Dense Granular Systems Research Articles

(Ir)reversibility in dense granular systems driven by oscillating forces.

We use computer simulations to study highly dense systems of granular particles that are driven by oscillating forces. We implement different dissipation mechanisms that are used to extract the injected energy. In particular, the action of a simple local Stokes' drag is compared with non-linear and history-dependent frictional forces that act either between particle pairs or between particles and an external container wall. The Stokes' drag leads to particle motion that is periodic with the driving force, even at high densities around close packing where particles undergo frequent collisions. With the introduction of inter-particle frictional forces this "interacting absorbing state" is destroyed and particles start to diffuse around. By reducing the density of the material we go through another transition to a "non-interacting" absorbing state, where particles independently follow the force-induced oscillations without collisions. In the system with particle-wall frictional interactions this transition has signs of a discontinuous phase transition. It is accompanied by a diverging relaxation time, but not by a vanishing order parameter, which rather jumps to zero at the transition.

Transmission of kinematic information in dense granular systems: local and nonlocal network sensing

We study how kinematic information propagates in plane strain compression tests for two granular samples, one comprising glass beads and the other is sand. Of interest are the structures of directed networks constructed from static linear relationships among grain-scale kinematical measurements obtained using digital image correlation. The exact form and kinematical information used in each linear relationship is selected using a data modelling algorithm that appeals to the information theory description length philosophy encapsulated by the principle of Occam’s Razor. For both tests, we find that the observation sites with the most complicated relationships (i.e., those which require the x- and y-coordinates of the displacements of both neighboring and distant sites to best represent their own kinematics) are located in that region where the persistent shear band develops. The static linear relationships for these sites involve a length scale that is around 7–15 times the mean particle diameter, consistent with the observed thickness of the shear band in each sample. Our findings corroborate earlier evidence from the extant literature that the kinematics inside shear bands are necessarily nonlocal and further highlights the crucial importance of incorporating shear band kinematics in constitutive modelling. We shed new insights not only for constitutive modelling but also in the use of sensors to detect motion in deforming granular systems: that sensors with local sensing and monitoring capabilities are sufficient for distilling information on kinematic transmission—except in the shear band where nonlocal information, or information from spatially distant sensors, is a necessity.

Quorum Sensing and Nonlocal Hydrodynamics of Swimming Bacteria

Water fluidity is modified, in a non trivial manner, by the presence ofbacteria, above a threshold number density. At such threshold conditionssuspensions of swimming bacteria impose a coordinated water movementon a length scale of the order of (10 − 100)m with bacterial size of theorder of 3m. This observation leads to fundamental questions relating tothe mechanism of cell-cell communication among bacteria, presently knownas quorum sensing. Hydrodynamic model of ”swimming” bacteria or bac-terial colonies seems to be one of the most comprehensive alternate modelin defining possible quorum sensing mechanism. Here the densely packedbacteria may be viewed as a”bacterial fluid” or ”living fluid” similar to thatof dense granular systems. Lega and Passot initially assumed a two-phasehydrodynamic equations taken the bacteria and water as two interpene-trating and interacting continuum. However, by considering the relativelyhigh bacterial density, given the fact that no water motion is observed (un-der isothermal conditions and in the sense of displacement sheer viscosity,while rotational bulk viscosity may be present) in absence of the bacteria,we assume the dynamics of the suspended bacteria is governed by bacterialdynamics. Under these conditions bacteria and water appear to move asa single fluid at hydrodynamic scale. We propose that ”bacterial fluid”is consistently described by weakly non-local hydrodynamics where kine-matic viscosity is generated due to self- induced noise. This viscosity leadsto form a metastable state of the actively moving bacteria. This meta-stablestate is necessary for the simultaneous activation of the bacteria to supportquorum, given the existence of non-local nature of stresses mediated byautoinducers. The stability of noisy Burger equation for this metastablesituation will be also studied in this approach.

Dense granular dynamics analysis by a domain decomposition approach

In this article a domain decomposition approach is combined with the NonSmooth Contact Dynamics approach for analysing the global behaviour and the micromechanical structure of large-scale dense granular systems. Previously introduced and theoretically investigated, this method is herein investigated precisely on two aspects: the properties of the interface operators, especially when applied to the corners of the subdomains, and the influence of the substructuring on the solution of a mechanical test. Such topics are specific to the dense granular systems characterized by the discreteness and the nonsmoothness of their behavior.

