Granular Packing Research Articles

Reduction of the bulk modulus with polydispersity in noncohesive granular solids.

We study the effect of grain polydispersity on the bulk modulus in noncohesive two-dimensional granular solids. Molecular dynamics simulations in two dimensions are used to describe polydisperse samples that reach a stationary limit after a number of hysteresis cycles. For stationary samples, we obtain that the packing with the highest polydispersity has the lowest bulk modulus. We compute the correlation between normal and tangential forces with grain size using the concept of branch vector or contact length. Classifying the contact lengths and forces by their size compared to the average length and average force, respectively, we find that strong normal and tangential forces are carried by large contact lengths, generally composed of at least one large grain. This behavior is more dominant as polydispersity increases, making force networks more anisotropic and removing the support, from small grains, in the loading direction thus reducing the bulk modulus of the granular pack. Our results for two dimensions describe qualitatively the results of three-dimensional experiments.

Structural and topological nature of plasticity in sheared granular materials

Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for microscopic plasticity in disordered granular packings. The elementary plastic events occur through flip events which correspond to a neighbor switching process among these coplanar tetrahedra (or equivalently as the rotation motion of 4-ring disclinations). These events are discrete in space and possess specific orientations with the principal stress direction.

Buckling of a rod penetrating into granular media.

We investigate experimentally the possible buckling of a thin rod when penetrating downwards into a granular packing. When its bottom end reaches a specific depth, the rod may start buckling provided that the embrace is not enough to stop that phenomenon. The critical rod depth z_{c} at buckling is observed to scale with the rod length L either as 1/L or 1/L^{2}. These two scalings are shown to arise from the two resistant force terms that come into play during the rod penetration: a pressure force at the bottom of the rod that increases linearly with depth and a frictional force on the rod side that increases quadratically with depth. At the buckling point, the destabilizing force corresponds to the expected value given from conventional Euler's critical load for a rod bottom end considered as fixed in the granular clutch. Finally, we draw a buckling-nonbuckling phase diagram in a parameter space given by the rod aspect ratio and a rod-to-grain stress ratio.

Translational and Rotational Dynamical Heterogeneities in Granular Systems

We use x-ray tomography to investigate the translational and rotational dynamical heterogeneities of athree dimensional hard ellipsoid granular packing driven by oscillatory shear. We find that particles which translate quickly form clusters with a size distribution given by a power law with an exponent that is independent of the strain amplitude. Identical behavior is found for particles that are translating slowly, rotating quickly, or rotating slowly. The geometrical properties of these four different types of clusters are the same as those of random clusters. Different cluster types are considerably correlated or anticorrelated, indicating a significant coupling between translational and rotational degrees of freedom. Surprisingly, these clusters are formed already at time scales that are much shorter than the α-relaxation time, in stark contrast to the behavior found in glass-forming systems.

Particle filtration characteristics of typical packing granular filters used in hot gas clean-up

Granular filter is a promising method in hot gas clean-up for advanced coal gasification technologies. Numerical simulations were performed in this paper for the particle filtration characteristics of granular filters with two typical packings: body centered cubic (BCC) and face centered cubic (FCC) packings. Fluid flow characteristics were investigated and pressure drop correlations for the two granular packings were obtained. The pressure drop of both packings increases linearly with the increase of velocity, and the pressure drop of the FCC packing is significantly higher than that of BCC. The discrete phase model (DPM) was employed to trace fly ash particle motion during the filtration process, and particle deposition characteristics on the granular surface, including the particle penetration, deposition distribution of different particle sizes, and deposition distribution along filter layers were determined. The deposition fraction of particles on each layer of granules decreases with the increase of row number, and the maximum deposition location is different for BCC and FCC packings. Large particles mainly deposit on the first four layers of granules, while small particles deposit over all layers. The collection efficiency of BCC and FCC packings increases with the increase of velocity, and they decrease first and then increase with particle diameter. Correlations of collection efficiency for the two granular packings are presented and they have good prediction accuracy.

Interaction Model for “Shelled Particles” and Small-Strain Modulus of Granular Materials

The elastic modulus of a granular assembly composed of spherical particles in Hertzian contact usually has a scaling law with the mean effective pressure p as K∼G∼p1/3. Laboratory test results, however, reveal that the value of the exponent is generally around 1/2 for most sands and gravels, but it is much higher for reclaimed asphalt concrete composed of particles coated by a thin layer of asphalt binder and even approaching unity for aggregates consisting of crushed stone. By assuming that a particle is coated with a thin soft deteriorated layer, an energy-based simple approach is proposed for thin-coating contact problems. Based on the features of the surface layer, the normal contact stiffness between two spheres varies with the contact force following kn∼Fnm and m∈[1/3, 1], with m=1/3 for Hertzian contact, m=1/2 soft thin-coating contact, m=2/3 for incompressible soft thin-coating, and m=1 for spheres with rough surfaces. Correspondingly, the elastic modulus of a random granular packing is proportional to pm with m∈[1/3, 1].

