Influence of particle breakage on the dynamic compression responses of brittle granular materials

The dynamic compression responses of dry quartz sand are tested with a modified spilt Hopkinson pressure bar (MSHPB), and the quasi-static compression responses are tested for comparison with a material testing system. In the experiments, the axial stress–strain responses and the confining pressure of the jacket are both measured. Comparison of the dynamic and the quasi-static axial stress–strain curves indicate that dry quartz sand exhibits obvious strain-rate effects. The grain size distributions of the samples after dynamic and quasi-static loading are obtained with the laser diffractometry technique to interpret the rate effects. Quantitative analyses of the grain size distributions show that at the same stress level, the particle breakage extent under quasi-static loading is larger than that under dynamic loading. Moreover, the experimental and the theoretical relationships of the particle breakage extent versus the plastic work show that the energy efficiency in particle breakage is higher under quasi-static loading, which is the intrinsic cause of the strain-rate effects of brittle granular materials. Using the discrete element method (DEM), the energy distributions in the brittle granular material under confined compression are discussed. It is observed that the input work is mainly transformed into the frictional dissipation, and the frictional dissipation under dynamic loading is higher than that under quasi-static loading corresponding to the same breakage extent. The reason is that more fragmentation debris is produced during dynamic breakage of single grains, which promotes particle rearrangement and the corresponding frictional dissipation significantly.     

Non-contact stress measurement in granular materials via neutron and X-ray diffraction: theoretical foundations

Model validation remains a serious problem within the field of computational granular materials research. In all cases the rigor of the validation process is entirely dependent on the quality and depth of the experimental data that forms the point of comparison. Neutron and X-ray diffraction methods offer the only quantitative non-contact method for determining the spatially resolved triaxial stress field within granular materials under load. Measurements such as this can provide an unprecedented level of detail that will be invaluable in validating many models. In this paper the theoretical foundation underpinning diffraction-based strain measurements, their conversion to local stress in the particles and ultimately into the bulk stress field is developed. Effects such as elastic anisotropy within the particles of the granular material, particle plasticity and locally inhomogeneous stress distribution are shown to not offer any obstacles to the method and a detailed treatment of the calculation of the bulk stresses from the particle stresses is given.     

Granular segregation studies for the development of a radar-based three-dimensional sensing system

The behavior of dense granular materials is difficult to measure in three-dimensions due to the opacity of the materials. We present a new radar-based sensing system that has the capability of measuring three-dimensional particle movement throughout the bulk of high solids fraction granular systems. A key component of the new system involves retroreflectors imbedded in objects resembling the particles in the bulk granular systems. These embedded retroreflectors may be used as tracers in systems comprised of relatively large particles. However, in systems of smaller particles the most versatile use of this new sensing system requires an understanding of the details of relative particle movement based on particle size and other particle properties. Towards this, we present new ongoing experimental and computational results toward building a versatile sensing system for high solids fraction granular systems. We then comment on additional research needed on the behavior of the components in granular mixtures for a fully versatile sensing system.     

3D Imaging of particle motion during penetrometer testing

We present the results of direct observation of material rearrangement due to penetration of a solid rod (penetrometer) through a granular medium. Two different techniques and their advantages are discussed in this paper. We investigate the motion of material within the bulk around the rod. Transparent, polydisperse, and irregularly shaped silica particles immersed in index matching fluid are used for detailed imaging of the interior of a granular pile. Motion of material is observed by confocal microscopy from the bottom boundary up to 100 particle diameters in height. Image analysis indicates that rearrangements spread furthest not directly under the penetrometer but in a ring around the penetrometer. In addition, the direction of preformed stress chains in the material influences the particle rearrangements. Material compressed from one side exhibits anisotropic particle rearrangements under penetrometer testing. Laser sheet scanning allows for direct imaging of individual particle motion with greater accuracy, but works best for spherical particles only.     

Investigation of the influence of frictional viscosity regularization on quasi-static gas-solid flow predictions in a conical spouted bed with non-porous draft tube

The stress in the quasi-static particle flow is often modeled through the Mohr-Coulomb failure criterion. In the extension to complex three-dimensional flows, a granular viscosity is introduced through a tensorial rheology and the deviatoric frictional stress tensor is assumed aligned with the strain rate tensor. This granular viscosity is singular as the shear rate approaches zero, regardless of the local rheology. We discuss the influence of regularizing such a frictional viscosity on the particle circulation rate and other measured characteristics in a laboratory scale draft tube spouted bed. The friction between particles is modeled either with a constant Coulomb rheology or using a local particle pressure and strain-rate based friction known as $\mu \left(I\right)$-rheology. The predictions appear very dependent on the regularization parameter introduced by the method. The mean properties of the flow (e.g. circulation and pressure drop) monotonically converge towards the measurements when the regularization parameter tends to zero. In other respects, the two regularization models regarded in this study induced similar hydrodynamics within the spouted bed of interest. But the analysis of the conditional averages of the inertial number and the fraction of the solids in the quasi-static regime shows that the extent and staticity of the quasi-static region is sensitive to changes to the regularization parameter or regularization function.     