Granular polymer composites

To advance our understanding of molecular packing in glassy nanocomposites, we adopt a macroscopic granular model—comprising spherical inclusions dispersed in ball-chain polymers—and ascertain from measurements of the bulk density the partial molar sphere volume at small but finite sphere volume fractions. By systematically varying the chain length, sphere size, and mixture composition, the ratio of the sphere radius to the chain loop size was found to be the primary dimensionless parameter that bridges solvent (small inclusion size) and continuum (large inclusion) scaling regimes. In the intermediate regime, where the inclusion and chain loop radius are comparable, the primary sphere–chain interaction increases free volume—up to twice the intrinsic inclusion volume per particle—and the primary sphere–sphere interaction decreases free volume. The results gleaned from these ‘granular nanocomposites’ may help to understand how geometrical constraints influence packing in dense granular systems and glassy molecular nanocomposites.

Complex networks in confined comminution

The physical process of confined comminution is investigated within the framework of complex networks. We first characterize the topology of the unweighted contact networks as generated by the confined comminution process. We find this process gives rise to an ultimate contact network which exhibits a scale-free degree distribution and small world properties. In particular, if viewed in the context of networks through which information travels along shortest paths, we find that the global average of the node vulnerability decreases as the comminution process continues, with individual node vulnerability correlating with grain size. A possible application to the design of synthetic networks (e.g., sensor networks) is highlighted. Next we turn our attention to the physics of the granular comminution process and examine force transmission with respect to the weighted contact networks, where each link is weighted by the inverse magnitude of the normal force acting at the associated contact. We find that the strong forces (i.e., force chains) are transmitted along pathways in the network which are mainly following shortest-path routing protocols, as typically found, for example, in communication systems. Motivated by our earlier studies of the building blocks for self-organization in dense granular systems, we also explore the properties of the minimal contact cycles. The distribution of the contact strain energy intensity of 4-cycle motifs in the ultimate state of the confined comminution process is shown to be consistent with a scale-free distribution with infinite variance, thereby suggesting that 4-cycle arrangements of grains are capable of storing vast amounts of energy in their contacts without breaking.

Granular pressure in a liquid‐fluidized bed as revealed by diffusing wave spectroscopy

AbstractThe granular pressure and granular temperature underpin various models of granular flows while they are playing an increasing role in modeling of other phenomena in granular systems such as heat transfer, segregation, erosion, attrition, and aggregation. The development and validation of these theories demand experimental determination of these two quantities. Diffusing wave spectroscopy (DWS) is now an accepted technique for measurement of granular temperature in dense granular systems. Using granular temperature data obtained from DWS with the kinetic theory of granular flow, we have derived the granular pressure data for a liquid‐fluidized bed. The determined variation of the mean bed granular pressure with mean bed solid volume fraction compares favorably with previously published experimental data and theoretical models of others. Where discrepancies do occur, they may be attributed to differences in particle inertia, suggesting further work on granular pressure models is required. Finally, we report the variation of the granular pressure with height above the distributor for several mean solids volume fractions. © 2011 American Institute of Chemical Engineers AIChE J, 2012

UNDERSTANDING FORCE CHAINS IN DENSE GRANULAR MATERIALS

When a load is applied to a dense granular material, the stress is largely transmitted by relatively rigid, heavily stressed chains of particles forming a sparse network of larger contact forces. Force chains act as the key determinant of mechanical properties such as stability, elasticity and flowability. To understand the structure and evolution of force chains, related physical processes and three corresponding characteristic time scales are analyzed in this study. We also propose three dimensionless numbers for the measurement of the relative importance of force chains. To solely study the effect of particle surface friction on force chains, uniaxial compression tests of 11,000 equal-sized particles in 2D were numerically simulated using the discrete element method. By proposing three conditions to define a force chain, the chain length distribution is found in the form of a power law. The exponent of 1.744 is independent of the surface friction. Although these results were obtained from partially crystallized jammed packings, they provide new insight into the physical processes and the structure of force chains, and thus will be helpful in the interpretation of force chains in other dense granular systems.

Structural stability and jamming of self-organized cluster conformations in dense granular materials

We examine emergent, self-organized particle cluster conformations in quasistatically deforming dense granular materials from the perspective of structural stability. A structural mechanics approach is employed, first, to devise a new stability measure for such conformations in equilibrium and, second, to use this measure to explore the evolving stability of jammed states of specific cluster conformations, i.e. particles forming force chains and minimal contact cycles. Knowledge gained on (a) the spatial and temporal evolution of stability of individual jammed conformations and (b) their relative stability levels, offer valuable clues on the rheology and, in particular, self-assembly of granular materials. This study is undertaken using data from assemblies of nonuniformly sized circular particles undergoing 2D deformation in two biaxial compression tests: a discrete element simulation of monotonic loading under constant confining pressure, and cyclic loading of a photoelastic disk assembly under constant volume. Our results suggest that the process of self-assembly in these systems is realized at multiple length scales, and that jammed force chains and minimal cycles form the basic building blocks of this process. In particular, 3-cycles are stabilizing agents that act as granular trusses to the load-bearing force chain columns. This co-evolutionary synergy between force chains and 3-cycles proved common to the different materials under different loading conditions. Indeed, the remarkable similarities in the evolution of stability, prevalence and persistence of minimal cycles and force chains in these systems suggest that these structures and their co-evolution together form a generic feature of dense granular systems under quasistatic loading.