Grating-box test: A testing method for filling performance evaluation of self-compacting mortar in granular packs

Grating-box test is proposed and applied to evaluate the resisting ability of granular packs to the filling movement of self-compacting cementing materials. Firstly, parameter “h2” (“h2N”), reflecting the filling performance of SCM, is obtained from theoretical analysis of self-compacting-mortar’s filling performance in quasi-three-dimensional (quasi-3D) granular packs. Second, experimental results of grating-box test with quasi-3D molds using cylindrical obstacles are found in good agreement with the theoretical analysis above. Third, damping coefficient “η”, an indicator being positive correlated with the resisting ability of granular packs to filling movement of SCM, is found to represent the inherent properties of granular packs.

Collapse and runout of granular columns in pendular state

It is well known that even small amounts of liquid can strongly modify the mechanical behavior of granular packings in static and dynamic conditions. This experimental work, therefore, focuses on the collapse of columns of wet granular materials in the pendular wetting regime. Different from previous studies, where idealized spherical materials (glass beads) are typically used, here experiments on irregular wet calcium carbonate particles (coarse sand) were carried out and compared with glass sphere results. Particles of different sizes (in the range 0.8-5 mm) were mixed with water from 0% to 4% w/w and poured in a rectangular box. Flow was then triggered by removing a lateral wall of the box. The measured runout distances showed marked differences between the two types of materials which could not be explained only in terms of particle shape or capillary forces. Ring shear tests and 3D tomographic reconstructions of the liquid distribution in the materials highlighted the role of additional mechanisms related to liquid spreading at the particle surface, inter-particle friction, and contact lubrication.

A granular Discrete Element Method for arbitrary convex particle shapes: Method and packing generation

A novel granular discrete element method (DEM) is introduced to simulate mixtures of particles of any convex shape. To quickly identify pairs of particles in contact, the method first uses a broad-phase and a narrow-phase contact detection strategy. After this, a contact resolution phase finds the contact normal and penetration depth. A new algorithm is introduced to effectively locate the contact point in the geometric center of flat faces in partial contact. This is important for a correct evaluation of the torque on each particle, leading to a much higher stability of stacks of particles than with previous algorithms. The granular DEM is used to generate random packings in a cylindrical vessel. The simulated shapes include non-spherical particles with different aspect ratio cuboids, cylinders and ellipsoids. More complex polyhedral shapes representing sand and woodchip particles are also used. The latter particles all have a unique shape and size, resembling real granular particle packings. All packings are analyzed extensively by investigating positional and orientational ordering.

Effect of the particle size ratio on the structural properties of granular mixtures with discrete particle size distribution

In this study, the discrete element method was used to examine the structural properties and geometric anisotropy of polydisperse granular packings with discrete uniform particle size distributions. Confined uniaxial compression was applied to granular mixtures with different particle size fractions. The particle size fraction (class) was defined as the fraction of the sample composed of particles with a certain size. The threshold value of number of particle size fractions (i.e., the value above which structural properties of assemblies remain constant) was determined. The effect of heterogeneity in particle size on the critical value of number of particle size fractions was investigated for packings with different ratios between diameters of the largest and smallest grains. The threshold number of particle size classes decreased from five to three as the diameter ratio between the largest and smallest grains increased. Regardless of the diameter ratio, the critical number of particle size fractions (above which the packing density and coordination number of the granular mixtures remained constant) was determined to be five. The study has also shown an increase in packing density of binary mixtures with particle size ratio increasing up to 2.5, which was followed by decrease in density of mixtures with larger particle size ratios, which has not so far been reported in the literature.

Force-chain evolution in a two-dimensional granular packing compacted by vertical tappings.

We experimentally study the statistics of force-chain evolution in a vertically-tapped two-dimensional granular packing by using photoelastic disks. In this experiment, the tapped granular packing is gradually compacted. During the compaction, the isotropy of grain configurations is quantified by measuring the deviator anisotropy derived from fabric tensor, and then the evolution of force-chain structure is quantified by measuring the interparticle forces and force-chain orientational order parameter. As packing fraction increases, the interparticle force increases and finally saturates to an asymptotic value. Moreover, the grain configurations and force-chain structures become isotropically random as the tapping-induced compaction proceeds. In contrast, the total length of force chains remains unchanged. From the correlations of those parameters, we find two relations: (i) a positive correlation between the isotropy of grain configurations and the disordering of force-chain orientations, and (ii) a negative correlation between the increasing of interparticle forces and the disordering of force-chain orientations. These relations are universally held regardless of the mode of particle motions with or without convection.

