Local Packing Fraction Research Articles

Link between permanent shear-banding and local concentration fluctuations in suspensions of compressible microgels

We uncover the occurrence of shear banding in dense suspensions of compressible microgels. Velocimetry measurements evidence the presence of permanent but unsteady shear-banding for sufficiently small Peclet numbers, with the formation of a central plug-like flow. Small-angle neutron scattering experiments under shear link the observed banding phenomenon to structural variations along the velocity gradient, providing a connection between the arrested band and the increase in structural correlations associated with changes in the local packing fraction. This provides unique evidence of a shear–concentration coupling mechanism in jammed suspensions of compressible particles.

Hole statistics of equilibrium 2D and 3D hard-sphere crystals.

The probability of finding a spherical "hole" of a given radius r contains crucial structural information about many-body systems. Such hole statistics, including the void conditional nearest-neighbor probability functions GV(r), have been well studied for hard-sphere fluids in d-dimensional Euclidean space Rd. However, little is known about these functions for hard-sphere crystals for values of r beyond the hard-sphere diameter, as large holes are extremely rare in crystal phases. To overcome these computational challenges, we introduce a biased-sampling scheme that accurately determines hole statistics for equilibrium hard spheres on ranges of r that far extend those that could be previously explored. We discover that GV(r) in crystal and hexatic states exhibits oscillations whose amplitudes increase rapidly with the packing fraction, which stands in contrast to GV(r) that monotonically increases with r for fluid states. The oscillations in GV(r) for 2D crystals are strongly correlated with the local orientational order metric in the vicinity of the holes, and variations in GV(r) for 3D states indicate a transition between tetrahedral and octahedral holes, demonstrating the power of GV(r) as a probe of local coordination geometry. To further study the statistics of interparticle spacing in hard-sphere systems, we compute the local packing fraction distribution f(ϕl) of Delaunay cells and find that, for d ≤ 3, the excess kurtosis of f(ϕl) switches signat a certain transitional global packing fraction. Our accurate methods to access hole statistics in hard-sphere crystals at the challenging intermediate length scales reported here can be applied to understand the important problem of solvation and hydrophobicity in water at such length scales.

Numerical Analysis of Non-Sphericity of Particles of Powder Material and their Effect on Packing Structure for Concentrated Solar Power Applications

Concentrated solar power technology represents a novel approach to generating solar power, characterized by high solar radiation density and uninterrupted operation. To store thermal energy and extend system operating hours, concentrated solar power systems rely on thermal energy storage. Selecting the appropriate heat storage media is crucial for designing a cost-efficient and straightforward system capable of withstanding high processing conditions. Among many powder materials, bauxite powder stands out as alternatives to conventional molten salt for thermal storage media due to its widespread availability and suitability for operating conditions. Particle shape, particularly its sphericity, plays a vital role in efficiently packing particles which directly affects to heat transfer properties. To investigate this effect, three samples of particles with different shape were formed: spheres, ellipses, and cylinders using Discrete Element Method with equal volume and material properties, and only variation of their sphericity factors. The study focused on the analysis of the porosity of the packed bed of particles with different shapes and its influence on the packing structure properties. The analysis of local packing fraction revealed that elliptical and cylindrical particles samples exhibited reduced heap formation and a more uniform distribution along z direction during vertical packing. The coordination number and radial distribution function analyses for these non-spherical particles showed a greater number of contacts between particles and disordered distribution of particles due to mechanical interlocking of non-spherical particles. The results indicated that the deviation of sphericity has a positive impact on the denser packing of particles generated more contacts and higher local packing fraction.

