Local Packing Fraction Research Articles

Dynamic self-assembly of non-Brownian spheres studied by molecular dynamics simulations.

Granular self-assembly of confined non-Brownian spheres under gravity is studied by molecular dynamics simulations. Starting from a disordered phase, dry or cohesive spheres organize, by vibrational annealing, into body-centered-tetragonal or face-centered-cubic structures, respectively. During the self-assembling process, isothermal and isodense points are observed. The existence of such points indicates that both granular temperature and packing fraction undergo an inversion process that may be in the core of crystal nucleation. Around the isothermal point, a sudden growth of granular clusters having the maximum coordination number takes place, indicating the outcome of a first-order phase transition. We propose a heuristic equation that successfully describes the dynamic evolution of the local packing fraction in terms of the local granular temperature, along the entire crystallization process.

Structural characterization of the packings of granular regular polygons.

By using a recently developed method for discrete modeling of nonspherical particles, we simulate the random packings of granular regular polygons with three to 11 edges under gravity. The effects of shape and friction on the packing structures are investigated by various structural parameters, including packing fraction, the radial distribution function, coordination number, Voronoi tessellation, and bond-orientational order. We find that packing fraction is generally higher for geometrically nonfrustrated regular polygons, and can be increased by the increase of edge number and decrease of friction. The changes of packing fraction are linked with those of the microstructures, such as the variations of the translational and orientational orders and local configurations. In particular, the free areas of Voronoi tessellations (which are related to local packing fractions) can be described by log-normal distributions for all polygons. The quantitative analyses establish a clearer picture for the packings of regular polygons.

Search for hyperuniformity in mechanically stable packings of frictionless disks above jamming.

We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction ϕ(J). For configurations with a fixed isotropic global stress tensor, we investigate the fluctuations of the local packing fraction ϕ(r) to test whether such configurations display the hyperuniformity that has been claimed to exist exactly at ϕ(J). For our configurations, generated by a rapid quench protocol, we find that hyperuniformity persists only out to a finite length scale and that this length scale appears to remain finite as the system stress decreases towards zero, i.e., towards the jamming transition. Our result suggests that the presence of hyperuniformity at jamming may be sensitive to the specific protocol used to construct the jammed configurations.

Non-universal Voronoi cell shapes in amorphous ellipsoid packs

In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure determines the macroscopic physical properties. We analyse local structure metrics derived from the Voronoi diagram of oblate ellipsoids, for various aspect ratios α and global packing fractions . We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. The rescaled distribution of local packing fractions , defined as the ratio of particle volume and its Voronoi cell volume, is found to be independent of the particle aspect ratio, and coincide with results for sphere packs. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index , points towards a difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape β of all cells with a given value of is similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true.

A proposal on alternative sampling-based modeling method of spherical particles in stochastic media for Monte Carlo simulation

Chord length sampling method in Monte Carlo simulations is a method used to model spherical particles with random sampling technique in a stochastic media. It has received attention due to the high calculation efficiency as well as user convenience; however, a technical issue regarding boundary effect has been noted. In this study, after analyzing the distribution characteristics of spherical particles using an explicit method, an alternative chord length sampling method is proposed. In addition, for modeling in finite media, a correction method of the boundary effect is proposed. Using the proposed method, sample probability distributions and relative errors were estimated and compared with those calculated by the explicit method. The results show that the reconstruction ability and modeling accuracy of the particle probability distribution with the proposed method were considerably high. Also, from the local packing fraction results, the proposed method can successfully solve the boundary effect problem. It is expected that the proposed method can contribute to the increasing of the modeling accuracy in stochastic media.

Coalescence preference in densely packed microbubbles.

A bubble merged from two parent bubbles with different size tends to be placed closer to the larger parent. This phenomenon is known as the coalescence preference. Here we demonstrate that the coalescence preference can be blocked inside a densely packed cluster of bubbles. We utilized high-speed high-resolution X-ray microscopy to clearly visualize individual coalescence events inside densely packed microbubbles with a local packing fraction of ~40%. The surface energy release theory predicts an exponent of 5 in a relation between the relative coalescence position and the parent size ratio, whereas our observation for coalescence in densely packed microbubbles shows a different exponent of 2. We believe that this result would be important to understand the reality of coalescence dynamics in a variety of packing situations of soft matter.

