Systems Of Nonspherical Particles Research Articles

Traction chain networks: Insights beyond force chain networks for non-spherical particle systems

Force chain networks are generally applied in granular materials to gain insight into inter-particle granular contact. For conservative spherical particle systems, i.e. frictionless and undamped, force chains are information complete due to symmetries resulting from isotropy and constant curvature of a sphere. In fact, for conservative spherical particle systems, given the geometry and material, the force chain network uniquely defines the contact state that includes elastic forces, penetration distance, overlap volume, contact areas and contact pressures in a particle system. This is, however, not the case for conservative non-spherical particle systems. The reason is that a force chain network is not sufficient to uniquely define the contact state in a conservative non-spherical particle system. Additional information is required to define the contact state of non-spherical granular systems. Traction chain networks are proposed to complement force chain networks for the improved quantification of the state of contact of a granular system.

A digital-based approach for characterising spread powder layer in additive manufacturing

Assessing the quality of a spread powder layer is critical to understanding powder spreadability in additive manufacturing. However, the small layer thickness presents a great challenge for a systematic and consistent characterisation of the spread powder layer. In this study, a novel digital-based characterisation approach is proposed based on space discretization, with an emphasis on the characteristics that is important to powder-bed-based additive manufacturing. With the developed approach, the spread powder layer can be qualitatively illustrated by contour maps and quantified by statistics of packing density, surface profile and pore characteristics. For the first time, two types of pores are proposed for the spread powder layer. The density pore can identify those less populated areas while the chamber pore is able to quantify the size of empty patches observed in the spread powder bed. Applicability of this approach is demonstrated via both simulation-generated and experimentally spread powder layers. Sensitivity tests on the sampling parameters are conducted. This digital-based characterisation method is general and can be applied to both polydisperse and non-spherical particle systems, not only enriching detailed structural analysis of the spread powder layer but also allowing us to quantitatively evaluate powder spreadability in additive manufacturing.

Influence of particle shape on mixing rate in rotating drums based on super-quadric DEM simulations

Fundamental research on the flow and mixing of non-spherical particles is critical for industrial production and design. In this paper, the Discrete Element Method (DEM) is used to study the flow and mixing of granular materials in the horizontal rotating drum, and the periodic boundary condition is employed to eliminate end wall effect. Super-quadric elements are adopted to describe spherical and non-spherical particles. The influences of rotating speed, blockiness, and aspect ratio on the mixing rate are investigated by the Lacey mixing index. The results show that the rotating speed has a primary effect on the mixing rate, whereas the effect of the particle shape on the mixing rate is a secondary factor for non-spherical granular systems. Moreover, the mixing rate of spherical and non-spherical particle systems is significantly different. The mixing rate of spheres is the lowest, and the cubes have a higher mixing rate than the cylinders. As the blockiness decreases or aspect ratio deviates from 1.0, the mixing rate decreases. Ordered face-to-face contacts and dense packing structures result in a higher mixing rate. The analysis of kinetic energy shows that particle shape affects the transfer efficiency of external energy to the granular systems. The translational kinetic energy of non-spherical particles is higher than that of spherical particles, and their rotational kinetic energy is lower than that of spheres. Meanwhile, the blockiness enhances the transfer efficiency of external energy to the non-spherical systems; in contrast, the aspect ratio reduces the energy conversion efficiency.

Numerical investigation on the mutual interaction between heat transfer and non-spherical particle dynamics in the blast furnace raceway

In this paper, the coupled computational fluid dynamics (CFD) and discrete element method (DEM) scheme is used to investigate the microstructure and heat transfer characteristics in a blast furnace (BF) raceway. The impact of gas velocity and particle shape on raceway evolution, microstructure characteristics, and particle temperature and voidage distributions is comprehensively explored based on the voidage change caused by the consumption of coke particles. Numerical results show that the oblate ellipsoidal particle system possesses higher average voidage in the original packing state and implements the faster burden descending rate than the prolate one under the same inlet velocity. For the non-spherical particle systems, larger contact forces exist in the oblate ellipsoidal particle system while the contact forces in the prolate ellipsoidal particle system are smaller. More uniform temperature distribution and higher average voidage can be caused by higher inlet gas velocities. Meanwhile, more prolate ellipsoidal particles are consumed than oblate ones under the same inlet velocity. These findings could be beneficial for understanding the kinetic and thermodynamic behaviors of particulate system within a BF raceway.