A microscale analytical study on the strength of two-dimensional frictional granular materials

We introduce an analytical study of the links between macroscopic strength and the grain-to-grain interactions in two-dimensional frictional granular packings. This study consists of two main parts that are developed and connected progressively. First, we obtain explicit expressions that enable us to relate microscale parameters such as contact forces and fabric to macroscopic stress and strength. Second, physical connections and interpretations between the aforementioned micro-parameters, micro-mechanisms, fabric anisotropy and macroscopic strength are derived. Furthermore, throughout this theoretical study, some fundamental physics related to a packing’s strength as well as contact buckling is extracted, providing a better understanding of the micro-mechanics that furnishes and builds up the macroscopic strength of this kind of materials.

ДОСЛІДЖЕННЯ ТЕПЛООБМІНУ МІЖ НАСКРІЗНИМ ПОТОКОМ ГАЗУ ТА ЩІЛЬНИМ ШАРОМ ГРАНУЛЬОВАНОГО МАТЕРІАЛУ

On the basis experimental studies, the specific features of the heat exchange process between the granular packing and the through flow of the gaseous (air) medium are determined. Experimental studies of heat exchange between a dense layer of granular material and a stream of heated air have been carried out. The conditions for increasing the efficiency of the heat recovery unit are established. The course of the temperature curve for the gas flow and solid components at the inlet and outlet of the installation indicates the presence of two clearly pronounced regions with different heating rates. It is assumed that it is expedient to set the heating time in the heat accumulator with a stationary nozzle within the first period, which is characterized by a high rate of heating. It is found that the heat exchange rate increases with a mixture of particles of different sizes. It is established that the coefficients of intercomponent heat transfer during heating of the fixed nozzle depend on the gas velocity, the velocity of the ball, the temperature of the gas at the inlet to the apparatus, the duration of the process, and are described by a function of the sigmoid class

Generation and filtration of O/W emulsions under near-wellbore flow conditions during produced water re-injection

Produced water in the oilfield contains oil droplets in the form of oil-in-water (O/W) emulsions. These oil droplets cannot be completely separated from the water by surface facilities, and produced water still containing suspended emulsions is re-injected into formations. These oil droplets plug the pore space in the near-wellbore or near-fracture region, resulting in rapid declines in the performance of water injection wells where the remediation processes can be expensive. Displaced oil droplets also contribute to the plugging of pore space near injection wells. These oil droplets are generated by high-velocity flow displacing residual oil in the rock. Because generation and filtration processes occur simultaneously, it is critical to understand both processes at high-velocity flow conditions.This paper experimentally quantifies the rate of generation and filtration of oil droplets in high-velocity flow. For the first time, empirical models were suggested to predict droplet size and rate of generation as a function of trapping number. For the filtration, synthetic dilute O/W emulsions were injected into granular packs to measure the filtration coefficient at various trapping numbers, grain sizes, and fluid velocities. We compared the measurements with known models. Also, filtration mechanisms of straining and interception are explained under high-velocity flow conditions experienced near injection wells. Based on this work, a macroscopic material balance model of O/W emulsion flow in porous media can precisely predict the near-well formation damage and the subsequent performance of injection wells during produced water re-injection (PWRI).

Morphodynamics of Fluid-Fluid Displacement in Three-Dimensional Deformable Granular Media

The simultaneous displacement of fluids through a porous medium and deformation of that host medium are crucial in applications as varied as hydraulic fracturing, methane venting from organic-rich sediments, volcanic eruptions, and desiccation cracking of soil. The authors present quantitative three-dimensional imaging of a deforming porous pack under immiscible fluid-fluid displacement. The data are modeled as the onset and evolution of cavity formation by overcoming the frictional resistance in the granular pack. These findings connect pore-scale observations to macroscopic behavior, and elucidate the physics at play in important natural processes and engineering applications.

Emergent Strain Stiffening in Interlocked Granular Chains.