Probing dense granular materials by space-time dependent perturbations

The manner in which signals propagate through dense granular systems in both space and time is not well understood. In order to probe this process, we carry out discrete element simulations of the system response to excitations where we control the driving frequency and wavelength independently. Fourier analysis shows that properties of the signal depend strongly on the space-time scales of the perturbation. The features of the response provide a test bed for models that predict statistical and continuum space-time properties. We illustrate this connection between microscale physics and macroscale behavior by comparing the system response to a simple elastic model with damping.

On Granular Stress Statistics: Compactivity, Angoricity, and Some Open Issues

We discuss the microstates of compressed granular matter in terms of two independent ensembles: one of volumes and another of boundary force moments. The former has been described in the literature and gives rise to the concept of compactivity: a scalar quantity that is the analogue of temperature in thermal systems. The latter ensemble gives rise to another analogue of the temperature: an angoricity tensor. We discuss averages under either of the ensembles and their relevance to experimental measurements. We also chart the transition from the microcanoncial to a canonical description for granular materials and show that one consequence of the traditional treatment is that the well-known exponential distribution of forces in granular systems subject to external forces is an immediate consequence of the canonical distribution, just as in the microcanonical description E = H leads to exp (-H/kT). We also put this conclusion in the context of observations of nonexponential forms of decay. We then present a Boltzmann-equation and Fokker-Planck approaches to the problem of diffusion in dense granular systems. Our approach allows us to derive, under simplifying assumptions, an explicit relation between the diffusion constant and the value of the hitherto elusive compactivity. We follow with a discussion of several unresolved issues. One of these issues is that the lack of ergodicity prevents convenient translation between time and ensemble averages, and the problem is illustrated in the context of diffusion. Another issue is that it is unclear how to make use in the statistical formalism the emerging ability to exactly predict stress fields for given structures of granular systems.

Coefficient of tangential restitution for the linear dashpot model

The linear dashpot model for the inelastic normal force between colliding spheres leads to a constant coefficient of normal restitution, epsilonn=const, which makes this model very popular for the investigation of dilute and moderately dense granular systems. For two frequently used models for the tangential interaction force we determine the coefficient of tangential restitution, epsilont, both analytically and by numerical integration of Newton's equation. Although epsilonn=const for the linear-dashpot model, we obtain pronounced and characteristic dependences of the tangential coefficient on the impact velocity, epsilont=epsilont(g). The results may be used for event-driven simulations of granular systems of frictional particles.

Signal propagation through dense granular systems

AbstractThe exact manner in which signals propagate through dense granular systems is still open for discussion. In this work, we present the results of discrete element simulations of the system response to space and time dependent perturbations. Fourier analysis of the system response shows that the properties of the propagating signal strongly depend on the spatial scales introduced by the perturbation itself. The presented results are expected to serve as a basis for development of a continuum model that will describe propagation of signals through dense granular systems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Computation of Screening Phenonema in a Vertical Tumbling Cylinder

AbstractGranular materials are an integral part of our environment. Due to their wide variety of applications in industrial and technological processes, they have captured a great interest in the recent research, see [1] and [2]. The related studies are often based on numerical simulations and it is considered as challenging to investigate computational phenomena of dense granular systems. Particle screening is an essential technology in many industrial fields and important in granular studies. The particular problem of interest is the separation of round shape particles of different geometrical sizes using a rotating tumbling vertical cylinder. The concept of discrete element method (DEM) that considers the motion of each single particle individually is applied in this study. Particle‐to‐particle and particle‐to‐wall collisions will appear under the tumbling motion of the rotating structure. The normal and frictional forces between particles themselves and particles and surrounding walls of the structure are calculated according to the rules of a penalty method, which employs spring‐damper models for this purpose. As a result of collisions, the particles will dissipate kinetic energy due to the normal and frictional contact losses. Particle distribution and sifting rate of the separated particles have been studied taking into consideration different rotational speeds of the machine, various damping and frictional coefficients and different sizes of holes in the sifting plates at different levels of the structure. In an attempt to better understand the mechanism of the particle transport between the different layers of the sifting system, different computational studies have been performed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Extension of PIV for measuring granular temperature field in dense fluidized beds

