Dense Random Packing Research Articles

Estimating random close packing density from circle radius distributions.

Circles of a single size can pack together densely in a hexagonal lattice, but adding in size variety disrupts the order of those packings. We conduct simulations which generate dense random packings of circles with specified size distributions and measure the area fraction in each case. While the size distributions can be arbitrary, we find that for a wide range of size distributions the random close-packing area fraction ϕ_{rcp} under this general protocol is determined to high accuracy by the polydispersity and skewness of the size distribution. At low skewness, all packings tend to a minimum packing fraction ϕ_{0}≈0.840 independent of polydispersity. In the limit of high skewness, ϕ_{rcp} becomes independent of skewness, asymptoting to a polydispersity-dependent limit. We show how these results can be predicted from the behavior of bidisperse or bi-Gaussian circle size distributions.

Dense random packing of disks with a power-law size distribution in thermodynamic limit.

The correlation properties of a random system of densely packed disks, obeying a power-law size distribution, are analyzed in reciprocal space in the thermodynamic limit. This limit assumes that the total number of disks increases infinitely, while the mean density of the disk centers and the range of the size distribution are kept constant. We investigate the structure factor dependence on momentum transfer across various number of disks and extrapolate these findings to the thermodynamic limit. The fractal power-law decay of the structure factor is recovered in reciprocal space within the fractal range, which corresponds to the range of the size distribution in real space. The fractal exponent coincides with the exponent of the power-law size distribution as was shown previously by the authors of the work of Cherny et al. [J. Chem. Phys. 158(4), 044114 (2023)]. The dependence of the structure factor on density is examined. As is found, the power-law exponent remains unchanged but the fractal range shrinks when the packing fraction decreases. Additionally, the finite-size effects are studied at extremely low momenta of the order of the inverse system size. We show that the structure factor is parabolic in this region and calculate the prefactor analytically. The obtained results reveal fractal-like properties of the packing and can be used to analyze small-angle scattering from such systems.

Effect of aspect ratio of ellipsoidal particles on segregation of a binary mixture in a rotating drum

In this work, the Discrete Element Method (DEM) is used to investigate the evolution of radial segregation and its dependence on the shape by varying the particle’s aspect ratio. A total of 37 different types of binary mixtures are created, where the aspect ratio of particles varies from 0.25 to 4.0. The results shows that in binary mixture the aspect ratio of both coarse and fine particles influence mixing. The initial well-mixed binary mixture of coarse and fine particles evolves into a radial segregated state where the fine particles occupy a central core of the drum surrounded by coarse particles. Spherical shape particles, whether acting as coarse or fine in binary mixture, promote segregation. Two characteristics of particles i.e., Monodisperse random packing density and sphericity are used to explain the segregation trend and its relationship to aspect ratio.

Short- and medium-range ordering in Al3Mn amorphous alloy prepared by magnetron sputtering

The structure of the Al3Mn amorphous alloy synthesized by magnetron sputtering was investigated using a combination of anomalous X-ray scattering and reverse Monte Carlo simulations. The geometrical features in the short- and medium-range regions around Mn were significantly different from those inferred by the dense random packing of the hard-sphere model, suggesting that the environmental structure around Mn is influenced by chemical interactions similar to those realized in the crystalline Al3Mn structure. The present advanced analysis also indicated that the medium-range ordering structure corresponding to a pre-peak signal in the X-ray diffraction profiles was because of the Al-Mn and Mn-Mn correlations accompanied by the modulation of number density and non-Bernal-type coordination geometry.

Dense random packing with a power-law size distribution: The structure factor, mass-radius relation, and pair distribution function.

We consider a dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation, and pair distribution function of the disk centers. A toy model of dense segments in one dimension (1D) is solved exactly. It is shown theoretically in 1D and numerically in 1D and 2D that such a packing exhibits fractal properties. It is found that the exponent of the power-law distribution and the fractal dimension coincide. An approximate relation for the structure factor in arbitrary dimensions is derived, which can be used as a fitting formula in small-angle scattering. These findings can be useful for understanding the microstructural properties of various systems such as ultra-high performance concrete, high-internal-phase-ratio emulsions, or biological systems.