A review of steric interactions of ions: Why some theories succeed and others fail to account for ion size

As nanofluidic devices become smaller and their surface charges become larger, the steric interactions of ions in the electrical double layers at the device walls will become more important. The ions’ size prevents them from overlapping, and the resulting correlations between the ions can produce oscillations in the density profiles. Because device properties are determined by the structure of these double layers, it is more important than ever that theories correctly include steric interactions between ions. This review analyzes what features a theory must have in order to accurately account for steric interactions. It also reviews several popular theories and compares them against Monte Carlo simulations to gauge their accuracy. Successful theories of steric interactions satisfy the contact density theorem of statistical mechanics and use locally averaged concentrations. Theories that do not satisfy these criteria, especially those that use local concentrations (instead of averaged concentrations) to limit local packing fraction, produce qualitatively incorrect double layer structure. For which ion sizes, ion concentrations, and surface charges monovalent ions steric effects are important is also analyzed.

Tribology of polymer brush: microscale modelling and simulation

In order to examine the tribological behaviour of the polymer brush, we constructed a mesoscale particle model of a polymer brush system, based on a Brownian dynamics scheme. The polymer model consists of coarse-grained beads connected with harmonic springs. The Lennard-Jones type interaction is assumed between beads. The flow velocity is affected by the local packing fraction of beads. With this model, we executed a series of molecular dynamics simulation to investigate the mechanical responses of brush to shear flow.

Effect of size polydispersity versus particle shape in dense granular media.

We present a detailed analysis of the morphology of granular systems composed of frictionless pentagonal particles by varying systematically both the size span and particle shape irregularity, which represent two polydispersity parameters of the system. The microstructure is characterized in terms of various statistical descriptors such as global and local packing fractions, radial distribution functions, coordination number, and fraction of floating particles. We find that the packing fraction increases with the two parameters of polydispersity, but the effect of shape polydispersity for all the investigated structural properties is significant only at low size polydispersity where the positional and/or orientational ordering of the particles prevail. We focus in more detail on the class of side/side contacts, which is the interesting feature of our system as compared to a packing of disks. We show that the proportion of such contacts has weak dependence on the polydispersity parameters. The side- side contacts do not percolate but they define clusters of increasing size as a function of size polydispersity and decreasing size as a function of shape polydispersity. The clusters have anisotropic shapes but with a decreasing aspect ratio as polydispersity increases. This feature is argued to be a consequence of strong force chains (forces above the mean), which are mainly captured by side-side contacts. Finally, the force transmission is intrinsically multiscale, with a mean force increasing linearly with particle size.

Macroscopic and Microscopic Packing Properties of Experimental and Computational Pebble Beds

In pebble bed-type nuclear reactors, the fuel pebbles form a randomly stacked bed with a nonuniform packing density. To investigate flow and heat transfer through these beds and to develop realistic models, we need a good understanding of the nature of randomly stacked beds and validated computational methods that can generate realistic beds. To this end, the average packing fraction (PF) and the radial and axial PF profiles were accurately measured of a bed containing 5400 acrylic pebbles with a diameter of 12.7 mm. In a second experiment, we determined the pebble locations of a bed containing 8900 glass pebbles with diameters of 1.66 to 2.00 mm using three-dimensional X-ray tomography, from which various microscopic stacking properties were evaluated for both the bulk of the bed away from the wall and in the near wall region. Results were compared with the properties of a bed that was generated by using a computational method based on the removal of overlaps to validate that method.Results for the computed bed are in good agreement with the experiments and with the literature, giving confidence that the method is capable of generating beds with realistic packing structures, although the experimental results for the microscopic stacking properties in the near-wall region are of insufficient quality for a meaningful comparison. Analysis of the various results shows different stacking properties near the wall than in the bulk of the bed, indicating the stacking is anisotropic near a boundary forming semiordered layers parallel to the wall with hexagonal-like stacking properties, which implies flow and heat transfer might also be isotropic near the wall and could need different models near the wall than in the bulk to be accurately described. Finally, the probability distribution of PFs of small clusters of around 45 pebbles showed that the local PF inside a packed bed can vary strongly, both in the bulk and near the wall, which might significantly affect flow rates and could result in hot spots.