DEM investigations of two-dimensional granular vortex- and anti-vortex-structures during plane strain compression

The paper presents simulation results of a quasi-static plane strain compression test on cohesionless initially dense sand under constant lateral pressure using a three-dimensional discrete element method. Grains were modelled by means of spheres with contact moments imitating irregular particle shapes. The material behaviour was studied at both global and local levels. The stress–strain and volumetric-strain curves, distribution of void ratio, resultant grain rotation and contact forces were calculated. The main attention was paid to the appearance of plane strain granular micro-structures like vortex and anti-vortex structures in the granular specimen during deformation. In order to detect two-dimensional vortex and anti-vortex structures, a method based on orientation angles of displacement fluctuation vectors of neighbouring single spheres was used. The effect of the method parameters was also analyzed.     

Effect of particle size and boundary conditions on the shear stress in an annular shear cell

The effect of particle size and boundary geometry in granular shear flows is investigated. The measured shear stress of glass spheres in an annular shear cell experiment is reported. In order to explore the particle size effect, the experiments are run using four different particle diameters, d = 2, 3, 4, and 5 mm. It is found that the shear stress follows the Bagnold scaling with respect to the apparent shear rate, but deviates from it with respect to particle size. For high solids concentration the results deviate qualitatively from the kinetic theory for bounded granular shear flows, where the non-dimensional shear stress measured with large particles exceeds that measured for small particles by as much as one order of magnitude. The effect of the boundary geometry is explored by using three different boundary types; type 1 employs aluminum radial half-cylinders, type 2 employs aluminum hemispheres arranged in a polar hexagonal closed packed configuration, and type 3 employs sandpaper. It is shown that the geometry of the boundary has an insignificant effect on dilute flows of small particles. For denser flows and/or larger particles the difference is evident. The sandpaper boundary, which is different from the aluminum ones both in geometry and in its material properties, yields the lowest stress. These results imply that in granular materials-structure interaction, the structure’s properties are just as important as the properties of the granular material. Their interaction may also depend on the relative size between the structure and the grain size.     

Analysis of the influence of crushing on the behavior of granular materials under shear

The behavior of granular materials mainly depends on the mechanical and engineering properties of particles in its structural matrix. Crushing or breakage of granular materials under compression or shear occurs when the energy available is sufficient to overcome the resistance of the material. Relatively little systematic research has been conducted regarding how to evaluate or quantify particle crushing and how it effects the engineering properties of the granular materials. The aim of this study is to investigate the effect of crushing on the bulk behavior of granular materials by using manufactured granular materials (MGM) rather than using a naturally occurring cohesionless granular material. MGM allow changing only one particle parameter, namely the “crushing strength”. Four different categories of MGM (with different crushing strength) are used to study the effect on the bulk shear strength, stiffness modulus, friction and dilatancy angle “engineering properties”. A substantial influence on the stress–strain behavior and engineering properties of granular materials is observed. Higher confining stress causes some non-uniformity (strong variations/jumps) in volumetric strain and a constant volumetric strain is not always observed under large shear deformations due to crushing, i.e. there is no critical state with flow regime (with constant volumetric strain).     

Investigation on instability modes of sand under biaxial shearing accounting various specimen generation techniques in DEM

Instabilities in granular material usually initiate at the microscale due to the presence of internal heterogeneity arising from variation in the particle packing arrangement. The present work elucidates the effect of various specimen generation techniques adopted in DEM on the initial sample heterogeneity and its subsequent influence on the instability response of sand under biaxial shearing. Dense and loose specimens are prepared using five different specimen generation techniques and homogeneity within the specimens has been analyzed in terms of spatial variation of porosity, anisotropy in the contact force and fabric structure. The initiation and subsequent evolution of different instability modes during shearing have been examined based on the spatial porosity distribution, relative particle displacement and particle rotation. Localized instability mode has been observed to emerge in dense specimens in form of cross-type shear bands with varying inclination and thickness for these different specimen generation techniques. Porosity and particle rotation based instability prediction indicate a delayed onset of shear band in comparison to identifications from relative particle displacement and bifurcation of local strains. The loose specimen exhibits bulging type diffused instability accompanied by large relative particle displacement and rotation scattered across the specimen.     