Identifying strain-dependent structural defects in granular materials from the hidden structure-plasticity relationship

When subjected to mechanical loads, granular materials exhibit heterogeneous local plastic responses. Although there is a general consensus that such plastic heterogeneity is closely correlated to the structure configuration, the extent and manner in which the initial particle structure determines the plastic dynamics remain ill-understood due to the complex local environment of granular materials. In this study, we present an investigation of the structural origin of shear-induced plastic heterogeneity through a series of numerical triaxial shear tests. A machine learning (ML) framework is employed to address the hidden relationship between the initial structure configuration and plasticity at different loading stages. It is confirmed that there are some pre-existing structural defects independent of loading protocol which is the origin of small strain plastic rearrangements and can be identified with outstanding accuracy by our trained ML models. We then show that the dominant structural features determining plasticity depend on strain, wherein the plastic activity at small strains is governed by contact number but becomes dominated by local packing fraction at large strains. By exploring the temporal correlation of the two structural features, we finally prove this transition results from the differences in their memory effects.

Effects of the Aspect Ratio and Cross-Sectional Area of Rectangular Tubes on Packing Characteristics of Mono-Sized Pebble Beds

The packing characteristics of a pebble bed are essential to understand the heat- and mass-transfer processes occurring within a granular system. Therefore, the packing characteristics of rectangular prismatic pebble beds randomly packed with mono-sized pebbles are analyzed. In terms of the average and local packing fraction distribution, coordination number, and radial distribution function, the effects of the rectangular tube aspect ratio and cross-sectional area on the packing properties of pebble beds are explored in depth. The findings indicate that the packing structures of the rectangular pebble bed exhibit noticeable fixed-wall effects. The average packing fraction and coordination number gradually decline as the rectangular tube aspect ratio rises. Close to the fixed wall, a noticeable wall effect can be seen in the distribution of axial and local packing fractions and the pebble center distribution. The wall effect has an increasing effect on the axial and local packing fraction distributions in rectangular tubes with increasing aspect ratios. Additionally, the average packing fraction and the average coordination number also increase as the cross-sectional area increases, indicating a gradual weakening of the wall effect as the cross-sectional area increases. Furthermore, the cross-sectional area and aspect ratio of the rectangular tubes affect the RDF values of the rectangular pebble beds but have no impact on the RDF features. The findings reported in this paper will be helpful for designing and optimizing pebble beds in the breeding blanket of fusion reactors.

Microswimmers under the spotlight: interplay between agents with different levels of activity.

The ability of active matter to assemble into reconfigurable nonequilibrium structures has drawn considerable interest in recent years. We investigate how active fluids respond to spatial light patterns through simulations and experiments on light-activated self-propelled colloidal particles. We examine the processes of inverse templated assembly, which involves creating a region without active particles through a bright pattern, and templated assembly, which promotes the formation of dense particle regions through a dark pattern. We identify scaling relations for the characteristic times for both processes that quantify the interplay between the dimension of the applied pattern and the intrinsic properties of the active fluid. We also explore the assembly mechanism and dynamics of large clusters and show how assembly and inverse assembly can be combined to create any arbitrarily complex template. In addition to providing protocols for templated assembly via light patterning, our results demonstrate how the local packing fraction can be fine-tuned by modulation of the light intensity. The protocol so obtained exceeds the capabilities of conventional assembly strategies, in which packing fraction is dictated by thermodynamics, and opens the door to arbitrarily precise and programmable nonequilibrium assembly strategies in active matter.

Mixing properties of bi-disperse ellipsoid assemblies: mean-field behaviour in a granular matter experiment.

The structure and spatial statistical properties of amorphous ellipsoid assemblies have profound scientific and industrial significance in many systems, from cell assays to granular materials. This paper uses a fundamental theoretical relationship for mixture distributions to explain the observations of an extensive X-ray computed tomography study of granular ellipsoidal packings. We study a size-bi-disperse mixture of two types of ellipsoids of revolutions that have the same aspect ratio of α ≈ 0.57 and differ in size, by about 10% in linear dimension, and compare these to mono-disperse systems of ellipsoids with the same aspect ratio. Jammed configurations with a range of packing densities are achieved by employing different tapping protocols. We numerically interrogate the final packing configurations by analyses of the local packing fraction distributions calculated from the Voronoi diagrams. Our main finding is that the bi-disperse ellipsoidal packings studied here can be interpreted as a mixture of two uncorrelated mono-disperse packings, insensitive to the compaction protocol. Our results are consolidated by showing that the local packing fraction shows no correlation beyond their first shell of neighbours in the binary mixtures. We propose a model of uncorrelated binary mixture distribution that describes the observed experimental data with high accuracy. This analysis framework will enable future studies to test whether the observed mean-field behaviour is specific to the particular granular system or the specific parameter values studied here or if it is observed more broadly in other bi-disperse non-spherical particle systems.

