Granular Packing Research Articles

Packings of micron-sized spherical particles – Insights from bulk density determination, X-ray microtomography and discrete element simulations

The quantitative description of packing behaviour of particulate systems under consideration of realistic particle size distributions and material properties poses one challenging problem in powder technology, with impacts on a broad range of technological areas. Here we investigate the packing characteristics of micrometer to millimeter-sized, polydisperse spherical particle systems of glass, zirconia and copper by means of experimental measurements of the bulk density, X-ray microtomography (CT) and numerical simulations of the granular packings using a 3d discrete element method (DEM). The applied DEM method takes realistic material properties into account and considers the experimentally obtained particle size distributions as well as attractive inter-particle forces including adhesion (Johnson, Kendall, Roberts (JKR)) and non-bonded van der Waals (vdW) interactions. Good agreement of the packing densities predicted by DEM and observed in the experiments (bulk density determination & CT) is found. Moreover, we show that a simple mathematical expression for the packing fraction as a function of average particle size of the polydisperse powder system describes well our experimental and simulation results for all investigated materials, with only two fitting parameters. From the DEM simulations, the mean (first) coordination number in the respective polydisperse packing is extracted and discussed with respect to the experimentally obtained direct neighborhood detection from X-ray tomography and in context of previous works. The mean coordination number shows a rather broad variance due to the polydispersity of the samples considered. It also shows a remarkable dependency on the definition of particle contact. Therefore, caution is advised when evaluating coordination numbers with this quantity being highly dependent on the instrumental resolution.

A DEM investigation on crushing of sand particles containing intrinsic flaws

Intrinsic flaws are an important factor affecting particle strength and breakage behavior and are closely related to the macroscopic behavior of granular soils, e.g., packing characteristics, strength, deformation, localization and failure behaviors, etc. In this paper, a novel DEM modeling approach for investigating the role of flaws on the particle crushing behavior is proposed. The idea is to use the realistic fracture surfaces obtained from the experiment as a basis for generating initial flaws in DEM in a statistical way. Firstly, nano-focus X-ray computed tomography technology was used to obtain the realistic particle information including particle morphology and a set of fracture surfaces. The particle information was then stored in several arrays and imported into the DEM to construct the particle model containing a reasonable set of initial flaws. Seven simulation cases were performed to study the role of initial flaws on the particle breakage behavior. Simulation results show that the proposed modeling approach is capable of reproducing the realistic particle breakage behaviors, including the small-strain stiffness, peak crushing load, fracture pattern and evolution of fragment shape parameters.

Cyclic martensitic transformations and damage evolution in shape memory zirconia: Single crystals vs polycrystals

AbstractIn zirconia‐based shape memory ceramics (SMCs), cracking during the martensitic transformation can be avoided in structures that reduce the relative presence of grain boundaries where high levels of transformation mismatch stress develop. This approach has been well established in single crystals, but only for sample sizes below about 5 microns. In this paper, we extend the strategy of eliminating grain boundaries to bulk specimen scales by fabricating mm‐scale single crystal SMCs via cold crucible induction melting. For 1.5 and 2.0 mol% Y2O3‐ZrO2, we study the cyclic martensitic transformation of both single crystal and polycrystal structures. Whereas single crystals have very repeatable transformation behavior in terms of hysteresis and strain amplitude, polycrystals degrade dramatically as they accumulate cracking damage with repeated cycling. As the polycrystal evolves from a pellet to granular packing of loose single crystals/grains, the energy dissipation converges with that of the single‐crystal structure, and the energy spent on cracking throughout that process is captured by calorimetry analysis. These results verify that grain boundaries play a key role in damage evolution during martensitic transformation and that microstructural control can extend the size‐scale of viable single crystal or oligocrystal SMCs from the micro‐ to the millimeter scale.

Acoustic waves in granular packings at low confinement pressure

Elastic properties of a granular packing show a nonlinear behavior determined by its discrete structure and nonlinear inter-grain force laws. Acoustic waves show a transition from constant, pressure-dependent sound speed to a shock-wave-like behavior with an amplitude-determined propagation speed. This becomes increasingly visible at low static confinement pressure as the transient regime shifts to lower wave amplitudes for lower static pressure. In microgravity, confinement pressure can be orders of magnitude lower than in a ground-based experiment. In addition, the absence of hydrostatic gradients allows for much more homogeneous and isotropic pressure distribution. We present a novel apparatus for acoustic wave transmission measurements at such low packing pressures. A pressure control loop is implemented by using a microcontroller that monitors static force sensor readings and adjusts the position of a movable wall with a linear-motor until the desired pressure is reached. Measurements of acoustic waves are possible using accelerometers embedded in the granular packing as well as piezos. For excitation, we use a voice-coil-driven wall, with a large variety of signal shapes, frequencies, and amplitudes. This enables experiments in both the linear and strongly nonlinear regimes.