The role of contact friction in the dynamic breakage behavior of granular materials

Based on the discrete element method, a multi-scale model is employed to investigate the role of contact friction in the dynamic compression responses of brittle granular materials. Four numerical granular samples with different particle friction coefficients ranging from 0.0 to 2.0 are tested and the particle breakage extent is quantified with the Einav breakage index. It is observed that the relationship of the breakage extent with the axial stress is apparently non-monotonic concerning the particle friction coefficient. At the same stress level, the breakage extent exhibits a minimum when the particle friction coefficient is around 0.1 but increases significantly with the particle friction coefficient to both sides. The micro physical origin of this non-monotonic behavior is a distinct transition in dominant particle-breakage modes from tension to shear. Moreover, energy analyses also show non-monotonic evolution of the frictional and damping dissipation with the particle friction coefficient. The joint effect of these two dissipation terms contributes to the non-monotonic behavior of particle breakage. In addition, the accuracy and competence of two frequently-used micro quantities, fraction of sliding contacts and average coordination number, are discussed.

     

Dense granular flow at the critical state: maximum entropy and topological disorder

After extensive quasi-static shearing, dense dry granular flows attain a steady-state condition of porosity and deviatoric stress, even as particles are continually rearranged. The paper considers two-dimensional flow and derives the probability distributions of two topological measures of particle arrangement—coordination number and void valence—that maximize topological entropy. By only considering topological dispersion, the method closely predicts the distribution of void valences, as measured in discrete element (DEM) simulations. Distributions of coordination number are also derived by considering packings that are geometrically and kinetically consistent with the particle sizes and friction coefficient. A cross-entropy principle results in a distribution of coordination numbers that closely fits DEM simulations.     

A phenomenological law for complex granular materials from Mohr-Coulomb theory

Manipulating powders still entails some clumsy and risky operations even now in the middle of the fourth industrial revolution. This is because there is a lack of well-understood theory about granular matter due to its ravelled complexity. However, granular matter is the second most handled material by man after water and is thus ubiquitous in daily life and industry only after water. Since the eighteenth century, mechanical and chemical engineers have been striving to manage the many difficulties of grain handling, most of which are related to flow problems. Many continuum models for dense granular flow have been proposed. Herein, we investigated Mohr–Coulomb failure analysis as it has been the cornerstone of stress distribution studies in industrial applications for decades. This research gathers over 130 granular materials from several industrial sectors, as varied as cement and flour, including raw materials, food, pharmaceuticals, and cosmetics. A phenomenological law derived from the yield locus and governed exclusively by one dimensionless number from adhesive interactions has been found. Surprisingly, and in contrast to the common perception, flow in the quasi-static regime is actually independent of the friction, the packing fraction and any other grains/bulk intrinsic properties. The simplicity and accuracy of the model are remarkable in light of the complex constitutive properties of granular matter.     

Enhanced Voidage Correlations for Packed Beds of Various Particle Shapes and Sizes

Mean voidage in packed beds of spherical, cylindrical, and nonconventional cylindrical particles has been accurately measured, and the data obtained were employed to develop predictive mean voidage correlations that were not only simpler to use and more accurate than existing correlations, but also helped in developing a single general voidage correlation incorporating a particle shape factor applicable to a variety of particle shapes. Such mean voidage correlations are highly sought in packed bed design for a multitude of applications and can also assist in minimizing pressure drop in such packed beds by guiding particle shape selection.     

Tensile stress relaxation in unsaturated granular materials

The mechanics of granular media at low liquid saturation levels remain poorly understood. Macroscopic mechanical properties are affected by microscale forces and processes, such as capillary forces, inter-particle friction, liquid flows, and particle movements. An improved understanding of these microscale mechanisms is important for a range of industrial applications and natural phenomena (e.g. landslides). This study focuses on the transient evolution of the tensile stress of unsaturated granular media under extension. Experimental results suggest that the stress state of the material evolves even after cessation of sample extension. Moreover, we observe that the packing density strongly affects the efficiency of different processes that result in tensile stress relaxation. By comparing the observed relaxation time scales with published data, we conclude that tensile stress relaxation is governed by particle rearrangement and fluid redistribution. An increased packing density inhibits particle rearrangement and only leaves fluid redistribution as the major process that governs tensile stress relaxation.     