Shear of granular materials composed of ellipses

Granular systems of disks (2D) and spheres (3D) under shear have been studied extensively. However, less attention has been paid to systems of non-spherical particles, i.e., ellipses, polygons, etc. Here we studied a quasi 2D granular system composed of ellipses under homogeneous simple shear. By tracking the positions and orientations of the ellipses, we have observed that they gradually rotate to align along a preferred direction as the shear strain increases. This preferred direction asymptotically approach a density-independent value at large strain. While first reported for disk systems, shear jamming is also observed for our ellipse system, as indicated by the increase of system pressure and coordination number with shear strain.

Jamming transition in non-spherical particle systems: pentagons versus disks

We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles with static friction coefficient $\mu\approx 1$. (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, $Z_{nr}$ , reaches 3, and the dependence of $Z_{nr}$ on the packing fraction $\phi$ changes again when $Z_{nr}$ reaches 4. (2) Though the packing fractions $\phi_{c1}$ and $\phi_{c2}$ at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of $\phi_{c1}$ and $\phi_{c2}$ for pentagons are around 1% smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs comparing to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution.

Mean field theory of jamming of nonspherical particles

Recent computer simulations have uncovered the striking difference between the jamming transition of spherical and non-spherical particles. While systems of spherical particles are isostatic at the jamming point, systems of nonspherical particles are not: the contact number and shear modulus of the former exhibit a square root singularity near jamming, while those of the latter are linearly proportional to the distance from jamming. Furthermore, while our theoretical understanding of jamming of spherical particles is well developed, the same is not true for nonspherical particles. To understand jamming of non-spherical particles, in the previous work Brito (2018 Proc. Natl Acad. Sci. 115 11736), we extended the perceptron model, whose SAT/UNSAT transition belongs to the same universality class of jamming of spherical particles, to include additional variables accounting for the rotational degrees of freedom of nonspherical particles. In this paper, we give more detailed investigations of the full scaling behavior of the model near the jamming transition point in both convex and non-convex phases.

Plasmonic Nanoparticles and Island Films for Solar Energy Harvesting: A Comparative Study of Cu, Al, Ag and Au Performance

Alternative materials that can potentially replace Au and Ag in plasmonics and broaden its application potential have been actively investigated over the last decade. Cu and Al have been usually overlooked as plasmonic material candidates because they are prone to oxidisation. In this work the plasmonic performance of Cu and Al is investigated using numerical simulations of different nanostructures (spheres, cubes, rods and particle dimers) and taking into account the presence of oxidisation. It is shown that geometry can play a dominant role over material properties and the performance of Cu and Al becomes comparable to that of Ag and Au for systems of non-spherical particles and strong electromagnetic coupling among particles. This observation is experimentally confirmed by the fabrication and characterisation of Cu and Al metal island films. Optical characterisation of the samples reveals a comparable performance of these metals to that obtained for Ag and Au and suggests that Cu and Al metal island films can offer an efficient low-cost platform for solar energy harvesting, as shown in water vapour generation proof of concept experiments.