Experimental investigation of segregation in a rotating drum with non-spherical particles

The focus of the current investigation is to study the influence of particles’ shape on segregation of bi-disperse mixture of particles in a rotating drum. The effects of various particle parameters such as shape, size, density and size ratio are investigated along with system parameters like time, rotational speed. The results show the shape of both coarse and fine particles influence mixing. For the coarse particles, decreasing trend of extent of radial segregation as follows: sphere > oblate > prolate > elongated-needle. For the fine particle, the trend follows as sphere > cube > prolate. These trends are strongly correlated to the mono-dispersed random packing density and particle angularity. The result shows that coarse particles with higher mono-dispersed random packing density show less segregation whereas fine particles with greater angularity improves mixing. Segregation can be controlled in multiple scenarios in industries by choosing the appropriate shape of the particles. • Coarse particles with higher mono-dispersed random packing density promote mixing. • For coarse particles segregation pattern: Sphere >oblate >prolate >elongated needle. • The fine particles with greater angularity promote mixing. • For fine particles segregation pattern: Sphere >cube >prolate.

Descriptor-free unsupervised learning method for local structure identification in particle packings.

Local structure identification is of great importance in many scientific and engineering fields. However, mathematical and supervised learning methods mostly rely on specific descriptors of local structures and can only be applied to particular packing configurations. In this work, we propose an improved unsupervised learning method, which is descriptor-free, for local structure identification in particle packing. The point cloud is used as the input of the improved method, which directly comes from spatial positions of particles and does not rely on specific descriptors. The improved method constructs an autoencoder based on the point cloud network combined with Gaussian mixture models for dimension reduction and clustering. Numerical examples show that the improved method performs well in local structure identification of quasicrystal disk and sphere packings, achieving comparable accuracy with previous methods. For disordered packings, which have been considered having nearly no local structures, the improved method identifies a nontrivial seven-neighbor motif in the maximally dense random packing of disks and finds acentric structural motifs in the random close packing of spheres, which demonstrate the ability on identification of new and unknown local structures. The improved unsupervised learning method would help obtain information from massive simulation and experimental results as well as devising new order parameters for particle packings.

Discrete element modeling of 3D irregular concave particles: Transport properties of particle-reinforced composites considering particles and soft interphase effects

Particles of complex morphologies and their surrounding soft interphase are main constituents that play a significant role in the transport properties of particle-reinforced composites (PRCs). It has been a crucial but unresolved issue how to derive the volume fraction of soft interphase around three-dimensional (3D) irregular concave particles, as well as it remains to be virgin to explore the effective transport properties of three-phase PRCs composed of homogeneous matrix, 3D irregular concave particles of a relatively high packing density and their surrounding soft interphase. To this end, this work initially develops a discrete element modeling (DEM) of 3D irregular concave particles with monodispersity in size to generate random dense packing structures, where an innovative mathematical-controllable parameterized method is proposed to devise diverse irregular concave particle shapes. The proposed particle design method is not only universal and controllable to generate a given particle shape, but also can be directly linked with an experimental measurement using digital scanning. In addition, an efficient two-step numerical strategy is presented to check the inter-particle contact detection and collision. Then, the volume fraction of soft interphase around monodisperse concave particles is numerically derived for the first time by using the Monte Carlo random point sampling simulation. The Monte Carlo simulation has good accuracy to obtain the soft interphase volume fraction, which is confirmed by comparing with the theoretical formulae for spherical particle systems. Next, a dual-probability-Brownian motion (DP-BM) scheme along with the level set algorithm is extended to investigate the effective transport properties like thermal conductivity of three-phase PRCs. Comparison against the finite element method (FEM), the proposed DP-BM scheme is more user-friendly and efficient to estimate the effective transport properties of PRCs within an accuracy level. The proposed DP-BM scheme can overcome the two intrinsic limitations of the classical effective medium approximations that one limitation is the ellipsoidal inclusion shape and another is a relative dilute level of inclusion volume fraction. Moreover, the effects of the concave particle shape and packing density, and the interphase dimension on the volume fraction of soft interphase and the effective normalized transport properties of PRCs are evaluated. The results elucidate rigorous component-structure–property relations, which can provide sound guidance for durability evaluation and material design of PRCs.