A local constitutive model with anisotropy for ratcheting under 2D axial-symmetric isobaric deformation

A local constitutive model for anisotropic granular materials is introduced and applied to isobaric (homogeneous) axial-symmetric deformation. The simplified model (in the coordinate system of the bi-axial box) involves only scalar values for hydrostatic and shear stresses, for the volumetric and shear strains as well as for the new ingredient, the anisotropy modulus. The non-linear constitutive evolution equations that relate stress and anisotropy to strain are inspired by observations from discrete element method (DEM) simulations. For the sake of simplicity, parameters like the bulk and shear modulus are set to constants, while the shear stress ratio and the anisotropy evolve with different rates to their critical state limit values when shear deformations become large. When applied to isobaric deformation in the bi-axial geometry, the model shows ratcheting under cyclic loading. Fast and slow evolution of the anisotropy modulus with strain. Lead to dilatancy and contractancy, respectively. Furthermore, anisotropy acts such that it works “against” the strain/stress, e.g., a compressive strain builds up anisotropy that creates additional stress acting against further compression.     

Development of micromechanical models for granular media

Micromechanical analysis has the potential to resolve many of the deficiencies of constitutive equations of granular continua by incorporating information obtained from particle-scale measurements. The outstanding problem in applying micromechanics to granular media is the projection scheme to relate continuum variables to particle-scale variables. Within the confines of a projection scheme that assumes affine motion, contact laws based on binary interactions do not fully capture important instabilities. Specifically, these contact laws do not consider mesoscale mechanics related to particle group behaviour such as force chains commonly seen in granular media. The implications of this are discussed in this paper by comparison of two micromechanical constitutive models to particle data observed in computer simulations using the discrete element method (DEM). The first model, in which relative deformations between isolated particle pairs are projected from continuum strain, fails to deliver the observed behaviour. The second model accounts for the contact mechanics at the mesoscale (i.e. particle group behaviour) and, accordingly, involves a nonaffine projection scheme. In contrast with the first, the second model is shown to display strain softening behaviour related to dilatancy and produce realistic shear bands in finite element simulations of a biaxial test. Importantly, the evolution of microscale variables is correctly replicated. This paper is dedicated to Professor Ching S. Chang on the occasion of his 60th birthday.     

Magnetism in nanoclusters and cluster-assembled thin films

Increasing attention has been focused on the magnetic behavior of nanoparticles with diameters of 1-5 nm (approximately 50-5000 atoms). In this size range fundamental magnetic parameters such as the orbital and spin magnetic moments per atom deviate significantly from bulk values, and studying clusters addresses fundamental problems in mesoscopic magnetism, which is not as well understood as in either the atomic or the bulk regimes. There is also a growing realization of the enormous industrial potential of materials built by depositing preformed nanoclusters instead of atoms. If the clusters are size-selected and deposited in conjunction with an atomic vapor of a matrix material, it is possible to produce granular films in which there is independent control over the particle size and volume fraction. Using this technique, it also becomes possible to make granular mixtures of miscible materials. This unprecendented degree of control over the properties of the films holds the promise of new magnetic materials with "engineered properties." To fully realize this potential requires a greater understanding of not only the individual particles, but also how they interact in dense assemblies. There has been great progress in understanding some aspects of the magnetic behavior of nanoclusters and cluster-assembled materials. The mechanisms that generate spin and orbital moments that are enhanced by up to 36 and 200%, respectively, relative to the bulk in isolated clusters are well understood as is the dynamical behavior of the magnetic moment. Not so well understood is the observed magnetic anisotropy, which often has a different symmetry than the bulk. In dense assemblies, the nature of the interparticle coupling and the relative importance of dipolar and exchange interactions also require further research.     

Powder Characteristics of Proteins Spray-Dried from Different Spray-Dryers

Abstract

The powder characteristics of bovine somatotropin and casein spray-dried from laboratory, pilot and production spray-dryers were investigated. The powder characteristics examined included particle size distribution and morphology; bulk density; and flowability as measured by angle of repose, compressibility index and shear cell indices. Morphology classification showed internal voidage, blowholes, expanded, smooth and folding for somatotropin and casein spray-dried from the various spray-dryers. Particle size distributions of the bovine somatotropin and casein were unimodal and skewed. As the drying-chamber size of the spray-dryer increased, the particle sizes of both somatotropin and casein increased from mean volume diameters of 6-8 μ using the laboratory and pilot spray-dryers to 13-24 μ when using the production size spray-dryers. Spray-dried bovine somatotropin and casein had bulk densities of 0.090 to 0.195 g/cm³. Three flowability tests showed casein and somatotropin spray-dried from the different spray-dryers exhibited poor flow which could result in pharmaceutical manufacture challenges. The morphology and flowability of the two spray-dried proteins remained the same when comparing material produced from all four spray-dryers. However, the mean volume diameter, particle size distribution and bulk density did vary which might change critical product characteristics during scale-up. In general, similar morphology, particle size distributions, flowability and bulk densities were observed when comparing spray-dried casein and bovine somatotropin produced from the same model spray-dryer. Casein is recommended as a model protein for powder characterization during spray-drying and early formulation manufacture process development when adequate quantities of the recombinant protein are not available.