Approximate Packing of Binary Mixtures of Cylindrical Particles.

Particle packing plays an essential role in industry and chemical engineering. In this work, the discrete element method is used to generate the cylindrical particles and densify the binary cylindrical particle mixtures under the poured packing conditions. The influences of the aspect ratio and volume fraction of particles on the packing structure are measured by planar packing fraction. The Voronoi tessellation is used to quantify the porous structure of packing. The cumulative distribution functions of local packing fractions and the probability distributions of the reduced free volume of Voronoi cells are calculated to describe the local packing characteristics of binary mixtures with different volume fractions. As a result, it is observed that particles with larger aspect ratios in the binary mixture tend to orient randomly, and the particles with smaller aspect ratios have a preferentially horizontal orientation. Results also show that the less dense packings are obtained for mixtures with particles of higher aspect ratios and mixtures with a larger fraction of elongated cylindrical particles.

Enhanced flow rate by the concentration mechanism of Tetris particles when discharged from a hopper with an obstacle.

We apply a holistic two-dimensional (2D) Tetris-like model, where particles move based on prescribed rules, to investigate the flow rate enhancement from a hopper. This phenomenon was originally reported in the literature as a feature of placing an obstacle at an optimal location near the exit of a hopper discharging athermal granular particles under gravity. We find that this phenomenon is limited to a system of sufficiently many particles. In addition to the waiting room effect, another mechanism able to explain and create the flow rate enhancement is the concentration mechanism of particles on their way to reaching the hopper exit after passing the obstacle. We elucidate the concentration mechanism by decomposing the flow rate into its constituent variables: the local area packing fraction ϕ_{l}^{E} and the averaged particle velocity v_{y}^{E} at the hopper exit. In comparison to the case without an obstacle, our results show that an optimally placed obstacle can create a net flow rate enhancement of relatively weakly driven particles, caused by the exit-bottleneck coupling if ϕ_{l}^{E}>ϕ_{o}^{c}, where ϕ_{o}^{c} is a characteristic area packing fraction marking a transition from fast to slow flow regimes of Tetris particles. Utilizing the concentration mechanism by artificially guiding particles into the central sparse space under the obstacle or narrowing the hopper exit angle under the obstacle, we can create a manmade flow rate peak of relatively strongly driven particles that initially exhibit no flow rate peak. Additionally, the enhanced flow rate can be maximized by an optimal obstacle shape, particle acceleration rate toward the hopper exit, or exit geometry of the hopper.

Effects of fixed wall and pebble size ratio on packing properties and contact force distribution in binary-sized pebble mixed beds at the maximum packing efficiency state

The binary-sized pebble mixed beds at the maximum packing efficiency state were numerical simulated by the DEM simulation to investigate the effect of fixed wall and pebble size ratios. The evolution of the distribution of packing fraction and porosity, radial distribution function and contact force were given and analyzed with emphasis on the effects of the fixed wall and pebble size ratio. The results showed that the fixed wall will result in a reduction of average packing fraction and an obvious wall effect in local porosity distribution. With the increase of the pebble size ratio, the volume fraction of the wall affected regions gradually decrease. The variation of the local packing fraction of the binary-sized pebble bed is mainly determined by the partial packing fraction of large pebbles and the partial packing fraction of small pebbles, respectively, in the regions close to the fixed wall. Furthermore, the fixed wall has little effect on the radial distribution function and contact force. However, the pebble size ratios have great influence on the radial distribution function and the contact force in binary-sized pebble bed at the maximum packing efficiency state. With the increase of the pebble size ratio, the radial distribution functions of the whole pebble beds are consistent with that of small pebbles, and approach to that of the mono-sized pebble bed. In addition, with the increase of the pebble size ratio, a higher contact force can be obtained in pebble beds.