Granular chain packings exhibit a striking emergent strain-stiffening behavior despite the individual looseness of the constitutive chains. Using indentation experiments on such assemblies, we measure an exponential increase in the collective resistance force F with the indentation depth z and with the square root of the number N of beads per chain. These two observations are, respectively, reminiscent of the self-amplification of friction in a capstan or in interleaved books, as well as the physics of polymers. The experimental data are well captured by a novel model based on these two ingredients. Specifically, the resistance force is found to vary according to the universal relation logF∼μsqrt[N]Φ^{11/8}z/b, where μ is the friction coefficient between two elementary beads, b is their size, and Φ is the volume fraction of chain beads when semidiluted in a surrounding medium of unconnected beads. Our study suggests that theories normally confined to the realm of polymer physics at a molecular level can be used to explain phenomena at a macroscopic level. This class of systems enables the study of friction in complex assemblies, with practical implications for the design of new materials, the textile industry, and biology.

Modelling the microstructure and computing effective elastic properties of sand core materials

In this article we model sand core materials on the micro-meter scale, resolving individual sand grains and binding bridges, to obtain effective elastic moduli of the composite by computational homogenization, laying the foundations for investigating the strength properties of core blown parts with foundry applications.We analyze sand core materials on the basis of X-ray micro-computed tomography (µXRCT) images and extract a couple of sand grains from this volume image. These grains enter a packing algorithm which can generate granular packs with high packing fraction and incorporate sand grains with high complexity. Furnished with binder the resulting microstructures are investigated, deriving their effective elastic properties and studying the sensitivity w.r.t. the entering parameters. If a realistic range of elastic parameters of both sand grains and binder are plugged into the simulation, the agreement with experimentally obtained P-wave moduli is excellent.

Effect of number of granulometric fractions on structure and micromechanics of compressed granular packings

The role of number of grain size fractions on structural and mechanical properties of uniaxially compressed granular packings with a uniform particle size distribution in terms of number of particles and with various particle size dispersities was studied using the discrete element method. The study addressed packing density, coordination number, contact forces, global stress, and energy dissipation in assemblies composed of frictional spheres. Packing density was found to change with increasing number of granulometric fractions in mixtures with a small ratio of the diameters of the largest to smallest particles. Results indicated a certain value of particle size ratio below which the number of particle size fractions strongly affected packing density. The average coordination number decreased with increasing number of fractions. Detailed analysis of the effect of particle size dispersity on mechanical coordination number, including particles with no less than four contacts, revealed that, contrary to the average coordination number, the mechanical coordination number increased with increasing ratio of the diameters of the largest to smallest particles in the sample. The composition of polydisperse samples strongly affected stress distribution and energy dissipation in granular packings.

Bending transition in the penetration of a flexible intruder in a two-dimensional dense granular medium.

We study the quasistatic penetration of a flexible beam into a two-dimensional dense granular medium lying on a horizontal plate. Rather than a buckling-like behavior we observe a transition between a regime of crack-like penetration in which the fiber only shows small fluctuations around a stable straight geometry and a bending regime in which the fiber fully bends and advances through series of loading and unloading steps. We show that the shape reconfiguration of the fiber is controlled by a single nondimensional parameter L/L_{c}, which is the ratio of the length of the flexible beam L to L_{c}, a bending elastogranular length scale that depends on the rigidity of the fiber and on the departure from the jamming packing fraction of the granular medium. We show, moreover, that the dynamics of the bending transition in the course of the penetration experiment is gradual and is accompanied by a symmetry breaking of the granular packing fraction in the vicinity of the fiber. Together with the progressive bending of the fiber, a cavity grows downstream of the fiber and the accumulation of grains upstream of the fiber leads to the development of a jammed cluster of grains. We discuss our experimental results in the framework of a simple model of bending-induced compaction and we show that the rate of the bending transition only depends on the control parameter L/L_{c}.

Tuning mechanical response in granular layers by adding rigid particle channel

The inhomogeneity of spatial packing by particles with different physical properties can significantly affect mechanical properties of granular packings. In this paper, a new approach by adding rigid particle channel is put forward to tune the mechanical response of granular layers induced by external loading. Based on the single-layer channel model, a phase diagram is firstly proposed to describe the crossover of mechanical response between a single-peaked and double-peaked feature, in which the tunable range of external loading and effective region of channel position are two key factors that reflect the tuning effect of this approach. Its tuning mechanism is further explored based on the variations of propagating feature of contact forces, and a linear function is proposed to predict the optimal position of the channel in systems with different sizes. Furthermore, the dependence of tuning effect on the spatial configuration and the number of rigid particle layers is also discussed in a double-layer and multi-layer rigid particle channel models, which can obviously improve the tunable effect but also undergo different tuning processes. By adding different rigid particle channels to actively change propagation paths of contact forces and weaken the anisotropy in vertical stress field within granular system, it has been verified that this approach is feasible to enhance the elasticity of whole system and tune its mechanical response.