A hybrid calibration approach to Hertz‐type contact parameters for discrete element models

SummaryThis study aims at providing a hybrid calibration framework to estimate Hertz‐type contact parameters (particle‐scale shear modulus and Poisson ratio) for both two‐dimensional and three‐dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle‐scale Hertz‐type contact parameters for granular systems are derived under small‐strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle‐level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro‐micro relationship in Hertz‐based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. The proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.

Fluid-induced fracture into weakly consolidated sand: Impact of confining stress on initialization pressure

This paper studies the process of fluid injection driven fractures in granular packs where particles are held together by external confining stresses and weak intergrain cohesion. We investigate the process of fracture formations in soft sand confined into a radial Hele-Shaw cell. Two main regimes are well known for fluid injection in soft sand. For low fluid injection pressures it behaves as a solid porous material while for high enough injection pressures grain rearrangement takes place. Grain rearrangements lead to the formation of fluid channels or "fractures," the structure and geometry of which depend on the material and fluid properties. Due to macroscopic grain displacements and the predominant role of dissipative frictional forces in granular system dynamics, these materials do not behave as conventional brittle, linear elastic materials and the transition between these two regimes cannot usually be described using poroelastic models. In this work we investigate the change in the minimum fluid pressure required to start grain mobilization as a function of the confining stresses applied to the system using a spatially resolved computational fluid dynamics-discrete element method numerical model. We show that this change is proportional to the applied stress when the confining stresses can be regarded as uniformly distributed among the particles in the system. A preliminary analytical expression for this change is presented.

Force chains and networks: wet suspensions through dry granular eyes

Recent advances in shear-thickening suspension rheology suggest a relation between (wet) suspension flow below jamming and (dry) granular physics. To probe this connection, we simulated the contact force networks in suspensions of non-Brownian spheres using the discrete element method, varying the particle friction coefficient and volume fraction. We find that force networks in these suspensions show quantitative similarities to those in jammed dry grains. As suspensions approach the jamming point, the extrapolated volume fraction and coordination number at jamming are similar to critical values obtained for isotropically compressed spheres. Similarly, the shape of the distribution of contact forces in flowing suspensions is remarkably similar to that found in granular packings, suggesting potential refinements for analytical mean field models for the rheology of shear thickening suspensions.Graphic abstract

Influence of the granular skeleton packing density on the static elastic modulus of conventional concretes

Particle packing methods are very useful for reducing the cement consumption of concrete mixtures and consequently the CO2 emissions associated with them. They usually also increase the solids concentration of the mixes, which fosters particle interlock. This work evaluates the influence of the packing of aggregates on the static modulus of elasticity of concretes with compressive strengths of 25 and 40 MPa. The granular skeleton was arranged using experimental particle packing methods, maintaining a constant compressive strength throughout the process. The packing density had a relative increase of 8% and 10% for the 25and 40 MPa concretes, respectively, and produced an average increase in the concrete static modulus of elasticity of 21% at 7 days and 8% at 28 days.

Impact on granular bed: validation of discrete element modeling results by means of two-dimensional finite element analysis

The study of processes characterized by impulsive nature (i.e. impacts) can be considered of great interest in both physics and engineering disciplines: in the geotechnical field, for instance, their effect on the interaction between soil and structures need to be investigated. The present work aims at the validation, by means of two-dimensional finite element simulations, of a methodology of force calibration which uses results obtained from three-dimensional discrete element analysis for predicting the stress at the base of a granular bed, retained by a movable wall, arising when the system is hit by a projectile. To approach this problem, the low-velocity impact has been modeled as a punctual impulsive force on a granular packing.

Structural and Micromechanical Properties of Ternary Granular Packings: Effect of Particle Size Ratio and Number Fraction of Particle Size Classes.

The confined uniaxial tests of packings with discrete particle size distribution (PSD) were modeled with the discrete element method. Ternary packings of spheres with PSD uniform or nonuniform by number of particles were examined in three-dimensional (3D) system. The study addressed an effect of the particle size ratio and the particle size fraction on structural and micromechanical properties of mixtures. A study of packing structure included porosity and coordination numbers, while the investigation of micromechanical properties included distribution of normal contact forces and stress transmission through the packing. A micro-scale investigation of the effect of particle size ratio on structure and mechanics of the ternary packings revealed a strong relationship between the properties of sample and the value of parameter till its critical value was reached. A further increase in particle size ratio did not significantly affect properties of packings. Contrary to the porosity and coordination numbers, the partial stresses were highly affected by the fraction of particle size classes in ternary mixtures. The contribution of the partial stress into the global stress was determined by number fraction of particles in packings with small particle size ratio, while it was mainly determined by particle size ratio in packings with small particle size ratio.