Morphological Tuning of Nanostructured Hydroxyapatite (HAp) Porous Microgranules by Evaporation-Induced Assembly

Porous biocompatible microgranules, such as hydroxyapatite (HAp), are potential candidates for various bio-medical applications including drug delivery and remediation. Using the principle of evaporation-induced assembly in contact free dispersion droplets, we have synthesized porous micrometric HAp granules consist of interlocked ellipsoidal nanoparticles. We have shown that the shape of the microgranules can be tuned from spherical to doughnut solely by controlling the drying temperature during assembly. The structure and interparticle correlation in the synthesized granules have been probed by electron microscopy and small-angle scattering. The observed morphological transition has been attributed to the buckling of elastic shell made of interlocked HAp nanoparticles. Alteration of granular morphology at higher drying rate does not affect the local packing fraction of the correlated HAp nanoparticles in the granules. The absorption of bovine serum albumin protein by the synthesized granules has been tested as a potential application.

New method for analysis of X-ray computed tomography scans of TRISO fuel forms

X-ray computed tomography (XCT) is a powerful characterization tool that has been used for examination of both tristructural-isotropic (TRISO) coated particles and fuel forms. Rapid, nondestructive imaging of complete specimens by XCT provides significant characterization advantages in both speed and comprehensiveness over traditional materialographic methods. This paper discusses a method that has been developed to analyze XCT images of pebble fuel forms containing ~18,000 TRISO particles each. The XCT images are three-dimensional with contrast based on relative x-ray transparency. In the case of TRISO fuel forms, XCT image intensity distinguishes between the high-density kernel, the medium-density SiC, and the low-density matrix and carbon layers. Image analysis software has been developed to process XCT data sets to extract spatial distribution information, including particle nearest-neighbor distances, local packing fraction, and fuel-free zone thickness in TRISO fuel forms. Although this type of high-resolution XCT analysis is likely not feasible as a quality control measurement for commercial TRISO fuel, it is highly useful in generating feedback for the development of fuel form fabrication processes.

Influence of particle size on vertical plate penetration into dense cohesionless granular materials (large-scale DEM simulation using real particle size)

The influence of the particle size on the vertical plate penetration into dense cohesionless granular materials was numerically investigated. Simulations were performed in quasi-two-dimensional conditions by changing the mean particle diameters d50 but maintaining the plate thickness B from B/d50 = 63–2.6. The initial bulk packing fraction was kept high, irrespective of the particle size. In the smallest particle size case (B/d50 = 63), the size ratio reached almost the same level as that in the laboratory experiments using natural sand particles. The results demonstrated that the mean penetration resistance force acting on the plate tip surface increases with a decrease of B/d50, while the tangential force acting on the side surfaces does not change with B/d50. Tip resistances increase linearly with the penetration depth, while the tangential resistances increase with the square of the depth regardless of B/d50. The behavior of the resistance fluctuations changes qualitatively between B/d50 = 31 and 21. For all cases, we confirmed the formation of a wedge-shaped flow with a high forward velocity in front of the plate tip. The wedge flow width was larger than the plate thickness by almost a mean particle diameter, and was responsible for the increase in the mean resistance depending on the particle size. For the large B/d50 cases only, the resistance exhibited quasi-periodic fluctuations, which was attributable to the intermittent nucleation and disappearance of the shear bands. Moreover, we investigated the dependence of B/d50 on the band evolutions by analyzing the band thickness.Graphic abstractThe influence of the particle size on the vertical plate penetration into dense cohesionless granular materials was numerically investigated using DEM. Simulations were performed in quasi-two-dimensional conditions by changing the median particle diameters d50 but maintaining the plate thickness B. The initial bulk packing fraction was kept high, irrespective of the particle size. Upper and lower figures show the result of small (B/d50 = 63) and large particle size case (B/d50 = 21), respectively. In the small particle size case (B/d50 = 63), the size ratio reached almost the same level as that in the laboratory and the dynamics of 35.5 million particles was considered. Right and left figures illustrate instantaneous shear strain rate and local packing fraction distributions, respectively. Large qualitative change in the granular behaviors as well as penetration resistance was observed between B/d50 = 31 and 21. The intermittent nucleation and disappearance of the shear bands were clearly observed only for large B/d50 cases.