DEM investigation of shear flows of binary mixtures of non-spherical particles

Discrete element method (DEM) simulations of shear flows of binary mixtures of large non-spherical glued-sphere particles and small spheres are conducted in order to investigate the effect of particle shape and solid volume fraction ratio on the behavior of binary granular flows. The shear stresses first decrease and then increase with total solid volume fraction. The shear stresses increase with the increasing solid volume fraction ratio of large particles. The orientation distributions of large particles show that, in dense regions, the binary system with a higher solid fraction ratio of small spheres exhibits a more uniform alignment in the shear flow direction for large particles. By incorporating the effective particle projected area in the plane perpendicular to the flow plane, the conventional kinetic theory for binary spherical systems is found capable of predicting the stresses for binary systems of non-spherical particles. Stresses for binary systems with various solid volume fraction ratios collapse into a single line by further incorporating the root-mean-cubed diameter, but this scaling is not adequate for dense flows. Comparing the shear stresses for different large particle shapes shows that shear stresses can be affected by the particle shape and particle aspect ratio, but the differences between different particle shapes and aspect ratios are minimized by increasing the solid volume fraction ratio of small spheres.

The fraction of overlapping interphase around 2D and 3D polydisperse non-spherical particles: Theoretical and numerical models

The fraction of interphase is an important microstructure parameter in the prediction of macroscopic properties of particulate composites. Currently, some researchers have presented theoretical and numerical investigations on the interphase fraction for spherical particle systems, and even quantify the influence of interphase fraction on the overall elastic and transport properties of particulate composites. However, the overlapping interphase fraction in polydisperse non-spherical particle systems is still an open issue. In this work, a generic theoretical model is formulated to derive the overlapping interphase fraction for polydisperse 2D non-circular and 3D non-spherical particle systems by means of the statistical geometry of composites. In this model, the morphology of interphase coated onto the surface of non-spherical particles can be characterized by circularity and sphericity of particles that are important parameters to describe the shape of particles. On the other hand, numerical simulations for the one-point probability function of interphase are presented to verify the proposed theoretical framework. In the numerical simulations, a novel algorithm is developed by reducing the problem of identifying the precise location between an arbitrary spatial point and interphase to the basic issue of finding the distance from the point to the surface of particles. If the distance is less than the interphase thickness, the point definitely locates inside interphase. In addition, the algorithm can be further used to detect the overlap between adjacent ellipsoidal particles (2D ellipses). Moreover, a variety of particle shapes (such as regular polygons and ellipses with the same circularity, and regular polyhedrons and ellipsoids with the same sphericity) are taken into account to generate particle packing structures. Then, the fraction of overlapping interphase in each packing structure is statistically obtained. Results show that statistical values are consistent with their theoretical values under the same conditions. This validates the reliability of the theoretical framework. Finally, the effects of particle size distributions and interphase thicknesses on the interphase fraction are investigated. It can be found that the interphase fraction increases with the increase of particle volume fraction, particle fineness and interphase thickness.

Kinematic Model of Transient Shape-Induced Anisotropy in Dense Granular Flow.

Nonspherical particles are ubiquitous in nature and industry, yet previous theoretical models of granular media are mostly limited to systems of spherical particles. The problem is that in systems of nonspherical anisotropic particles, dynamic particle alignment critically affects their mechanical response. To study the tendency of such particles to align, we propose a simple kinematic model that relates the flow to the evolution of particle alignment with respect to each other. The validity of the proposed model is supported by comparison with particle-based simulations for various particle shapes ranging from elongated rice-like (prolate) to flattened lentil-like (oblate) particles. The model shows good agreement with the simulations for both steady-state and transient responses, and advances the development of comprehensive constitutive models for shape-anisotropic particles.

