form of an additional dimensionless parameter. This constitutive relation is then used to describe the case of sandy flows. We show a quantitative agreement as far as the effective flow rules are concerned. A fundamental feature is identified in PFT as the existence of a jammed layer developing in the vicinity of the flow arrest that corroborates the experimental findings. Finally, we study the case of solitary erosive granular avalanches and relate the outcome with the PFT analysis.

Relationship between interparticle contact lifetimes and rheology in gravity-driven granular flows

The validity of the Bagnold constitutive relation in gravity-driven granular flow down an inclined plane is studied by discrete element (DEM) simulations. In the limit of infinitely hard particles, the Bagnold relation is known to hold exactly. We determine deviations from this relation as a function of all parameters governing interparticle interactions. These include elastic compliance, inelastic dissipation, friction coefficient, and interparticle cohesion. We find significant deviations from Bagnold rheology in some regions of this parameter space and propose a generalized Bagnold relation to account for this effect. Moreover, we note a significant correlation between the breakdown of Bagnold rheology in the bulk and the appearance of a long-time tail in the two-particle contact time distributions.