Packing Fraction, Tortuosity, and Permeability of Granular‐Porous Media With Densely Packed Spheroidal Particles: Monodisperse and Polydisperse Systems

AbstractThe geometrical and topological configurations of particles have great influences on their surrounding pore tortuosity and the permeability of granular‐porous media. In this work, we develop a relaxation iteration scheme to create random dense packings of different anisotropic‐shaped spheroidal particles with monodispersity and polydispersity in sizes, which manifest the effects of particle shape, fineness, and size distribution on the random packing fraction of particles. Subsequently, we propose a direction‐guided rapidly exploring random tree (DGRRT) algorithm to probe the geometrical tortuosity of complex pore space interstitial to spheroidal particles. A non‐linear pore tortuosity prediction model that relies on the specific surface area and packing fraction of particles, is developed to suit for polydisperse and monodisperse spheroidal particle systems. We further investigate the permeability of granular‐porous media through the lattice Boltzmann method (LBM) of fluid flow. These proposed methods can accurately predict the tortuosity and permeability by comparing against available experimental, theoretical, and numerical results reported in literature. Moreover, the effects of particle packing fraction (i.e., porosity), shape, fineness, and size distribution on the pore tortuosity and permeability of granular‐porous media are evaluated. The results reveal that these microstructural configurations have important influences on the permeability and tortuosity. Our results give an intrinsic interplay between the geometrical tortuosity and permeability of monodisperse and polydisperse particle systems, which have implications for a broad range of scientific disciplines, including the properties of rocks, sandstones and soils, and the design of ultra‐high performance concrete.

Experimental study on bulk modulus and dissipation of dry and wet granular samples under vertical vibration

Dry granular materials are composed of a dense random packing of macroscopic grains. As a small amount of liquid is added to granular samples, the liquid bridge forces, i.e. the forces between liquid and the grains, have an influence on the mechanical properties of wet granular material, and some of these properties are quite different from those of dry granular materials. In this work, by measuring the acceleration of the sample chamber and the force exerted on it by the shaker, the variations of bulk modulus and energy dissipation of both dry and wet glass bead samples with pressure and viscosity under vertical vibration are studied. The results are shown below. 1) Under low saturation, the bulk modulus of dry and wet glass bead sample are both described by a power law scaling law with pressure, which is close to the power law relationship predicted by the efficient medium theory on the basis of Hertz contact potential. A small amount of liquid can increase the bulk modulus of glass bead sample. At the same pressure and liquid content, the bulk modulus of wet glass bead sample increases with liquid viscosity increasing. Based on Hertzian contact mechanics, an efficient elastic network model is proposed to illustrate the mechanism of increasing bulk modulus of wet glass bead samples. 2) The energy dissipation of dry and wet glass bead sample decrease following the power law of pressure, and the energy dissipation of wet glass bead samples is proportional to the kinematic viscosity of liquid. 3) With the increase of strain amplitude, the softening behavior of the wet glass bead sample is similar to that of the dry glass bead sample, when the strain amplitude is higher than the strain threshold value. The kinematic viscosity of liquid inhibits the softening behavior of glass bead sample.

Prediction of random packing density and flowability for non-spherical particles by deep convolutional neural networks and Discrete Element Method simulations

Non-spherical particles can be found in many industrial processes. Unfortunately, scalar shape parameters are often insufficient to predict their complex behavior. Therefore, this study used convolutional neural networks (CNN), which are able to interpret abstract shape features to derive the flow and packing behavior. For training data generation, experimentally validated Discrete Element Method simulations of silo filling and discharge were conducted. The subsequent training of the neural network was achieved with extensive input data augmentation. The CNN was then applied for the investigation of common shapes like ellipsoids or frustums for validation. The trained network showed good accordance to literature and high predictive robustness. Finally, the CNN assessed various food grains and tablet shapes. The network predicted the densest packing and best flowability for rounded lentils, whereas long rice kernels showed poor flow behavior. For pharmaceutical tablets, rounded and hexagonal shapes were predicted to yield denser packings than plain cylinders.