Density difference-driven segregation in a dense granular flow

AbstractWe consider the segregation of spheres of equal size and different density flowing over an inclined plane, theoretically and computationally by means of distinct element method (DEM) simulations. In the first part of the work, we study the settling of a single higher-density particle in the flow of otherwise identical particles. We show that the motion of the high-density tracer particle can be understood in terms of the buoyancy and drag forces acting on it. The buoyancy force is given by Archimedes principle, with an effective volume associated with the particle, which depends upon the local packing fraction, $\phi $. The buoyancy arises primarily from normal forces acting on the particle, and tangential forces have a negligible contribution. The drag force on a sphere of diameter $d$ sinking with a velocity $v$ in a granular medium of apparent viscosity $\eta $ is given by a modified Stokes law, ${F}_{d} = c\pi \eta dv$. The coefficient ($c$) is found to decrease with packing fraction. In the second part of the work, we consider the case of binary granular mixtures of particles of the same size but differing in density. A continuum model for segregation is presented, based on the single-particle results. The number fraction profile for the heavy particles at equilibrium is obtained in terms of the effective temperature, defined by a fluctuation–dissipation relation. The model predicts the equilibrium number fraction profiles at different inclination angles and for different mass ratios of the particles, which match the DEM results very well. Finally, a complete model for the theoretical prediction of the flow and number fraction profiles for a mixture of particles of different density is presented, which combines the segregation model with a model for the rheology of mixtures. The model predictions agree quite well with the simulation results.

Attractive emulsion droplets probe the phase diagram of jammed granular matter

It remains an open question whether statistical mechanics approaches apply to random packings of athermal particles. Although a jamming phase diagram has recently been proposed for hard spheres with varying friction, here we use a frictionless emulsion system in the presence of depletion forces to sample the available phase space of packing configurations. Using confocal microscopy, we access their packing microstructure and test the theoretical assumptions. As a function of attraction, our packing protocol under gravity leads to well-defined jammed structures in which global density initially increases above random close packing and subsequently decreases monotonically. Microscopically, the fluctuations in parameters describing each particle, such as the coordination number, number of neighbors, and local packing fraction, are for all attractions in excellent agreement with a local stochastic model, indicating that long-range correlations are not important. Furthermore, the distributions of local cell volumes can be collapsed onto a universal curve using the predicted k-gamma distribution, in which the shape parameter k is fixed by the polydispersity while the effect of attraction is captured by rescaling the average cell volume. Within the Edwards statistical mechanics framework, this result measures the decrease in compactivity with global density, which represents a direct experimental test of a jamming phase diagram in athermal systems. The success of these theoretical tools in describing yet another class of materials gives support to the much-debated statistical physics of jammed granular matter.

Compacity influence in reorganization of two dimensional granular packings: Numerical model

Rearrangements (movements of disks) of different sizes are observed before the avalanche onset while studying avalanche process in 2D packings of disks of diameter d. A stochastic cellular automata model based on experimental observations is proposed to understand the influence of local packing fraction in the appearance of rearrangements in a two dimensional packing of disks. In numerical simulations, rearrangements of different sizes are also observed and evolution of the packing fraction is studied. The cellular automata retrieves experimental results when it considers a range of influence for rearrangements larger than 9 d. Rearrangements are also found to be responsible for the decreasing of the system global packing fraction in discrete steps.

A Stochastic Description of TransitionBetween Granular Flow States

Two-dimensional granular flow in a channel with small exit is studiedby molecular dynamics simulations. We firstly define a key area nearthe exit, which is considered to be the choke area of the system.Then we observe the time variation of the local packing fraction andflow rate in this area for several fixed inflow rate, and find thatthese quantities change abruptly when the transition from dilute flowstate to dense flow state happens. A relationship between the localflow rate and the local packing fraction in the key area is also given.The relationship is a continuous function under the fixed particlenumber condition, and has the characteristic that the flow rate has amaximum at a moderate packing fraction and the packing fraction isterminated at a high value with negative slope. By use of the relationship,the properties of the flow states under the fixed inflow rate conditionare discussed in detail, and the discontinuities and the complex timevariation behavior observed in the preexisting works are naturallyexplained by a stochastic process.