Shape effects on time-scale divergence at athermal jamming transition of frictionless non-spherical particles

The critical behaviors of a granular system at the jamming transition have been extensively studied from both mechanical and thermodynamic perspectives. In this work, we numerically investigate the jamming behaviors of a variety of frictionless non-spherical particles, including spherocylinder, ellipsoid, spherotetrahedron and spherocube. In particular, for a given particle shape, a series of random configurations at different fixed densities are generated and relaxed to minimize interparticle overlaps using the relaxation algorithm. We find that as the jamming point (i.e., point J) is approached, the number of iteration steps (defined as the “time-scale” for our systems) required to completely relax the interparticle overlaps exhibits a clear power-law divergence. The dependence of the detailed mathematical form of the power-law divergence on particle shapes is systematically investigated and elucidated, which suggests that the shape effects can be generally categorized as elongation and roundness. Importantly, we show the jamming transition density can be accurately determined from the analysis of time-scale divergence for different non-spherical shapes, and the obtained values agree very well with corresponding ones reported in literature. Moreover, we study the plastic behaviors of over-jammed packings of different particles under a compression–expansion procedure and find that the jamming of ellipsoid is much more robust than other non-spherical particles. This work offers an alternative approximate procedure besides conventional packing algorithms for studying athermal jamming transition in granular system of frictionless non-spherical particles.

A Granular System of Ellipses under Linear Shear

Shear of granular systems of disks (in 2D) and spheres (3D) has been studied extensively. However, less is known about systems of non-spherical particles, i.e., ellipses and polygons, etc. Here we studied a quasi 2D granular system composed of ellipses in a novel apparatus, which provided homogeneous simple shear by utilizing the weak friction between ellipses and the deformable base of the apparatus. Shear jamming, which was first reported for a disk system [1], was also observed for our ellipse system. We contrast shear jamming for systems of disks and systems of ellipses. By tracking the positions and orientations of the ellipses, we observed that the ellipses gradually rotated to align along a preferred direction as the shear strain increased. We also applied Voronoi tessellation to the packing of ellipses, showing that the distribution of the local density changed during shear. By contrast, such a change in the distribution was not observed in a disk system [2].

非球形颗粒碰撞过程硬颗粒与软颗粒模型比较研究

在能源化工过程、矿业冶金及安全生产过程中均会涉及复杂的实际非球形颗粒体系，而颗粒的非球形碰撞动力学过程是对复杂颗粒体系进行研究必须要考虑的基本问题。离散元方法通过弹簧、阻尼、摩擦三种力学特性对颗粒-颗粒接触力进行建模，是目前国际上最为广泛使用的针对球形颗粒体系的模型。本文对典型三角形非球形碰撞动力学工程过程进行理论分析和模型比较研究，对国际上目前正在研究的硬颗粒和软颗粒非球形碰撞模型进行了比较。通过模型比较，证明了在工程上可以接受的计算误差范围内，软颗粒和硬颗粒计算结果吻合较好，两者在计算精度、稳定性、适用性方面各有优势，可以在不同的应用场合分别采用不同的计算模型。 Non-spherical particles and complex non-spherical particle systems are commonly encountered in energy chemical engineering, mineral engineering, and safety manufacturing engineering. The collision dynamics of non-spherical particles are fundamental issues in the investigations of complex particle systems. Discrete element method is the most prevalent models for particle-particle collision of spherical shapes, which incorporates a spring, a dashpot, and a frictional interaction. In this work, a comparative and analytical study on the mathematical models of collision dynamics for non-spherical particles is carried out. The hard non-spherical particle model and the soft-par- ticle model have been compared. It indicates that agreeable simulation results can be found for the two models. The two models have different advantages or disadvantages in accuracy, computational stability, and feasibility, with particular suitability for different cases.

Efficient computation of the scattering intensity from systems of nonspherical particles

The analysis of the angle dependence of the elastic scattering of radiation from a sample is an efficient and non-invasive technique that is used in fundamental science, in medicine and in technical quality control in industry. Precise information on the shape, size, polydispersity and interactions of a colloidal sample is readily obtained provided an underlying scattering model, i.e. form and structure factors, can be computed for the sample. Here, a numerical method that can efficiently compute the form factor amplitude (and thus the scattering intensity) of nonspherical scatterers through an importance sampling algorithm of the Fourier integral of the scattering density is presented. Using the precomputed form factor amplitudes, the calculation of the scattering intensity at any particle concentration then scales linearly with the particle number and linearly with the number of q points for its evaluation. This is illustrated by an example calculation of the scattering by concentrated suspensions of ellipsoidal Janus particles and the numerical accuracy for the computed form factor amplitudes is compared with analytical benchmarks.

Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra

Numerous recent investigations have been devoted to the determination of the equilibrium phase behavior and packing characteristics of hard nonspherical particles, including ellipsoids, superballs, and polyhedra, to name but just a few shapes. Systems of hard nonspherical particles exhibit a variety of stable phases with different degrees of translational and orientational order, including isotropic liquid, solid crystal, rotator and a variety of liquid crystal phases. In this paper, we employ a Monte Carlo implementation of the adaptive-shrinking-cell (ASC) numerical scheme and free-energy calculations to ascertain with high precision the equilibrium phase behavior of systems of congruent Archimedean truncated tetrahedra over the entire range of possible densities up to the maximal nearly space-filling density. In particular, we find that the system undergoes two first-order phase transitions as the density increases: first a liquid-solid transition and then a solid-solid transition. The isotropic liquid phase coexists with the Conway-Torquato (CT) crystal phase at intermediate densities, verifying the result of a previous qualitative study [ J. Chem. Phys. 2011 , 135 , 151101 ]. The freezing- and melting-point packing fractions for this transition are respectively ϕF = 0.496 ± 0.006 and ϕM = 0.591 ± 0.005. At higher densities, we find that the CT phase undergoes another first-order phase transition to one associated with the densest-known crystal, with coexistence densities in the range ϕ ∈ [0.780 ± 0.002, 0.802 ± 0.003]. We find no evidence for stable rotator (or plastic) or nematic phases. We also generate the maximally random jammed (MRJ) packings of truncated tetrahedra, which may be regarded to be the glassy end state of a rapid compression of the liquid. Specifically, we systematically study the structural characteristics of the MRJ packings, including the centroidal pair correlation function, structure factor and orientational pair correlation function. We find that such MRJ packings are hyperuniform with an average packing fraction of 0.770, which is considerably larger than the corresponding value for identical spheres (≈ 0.64). We conclude with some simple observations concerning what types of phase transitions might be expected in general hard-particle systems based on the particle shape and which would be good glass formers.

Characterisation of the effects of particle shape using a normalised contact eccentricity

In discrete element modelling it is quite common to employ rolling friction models to mimic the effects of particle shape. This paper presents an investigation of the mechanisms at play when using this technique and compares the behaviour of a rolling friction model with various non-spherical particle systems. The motivation behind this work revolves around forming a theoretical framework behind the selection of a coefficient of rolling friction. As a part of this study, we describe an approach where the normalised average contact eccentricity of non-spherical particles (in this case multispheres) is used to characterise the effects of shape. This description is found to capture some aspects of material behaviour reasonably well. When compared to the behaviour of a common rolling friction model, it was found that similar behaviour could be approximated by spheres with a coefficient of rolling friction equal to one half of the normalised eccentricity of non-spherical material. This is approximately in-line with previous studies involving 2D polyhedral particles (Estrada et al. in Phys Rev E 84:011306, 2011).