The critical state line of nonplastic tailings

The probability of failure of tailing dams and associated risks demand improvements in engineering practice. The critical state line provides a robust framework for the characterization of mine tailings. New experimental data for nonplastic platinum tailings and a large database for tailings and nonplastic soils (grain size between 2 and 500 μm) show that the critical state parameters for nonplastic tailings follow the same trends as nonplastic soils as a function of particle-scale characteristics and extreme void ratios. Critical state lines determined for extreme tailings gradations underestimate the range of critical state parameters that may be encountered in a tailings dam; in fact, mixtures with intermediate fines content exhibit the densest granular packing at critical state. The minimum void ratio emin captures the underlying role of particle shape and grain size distribution on granular packing and emerges as a valuable index property to inform sampling strategies for the assessment of spatial variability. Mineralogy does not significantly affect the intercept Γ100, but it does affect the slope λ. The friction coefficients M of tailings are similar to those of other nonplastic soils; while mineralogy does not have a significant effect on friction, more angular grains lead to higher friction coefficients.

The effect of mechanical cleaning technology (MCT) on membrane fouling in a novel hybrid membrane photobioreactor (HMPBR) containing Arthrospira platensis (Spirulina)

Membrane fouling is considered in a novel hybrid membrane photobioreactor (HMPBR) including airlift, membrane, and granular particles. In microalgae systems, cake resistance is the main fouling resistance. To mitigate membrane fouling, this system works under varied granular packing ratios, such as 0, 0.5, 1, and 1.5% (v/v). The results confirm the good effect of polymeric granules on the reduction of the cake resistance. Compared with the absence of granular particles, the addition of these particles up to 1.5% decreases cake resistance by 53%, whereas cake resistance is the most part of total fouling resistance. Regarding the major foulants, FTIR analysis demonstrates protein which has been known as a major foulant. Moreover, with the increase in the granular packing ratio, the protein concentration in the cake layer increases. This issue could be related to the increase in pore blocking owing to the blockage of the membrane pores and the inability of the protein-like substances to pass the membrane and stay on the membrane surface.

A spatially resolved fluid-solid interaction model for dense granular packs/soft-sand

Fluid flow through dense granular packs or soft sands can be described as a Darcy’ s flow for low injection rates, as the friction between grain-grain and grain-walls dominate the solid system behaviour. For high injection rates, fluid forces can generate grain displacement forming flow channels or “fractures”, which in turn modify local properties within the system, such as permeability and stress distribution. Due to this kind of “self organized” behaviour, a spatially resolved model for these interactions is required to capture the dynamics of these systems. In this work, we present a resolved model based on the approach taken by the CFDEM open source project which uses LIGGGHTS – a discrete elements method (DEM)– to model the granular behaviour and OpenFoam finite volume library for computational fluid dynamics (CFD), to simulate the fluid behaviour. The capabilities provided by the DEM engine allows the properties of the solid phase, such as inter-grain cohesion and solid confinement stress to be controlled. In this work the original solver provided by the CFDEM project was modified so as to deal with dense granular packs more effectively. Advantages of the approach presented are that it does not require external “scaling parameters” to reproduce well known properties of porous materials and that it inherits the performance provided by the CFDEM project. The model is validated by reproducing the well-known properties of static porous materials, such as its permeability as a function of the system porosity, and by calculating the drag coefficient for a sphere resting inside a uniform flow. Finally, we present fracture patterns obtained when modelling water injection into a Hele-Shaw cell, filled with a dense granular pack.

Scaling Law for Cracking in Shrinkable Granular Packings.

Hydrated granular packings often crack into discrete clusters of grains when dried. Despite its ubiquity, an accurate prediction of cracking remains elusive. Here, we elucidate the previously overlooked role of individual grain shrinkage-a feature common to many materials-in determining crack patterning using both experiments and simulations. By extending classical Griffith crack theory, we obtain a scaling law that quantifies how cluster size depends on the interplay between grain shrinkage, stiffness, and size-applicable to a diverse array of shrinkable granular packings.