AbstractIn this work a particle image velocimetry (PIV) technique has been extended to enable the simultaneous measurement of the instantaneous velocity and granular temperature fields. The PIV algorithm has been specifically optimized for dense granular systems and has been thoroughly tested with artificially generated images. The new PIV technique has been successfully applied to a fluidized bed at incipient fluidization conditions in which a single bubble is injected by a jet and to a freely bubbling fluidized bed. The instantaneous spatial distribution of the solids‐phase velocity and granular temperature that can be measured with this new technique can be used to validate CFD models for dense granular systems, such as multifluid continuum models using the KTGF (kinetic theory of granular flow) to describe the internal momentum transport in the particulate phase. © 2006 American Institute of Chemical Engineers AIChE J, 2007

Review and extension of normal force models for the Discrete Element Method

For the simulation of dense granular systems the Discrete Element Method based on a soft-sphere approach is commonly used. In such simulations collisions between particles take a finite time. The equations of motion are applied for each particle and solved numerically. Therefore models for the forces acting between particles in contact need to be specified. In this paper the focus is set on normal contacts. Based on macroscopic and microscopic accessible parameters like coefficient of restitution, collision time, force, displacement and displacement rate a wide range of commonly used force schemes are reviewed. Results obtained from these commonly used models are compared to experimental data on collisions of different metal alloys, ice and marble as reported in literature. Due to obvious limitations extensions are presented. The new extended models based on linear and non-linear models are compared to experimental data and their accuracy and applicability are discussed.

Fine structures in sheared granular flows.

Computer simulations were used to investigate shear flows of large numbers of viscoelastic, monosized, spherical particles in unbounded and bounded systems with solid fractions ranging from 0.16 to 0.59. A modified hard-sphere model with inelastic, instantaneous particle interactions was found to replicate some results predicted by kinetic theory in an unbounded shear flow at low and moderate solids fractions. This model was found to predict features such as particle lateral diffusive motion even for systems at solid fractions as high as 0.56. However, for higher solid fractions where phenomena such as jamming could occur, a particle dynamics model accounting for particle contacts of finite duration has been developed, in which the viscoelastic behavior of the particles was represented using a nonlinear Hertzian model. The nonlinear viscoelastic model was found to give more reasonable predictions for cluster formation than previously reported linear models, especially when accounting for surface friction in the model. However, neither frictionless nor frictional particle models could predict particle ordering in unbounded flows. As such, simulations were performed for bounded systems using both the modified hard-sphere model and the nonlinear particle dynamic model. For a bounded shear flow, particle ordering could be predicted by the hard-sphere model even in the absence of both particle friction and gravity, with the local solid fraction and wall separation distance governing the flow stability. For these conditions chain formation was found to be quite likely in the disordered layers for frictional particles. The interesting stick-slip dynamics could be clearly observed in the normal stress signal at the bottom wall. Interpretations were proposed for the complex processes observed, which could lay the foundation for further investigations in sheared dense granular systems.

Stress relaxation in dense and slow granular flows

In a dense granular system, particles interact in networks containing many particles and interaction times are long compared with the particle binary collision time. In these systems, the streaming part of the granular stress is negligible. We only consider the collisional stress in this paper. The average behavior of particle contacts is studied. By following the statistical method developed recently by the authors [Zhang and Rauenzahn, J. Rheol. 41, 1275 (1997)], we derive an evolution equation for the collisional stress. This equation provides guidance to collateral numerical simulations, which show that the probability distribution of particle contact times is exponential for long contact times. This can be explained by network interactions in a dense granular system. In general, the relaxation of the collisional stress is a combined effect of the decay of the contact time probability and the relaxation of collisional forces among particles. In the numerical simulations, the normal force between a pair of particles is modeled as parallel connect of a spring and a dashpot. In this case, the relaxation of the force magnitude conditionally averaged given a specific contact time is negligible, and the major contribution to the stress relaxation is from the exponential decay of the contact time probability. We also note that the probability decay rate is proportional to the imposed strain rate. Consequently, in a simple shear flow with a constant particle volume fraction, as the shear rate approaches zero, the shear stress approaches a finite value. This value is the yield stress for that particle volume fraction. Hence, the evolution equation of the collisional stress predicts viscoplasticity of dense granular systems.

Three-Dimensional Apollonian Packing as a Model for Dense Granular Systems.

An iterative procedure according to which new spheres are inserted between existing ones is realized for computer simulation of dense granular systems. The method is based on the rigorous geometrical Voronoi-Delaunay approach generalized for pore volume analysis inside an ensemble of polydisperse hard spheres [N. N. Medvedev, Dokl. Akad. Nauk 337, 767 (1994)] [Dokl. Phys. Chem. 337, 157 (1994)]]. Models with packing fraction $\ensuremath{\eta}\ensuremath{\sim}0.9$ are constructed. The particle size distribution and fractal nature of the packings are investigated. The fractal dimension $D=2.45$ is obtained.