Smoothed particle hydrodynamics simulation of granular system under cyclic compressions

The response of two-dimensional frictionless granular material to isotropic cyclic compression is simulated using an improved version of the Smoothed Particle Hydrodynamics (SPH) method, which includes realistic constitutive model for deformation of individual grains. The study reveals the evolution of mean coordination number and global pressure over cycles. The probability distribution function (PDF) of contact forces for different compression cycles is also reported. The global pressure at maximum compression shows downward trend for packing fractions below a certain value. The structural rearrangement that can give rise to such stress relaxation is studied by mapping relative particle mobilities and quantifying dynamic heterogeneity using a four-point susceptibility measure. The four-point susceptibility measure reveals length and time scales that can characterize the dynamics of driven system. Meso-scale structural rearrangement is studied using Falk-Langer measure of affine and non-affine deformation. The affine and non-affine deformations drop to a stable value and oscillates around it, which suggest that the structure is driving towards a more stable configuration. A negative correlation is found between the local packing fraction and the non-affine squared displacement. Finally, a complex network analysis is employed to better understand the structural rearrangement at meso-scale. The average degree and average clustering coefficient obtained from the complex network analysis show peaks at maximum compressions, but the peak values increase with cycles. The degree per particle is found to be positively correlated with local packing fraction and negatively correlated with the non-affine squared deformation. An enrichment of three-cycle population is seen, suggesting it as the most preferred conformation for particles at the meso-scale.

Unified size-density and size-topology relations in random packings of dry adhesive polydisperse spheres.

We study the size-density and size-topology relations in random packings of dry adhesive polydisperse microspheres with Gaussian and lognormal size distributions through a geometric tessellation. We find that the dependence of the neighbor number on the centric particle size is always quasilinear, regardless of the size distribution, size span, or interparticle adhesion. The average local packing fraction as a function of normalized particle size for different size variances is well regressed on the same profile, which increases to larger values as the relative strength of adhesion decreases. The variations of the local coordination number with the particle size converge onto a single curve for all adhesive particles, but gradually transfer to another branch for nonadhesive particles. Such adhesion-induced size-density and size-topology relations are interpreted theoretically with a modified geometrical "granocentric" model, where the model parameters are dependent on a single dimensionless adhesion number. Our findings, together with the modified theory, provide a more unified perspective on the substantial geometry of amorphous polydisperse systems, especially those with fairly loose structures.

A fast adhesive discrete element method for random packings of fine particles

Introducing a reduced particle stiffness in discrete element method (DEM) allows for bigger time steps and therefore fewer total iterations in a simulation. Although this approach works well for dry non-adhesive particles, it has been shown that for fine particles with adhesion, system behaviors are drastically sensitive to the particle stiffness. Besides, a simple and applicable principle to set the parameters in adhesive DEM is also lacking. To solve these two problems, we first propose a fast DEM based on scaling laws to reduce particle Young’s modulus, surface energy and to modify rolling and sliding resistances simultaneously in the framework of Johnson-Kendall-Roberts (JKR)-based contact theory. A novel inversion method is then presented to help users to quickly determine the damping coefficient, particle stiffness and surface energy to reproduce a prescribed experimental result. After validating this inversion method, we apply the fast adhesive DEM to packing problems of microparticles. Measures of packing fraction, averaged coordination number and distributions of local packing fraction and contact number of each particle are in good agreement with results simulated using original value of particle properties. The new method should be helpful to accelerate DEM simulations for systems associated with aggregates or agglomerates.