Structure of basaltic glass at pressures up to 18 GPa

Abstract The structures of cold-compressed basaltic glass were investigated at pressures up to 18 GPa using in situ X-ray and neutron diffraction techniques to understand the physicochemical properties of deep magmas. On compression, basaltic glass changes its compression behavior: the mean O-O coordination number (CNOO) starts to rise while maintaining the mean O-O distance (rOO) above about 2–4 GPa, and then CNOO stops increasing, and rOO begins to shrink along with the increase in the mean coordination number of Al (CNAlO) above ~9 GPa. The change around 9 GPa is interpreted by the change in contraction mechanism from bending tetrahedral networks of glass to increasing oxygen packing ratio via the increase in CNAlO. The analysis of the oxygen packing fraction (ηO) under high pressure reveals that ηO exceeds the value for dense random packing, suggesting that the oxygen-packing hypothesis recently proposed cannot account for pressure-induced structural transformations of silica and silicate glasses. The rise of the CNOO at 2–4 GPa reflects the elastic softening of fourfold-coordinated silicate glass, which may be the origin of anomalies of elastic moduli in basaltic glass at ~2 GPa previously reported by Liu and Lin (2014). The widths of both the first sharp diffraction peak and the principal peak show contrastive compression behaviors between modified silicate and silica glasses. This result suggests that modified silicate glasses represent different pressure evolutions in the intermediate- and extended-range order structures from those of silica glass, likely due to the presence of modifier cations and the resultant formations of smaller rings and cavity volume.

Fine Structure of Zr<sub>80</sub>Pt<sub>20</sub> Amorphous Alloy Determined from Anomalous X-ray Scattering (AXS) Data by Applying Reverse Monte-Carlo (RMC) Simulation Method

The fine structure of a Zr80Pt20 amorphous alloy was evaluated by anomalous X-ray scattering (AXS) coupled with reverse Monte Carlo (RMC) simulation. Featureless short-range ordered structures were preferentially formed by the Zr component, similar to those described by dense random packing (DRP), while the Pt atoms adopted a somewhat different structure. The Pt atoms adopted Zr-rich coordination and an icosahedral local atomic arrangement, in unique chemical short-range ordering (CSRO) as well as topological short-range ordering (TSRO). The present AXS-RMC analysis also suggested that the pre-peak signal at 17 nm−1 in the X-ray diffraction profile was largely attributed to the correlation between the Pt–Pt pair with a separation of approximately 0.4–0.5 nm. The geometrical and chemical features of the common neighbors of the middle-range Pt–Pt pairs indicate the unique CSRO and TSRO, where both chemical and density fluctuations were observed in two distinct regions: a Zr-rich region with high packing density and a Pt-rich region with low packing density.

Magnetic ordering of random dense packings of freely rotating dipoles

We study random dense packings of Heisenberg dipoles by numerical simulation. The dipoles are at the centers of identical spheres that occupy fixed random positions in space and fill a fraction $\Phi$ of the spatial volume. The parameter $\Phi$ ranges from rather low values, typical of amorphous ensembles, to the maximum $\Phi$=0.64 that occurs in the random-close-packed limit. We assume that the dipoles can freely rotate and have no local anisotropies. As well as the usual thermodynamical variables, the physics of such systems depends on $\Phi$. Concretely, we explore the magnetic ordering of these systems in order to depict the phase diagram in the temperature-$\Phi$ plane. For $\Phi \gtrsim0.49$ we find quasi-long-range ferromagnetic order coexisting with strong long-range spin-glass order. For $\Phi \lesssim0.49$ the ferromagnetic order disappears giving way to a spin-glass phase similar to the ones found for Ising dipolar systems with strong frozen disorder.

Detailed modeling of sorptive and textural properties of CaO-based sorbents with various porous structures

In the current study, the volume-sintering model was implemented for the simulation of sorption/desorption and textural evolution of the set of CaO-based sorbents with broad differences in porous structure. The porous structure of the materials was modeled with the dense random packing of spheres using the Lubachevsky–Stillinger compression algorithm. The simulated packages were fitted to the parameters of the porous structure of real templated and non-templated CaO-based sorbents. The sintering of the packages during sorption/regeneration cycles was carried out based on the assumptions of the lattice diffusion mechanism and the sintering rate of CaCO3 being higher than that of CaO in the proposed model. The obtained model predicts well the dependence of textural changes and the recarbonation extent on the number of the sorption/regeneration cycles for the sorbents with different porosity and grain size.