Granular shear flows of flat disks and elongated rods without and with friction

Granular shear flows of flat disks and elongated rods are simulated using the Discrete Element Method. The effects of particle shape, interparticle friction, coefficient of restitution, and Young's modulus on the flow behavior and solid phase stresses have been investigated. Without friction, the stresses decrease as the particles become flatter or more elongated due to the effect of particle shape on the motion and interaction of particles. In dense flows, the particles tend to have their largest dimension aligned in the flow direction and their smallest dimension aligned in the velocity gradient direction, such that the contacts between the particles are reduced. The particle alignment is more significant for flatter disks and more elongated rods. The interparticle friction has a crucial impact on the flow pattern, particle alignment, and stress. Unlike in the smooth layer flows with frictionless particles, frictional particles are entangled into large masses which rotate like solid bodies under shear. In dense flows with friction, a sharp stress increase is observed with a small increase in the solid volume fraction, and a space-spanning network of force chains is rapidly formed with the increase in stress. The stress surge can occur at a lower solid volume fraction for the flatter and more elongated particles. The particle Young's modulus has a negligible effect on dilute and moderately dense flows. However, in dense flows where the space-spanning network of force chains is formed, the stress depends strongly on the particle Young's modulus. In shear flows of non-spherical particles, the stress tensor is found to be symmetric, but anisotropic with the normal component in the flow direction greater than the other two normal components. The granular temperature for the non-spherical particle systems consists of translational and rotational temperatures. The translational temperature is not equally partitioned in the three directions with the component in the flow direction greater than the other two. The rotational temperature is less than the translational temperature at low solid volume fractions, but may become greater than the translational temperature at high solid volume fractions.

ROLE OF MODEL PARTICLE SHAPE IN DISCRETE ELEMENT MODELS OF BED STRUCTURE IN CONTAINERS

ABSTRACT A container comprising 5,000 particles was simulated to investigate the role of particle shape on the bed structure of particulate materials. The effect of particle shape on the packing structure of granular beds was investigated in terms of bed height, the distribution of solid fraction, coordination number and the force acting at the bottom of the container. The solid fraction of the beds, which ranged from 0.7–0.9 for spherical particles and 0.6–0.8 for elongated particles, shows a compacted structure for beds of spherical particles. The average bed's solid fraction was 0.825 and 0.750 for beds of spherical and elongated particles, respectively. The overall reduction in the average solid fraction was about 8% as aspect ratio of particles changed from 1 to 4. The solid fraction frequency distribution of the beds implied a wider variety of void shape and size for elongated particles. There was also a significant difference between the coordination number of spherical particles and nonspherical particles. The coordination number was 4.7 and 3.6 for spherical and elongated particles, respectively. However, the change in the magnitude of coordination number was greater (15.1%) in between beds of spherical and nonspherical particles (particles of aspect ratio 2), than in between beds with aspect ratio 2 and 4 (11.3%). The numerical results indicated that for a reliable prediction of real material behavior via discrete element models, the employed model should be capable of manipulating individual elements with shape as close as possible to the shape of real particles. PRACTICAL APPLICATIONSAs most of the agricultural materials comprise a system of individual nonspherical particles, a suitable discrete element (DE) model should be employed to gain realistic results. The DE models with spherical particles are very simple, which are less costly, while these models cannot predict the accurate behavior of systems comprising nonspherical particles. Hence, for such materials, using nonspherical models such as multisphere models is a must. Examples of such produce that need models with nonspherical or elongated elements are kernels and some fruits, whereas some other agricultural particles that are nearly spherical can be successfully simulated with DE models of spherical elements. The DE model employing the multisphere method (MSM) can be used for either case (spherical or nonspherical) to study the agricultural particulate materials processing operations on a particle scale (microscale), such as collision forces between individual grain and fruits that cannot easily be gained from experiments.

Incoherent and coherent backscattering of light by a layer of densely packed random medium

The problem of light scattering by a layer of densely packed discrete random medium is considered. The theory of light scattering by systems of nonspherical particles is applied to derive equations corresponding to incoherent (diffuse) and interference parts of radiation reflected from the medium. A solution of the system of linear equations describing light scattering by a system of particles is represented by iteration. It is shown that the symmetry properties of the T -matrices and of the translation coefficients for the vector Helmholtz harmonics lead to the reciprocity relation for an arbitrary iteration. This relation is applied to consider the backscattering enhancement phenomenon. Equations expressing the incoherent and interference parts of reflected light from statistically homogeneous and isotropic plane-parallel layer of medium are given. In the exact backscattering direction the relation between incoherent and interference parts is identical to that of sparse media.