Thermal discrete element method for transient heat conduction in granular packing under compressive forces

A thermal discrete element method is introduced in granular packs. This method is applicable to 3D packing in either static or dynamic states coupled with the ordinary discrete element method code. This method resolves the local heat fluxes and temperature of particles relying on particles conductivity and the deformation of particles at various contact points. Using this method, the time evolution of temperature is studied within packed beds under various compressive forces. Our results match very well with the analytical solution as if the value of the effective conductivity is properly adjusted, which is found to be related to the pressure exponentially. We have also shown that the compression of the granular packing exponentially increases the thermal characteristic time of the bed.

Influence of the size of the intruder on the reorganization of a 2D granular medium

We consider the rearrangements of a vertical two-dimensional granular packing induced by the withdrawal of an intruder. Here, we focus on the influence of the size of the intruder on the reorganization process. The long term evolution of the granular packing is investigated as well as the avalanche dynamics that characterize the short term rearrangements around the intruder. For small enough intruder, we observe the formation of arches that periodically destabilize and influence the reorganization dynamics of the two-dimensional packing through larger rearrangement events.

Elastic and Mechanical Properties of Dune Sand: Experiments and Models

AbstractUltrasonic elastic‐wave velocities, as well as the stress‐strain behavior, were measured on dry dune sand from Saudi Arabia under hydrostatic loading from 0 to 50 MPa. The samples came from the dune's crest, limb, and base. The experiments included several loading and unloading cycles. All samples exhibited irreversible deformation and porosity reduction during the tests due to grain repacking in low‐stress regimes and grain breakage at higher stress. The loading behavior was plastic, while the unloading/reloading behavior was elastic. In spite of noticeable porosity variations during the experiments, the elastic‐wave velocities mainly depended on the stress rather than on porosity. Our velocity versus stress data is very close to earlier published results, although the provenance of the sand is very different, pointing at a universality of such behavior in loose sand. Our results were matched by the contact Hertz‐Mindlin theory with varying coordination number and shear‐stiffness adjustment. We also offer a new theoretical model for the static bulk modulus measured in these experiments. This model is based on the concept of stress heterogeneity (stress chains or patches) in a granular pack and uses elastic bound averaging of the respective moduli of stressed and unstressed parts of the pack. The same model is used to describe the velocity versus stress behavior. These results and theory constitute a new installment into the published sparse data of the mechanical properties of unconsolidated sand as well as theoretical analyses thereof and are the first ever such data generated in Saudi Arabia.

Cratering response during droplet impacts on granular beds.

This experimental work focuses on the cratering response of granular layers induced by liquid droplet impacts. A droplet impact results in severe granular layer deformation, crater formation and deposits in the vicinity of the impact center. High-precision three-dimensional imaging of the granular layer surface revealed important characteristics of liquid impacts on granular matter, such as singular asymmetric deformations of the layer. Our analysis also demonstrated that the impact energy and the granular packing, and its inherent compressibility, are not the unique parameters controlling the bed response, for which granular fraction heterogeneities may induce strong variations. Such heterogeneous conditions primarily influence the magnitude but not the dynamics of liquid impacts on granular layers. Finally, a general equation can be used to relate the enery released during cratering to both the impact energy and the compressibility of the granular matter. However, our results do not support any transition triggered by the compaction-dilation regime. Hence, higly detailed numerical simulations could provide considerable insights regarding the remaining questions related to heterogeneous packing conditions and its influence over the bulk compressibility and the compaction-dilation phase transition.

Filtro de cascarilla de Ricinus communis y carbón vegetal para tratamiento de agua contaminada con hidrocarburos: diseño de un sistema en serie por etapas

<p>El objetivo del trabajo fue evaluar un sistema de tres filtros en serie, usando cascarillas de Ricinus communis y carbón vegetal. Se construyó cada filtro con tubos de plástico PVC y se colocaron los paquetes filtrantes granulares, dos de cascarilla y uno de carbón vegetal, para filtrar el agua de manera descendente por gravedad. Se utilizó agua contaminada con 5 y 10% Diésel y se tomaron muestras a la salida de cada uno para medir las variables SST y AyG, mediante las normas ASTM D5907 y EPA Method 1664 A. Los ensayos se hicieron por triplicado, con un diseño factorial con prueba ANAVA y DMS de Fisher con significancia α = 0.05. El sistema filtrante fue eficiente para disminuir los parámetros a valores permitidos por las normas ambientales peruanas, siendo más eficiente para AyG. Las eficiencias mostraron diferencias significativas por Etapas de filtración, pero fueron iguales en función al % Diésel.</p>

Compaction of liquid immersed granular packings by small upward flows

We conduct experiments to examine the compaction dynamics of a liquid immersed granular packing under an upward flow which is either continuous or made up of repeated short bursts. We find that compaction is possible in the continuous case and compaction efficiency can be enhanced for short bursts.