Uniform shape elongation effects on the random packings of uniaxially variable superellipsoids

Uniaxially variable (rod-like) particles are common in nature and industry. However, the aspect ratio effects on the random packings for differently shaped rod-like particles are not uniform by their innate definitions of aspect ratios. In this work, we propose new definitions of effective aspect ratios that take the surface shape information into account and observe uniform shape elongation effects on the random packing densities. The packing density reaches a maximal value with the effective aspect ratio to be about 1.5. We also observe symmetric high-density regions on the packing-density map. Finally, we carry out the Voronoi analysis and find that the surface shape of particles plays a more important role in changing the local packing properties than the aspect ratio. Our work provides a uniform definition for the aspect ratio of differently shaped rod-like particles and leads to a better understanding towards the particle shape effects on random packings.

A discrete element study of the effect of particle shape on packing density of fine and cohesive powders

Fine and cohesive powders typically exhibit low packing density, with solid volume fraction around 0.3. Discrete element modelling (DEM) of particulate materials and processes typically employs spherical particles which have much larger solid fractions (e.g. 0.64 for dense random packing of frictionless spheres). In this work a range of quasi-spherical particles are designed, represented by a number of small satellites connected rigidly to a larger centre sphere. Using DEM, packing density is found to be controlled by the interplay between particle shape, size and inter-particle cohesion and friction. Low packing density is obtained for an appropriate combination of (1) particle shape that allows the creation of geometrically loose structures via separation of the central particles by the satellites, (2) particle size that should be sufficiently small so that adhesive forces between particles become dominant over gravity, (3) adhesive forces, determined from surface energy, should be sufficiently large, and (4) friction (static friction was found to have a dominant role compared to rolling friction, but negligible compared to adhesive forces for small particle size). By using the proposed quasi-spherical particle designs it becomes possible to calibrate more realistic DEM models for particulate processes that reproduces not only packing, but also other behaviours of bulk powders.

Shape effects on packing properties of bi-axial superellipsoids

We generate the maximally random jammed (MRJ) packings and maximally dense random packings (MDRPs) of bi-axially elongated superballs with different shape parameters. On the MRJ packing state, the packings of ellipsoids, general superellipsoids and cuboids are on different random degrees and the shape elongation effects on the disordered-packing densities are not uniform. The effects of order degree and particle shape are compounded. However, we find uniform shape elongation effects on the MDRP state. Bi-axial elongation will improve the random-packing densities. The packing densities reach the maximum when the aspect ratio is about 1.5 for all the surface shape parameters and oblateness. The influence of order degree is eliminated on the MDRP state, which demonstrates the advantages of the MDRP state as a platform for comparing the packing density of disordered packings. Our work helps to explore the shape effects on disordered packings of non-spherical particles.

Review of structural models for the compositional interpretation of metallic glasses

ABSTRACTComposition interpretation of metallic glasses with high glass-forming abilities is an important issue, which relies on insights into their complex atomic structures. With the aim of illustrating the advance in structural modelling of metallic glasses, representative atomic and electronic structural models are summarised in this review, including Bernal’s dense random packing model, Gaskell’s stereochemical model, Miracle’s efficient cluster packing model, Nagel and Tauc’s nearly free electron model, Häussler’s global resonance model, and our cluster-plus-glue-atom and cluster-resonance models. Their capabilities as well as limitations to interpret compositions of good glass formers are focused. With aides of these theoretical models, fairly accurate interpretation and eventually design of metallic glasses with large glass-forming abilities could be envisaged.

Maximum Possible Densities of Random Sphere Packing Within the Composite

The maximum possible densities of random equal-sphere packing have been established. The maximum random packing densities Φn for spaces with dimensions n = 1–4 have been determined by numerical experiment based on the Monte Carlo simulation. If the established maximum possible density is exceeded, spatial correlations occur in the system. They are manifested as oscillations of the pair correlation function at small distances and as significantly greater viscosity of the sphere system. The application of the experimental results to polymer matrices reinforced with glass or basalt microspheres is under discussion. In particular, it has been reasonably assumed that compositions suitable for producing high-quality composites by die casting should not have packing density higher than Φ3 = 0.359 for a three-dimensional space.