Topologically close-packed characteristic of amorphous tantalum.

The structural evolution of tantalum (Ta) during rapid cooling was investigated by molecular dynamics simulation, in terms of the system energy, the pair distribution function and the largest standard cluster analysis. It was found that the critical cooling rate for vitrification was about R ≥ 0.25 K ps-1, two orders lower than other metals (such as Au, Ag, Al, Zr and Zn) and that the meta-stable σ phase (β-Ta) not only appears on the pathway from liquid to the stable body-centred cubic crystal, but is also easily obtained at room temperature as a long-lived metastable phase with some probability. The most interesting point is that the liquid, amorphous and β-Ta phases share a nontrivial structural homology; the intrinsic topologically close-packed (TCP) structures in liquids are inherited and developed in different ways, resulting in amorphous or crystalline solids, respectively. With highly local packing fractions and geometrical incompatibility with the global close-packed (such as hcp, fcc and bcc) crystals, TCP structures inevitably result in structural heterogeneity and favour vitrification. As a superset of icosahedrons, TCP structures are ubiquitous in metallic melts, and just before the onset of crystallization reach their maximal number, which is much bigger in Ta than in other poor-GFA metals; so we argue that the strong forming ability of TCP local structures significantly enhances the glass forming ability of pure metals. These findings open up a new perspective that could have a profound impact on the research into metallic glasses.

Cluster growth in driven granular gases.

We investigate numerically and theoretically the internal structures of a driven granular gas in cuboidal cell geometries. Clustering is reported and particles are classified as gaseous or clustered via a local packing fraction criterion based on a Voronoi tessellation. We observe that small clusters arise in the corners of the box, elucidating early reports of partial clustering. These aggregates have a condensation-like surface growth. When a critical size is reached, a structural transition occurs and all clusters merge together, leaving a hole in the center of the cell. This hole then becomes the new center of particle capture. Taking into account all structural modifications and defining a saturation packing fraction, we propose an empirical model for the cluster growth.

Towards minimal models for realistic granular materials: Tomographic analysis of bidispersed assemblies of ellipsoids

In this paper, we report experimental results on granular compaction in a model system made of mono- and bidisperse ellipsoidal packings as well as sand packings with grain size polydispersity. The packings are subject to vertical tapping of varying duration (number of taps) and their internal three-dimensional structure is obtained using x-ray computed tomography. Particles positions and orientations are reconstructed and the global packing densities are computed. The analysis of the vertical and horizontal local packing fraction profiles reveal a homogeneous densification in the ellipsoidal packings, however, sand packings exhibit radial density gradient, possibly linked to the onset of convection.

Model of the saltation transport by Discrete Element Method coupled with wind interaction

We study the Aeolian saltation transport problem by analysing the collision of incident energetic beads with granular packing. We investigate the collision process for the case where the incident bead and those from the packing have identical mechanical properties. We analyse the features of the consecutive collision process. We used a molecular dynamics method known as DEM (soft Discrete Element Method) with 20000 particles (2D). The grains were displayed randomly in a box (250X60). A few incident disks are launched with a constant velocity and angle with high random position to initiate the flow. A wind velocity profile is applied on the flowing zone of the saltation. The velocity profile is obtained by the calculi of the counter-flow due to the local packing fraction induced by the granular flow. We analyse the evolution of the upper surface of the disk packing. In the beginning, the saltation process can be seen as the classical “splash function” in which one bead hits a fully static dense packing. Then, the quasi-fluidized upper layer of the packing creates a completely different behaviour of the “animated splash function”. The dilation of the upper surface due to the previous collisions is responsible for a need of less input energy for launching new ejected disks. This phenomenon permits to maintain a constant granular flow with a “small” wind velocity on the surface of the disk bed.