Behavior of icosahedral clusters in computer simulated hard sphere systems

The model of densely packed hard spheres is used as a first-order approach to the structure of liquid metals and liquid metallic alloys. The concept of local packing fraction is applied to characterize the local structure. Starting from dilute systems of randomly distributed spheres, densification does not lead to the formation of local icosahedral order. A second type of initial structures consisting of icosahedral clusters embedded in a system of randomly packed hard spheres is also analyzed. Densification of such systems leads to a continuous retrogression of the degree of local icosahedrality, and the frequency distribution of local packing fraction approaches that of the arrangements obtained by densification of uncorrelated random initial structures. We conclude that global densification and formation of icosahedral clusters with high local packing fraction are competing processes in hard sphere systems.

Relationship between the flow rate and the packing fraction in the choke area of the two-dimensional granular flow

Two-dimensional granular flow in a channel with small exit is studied by both experiments and simulations. We first observe the time variation of the transition from dilute flow state to dense flow state by both experiments and simulations. Then we obtain a relationship between the local flow rate and the local packing fraction in the choke area by use of molecular dynamics simulations. The relationship is a continuous function rather than a discontinuous one. The flow rate has a maximum at a moderate packing fraction and the packing fraction is terminated at high value with negative slope. According to the relationship, four flow states--i.e., stable dilute flow state, metastable dilute flow state, unstable dense flow state, and stable dense flow state--are defined for fixed inflow rate. The discontinuities and the complex time variation behavior occurring in the transition between dilute and dense flow states can be attributed to the abrupt variation through unstable flow state.

Local and global relations between the number of contacts and density in monodispersesphere packs

The topological structure resulting from the network of contacts between grains (contactnetwork) is studied for large samples of monosized spheres with densities (fractionof volume occupied by the spheres) ranging from 0.59 to 0.64. We retrieve thecoordinates of each bead in the pack and we calculate the average coordinationnumber by using three different methods. We show that, in the range of densityinvestigated, the coordination number is larger than four and it increases with thepacking fraction. At local level we also observe a positive correlation between localpacking fraction and number of neighbours. We discover a dependence between thelocal densities of configurations with few neighbours in contact and the globalsample densities. This might indicate that local configurations with small numbersof neighbours are able to deform plastically when the sample is compactifying.

液圧測定によるスラリー評価―沈降挙動に及ぼすスラリー初期高さの影響―

Slurry compressibility was evaluated by using hydrostatic pressure measurement. The dependency of sedimentation behavior and final packing fraction of sediment on the initial slurry height was studied. The final packing fraction of sediment decreased with the initial slurry height for slurries with pH5.5. It was also found that the hydrostatic pressure at the vessel bottom decreased gradually in the initial stage of sedimentation but dropped abruptly after 20h. These results suggested that the particles were well dispersed in the initial stage of sedimentation, however the flocculation of particles proceeded during the sedimentation. The local packing fraction of final sediment layer was measured from the intensity of gamma ray penetration through the sediment layer. We found that the sediment layer formed from the slurry with pH5.5 consisted of two layers, i. e., dense and loose zones, and that the loose zone increased with the initial height, which led to a smaller final packing fraction of sediment layer.

Flow distribution in a randomly packed hollow fiber membrane module

Shell side flow distribution in a randomly packed hollow fiber module was analyzed using the random cell model. The module was divided into subchannels. The hydrodynamics in each channel was described according to Happel’s free surface model and then it was just the function of the local cell packing fraction. Based on the theoretical probability density distribution function of local packing fraction, the shell side flow distribution was presented. The results showed that a serious flow mal-distribution occurred in the shell side. More than the 40% fluid flowed through the largest 20% void area of the total module void area (cells with high void fraction), and the smallest 20% void area (cell with low void fraction) carried less than 6% of the flow. This mal-distribution became more serious as the mean packing density increased.

Monte Carlo simulations of primitive water in planar slits with molecularly rough walls: surface self-organization

The behaviour of primitive water confined to molecularly rough slit-like pores is simulated by Metropolis MC in a NVT ensemble. Two models of molecular roughness are introduced covering the smooth pore walls by discrete surface molecules. One model called `hydrophobic', restricts the surface–surface and the surface–fluid potentials to hard-core interactions only. The other model called `hydrophilic', additionally takes into account associative surface–surface and water–surface interactions. The interplay between the self-organized molecular roughness of the pores and the network structure of primitive water in these confinements is studied in detail for several slit widths. Based on these results problems concerning the defining geometrical properties of molecularly rough pores are discussed on a molecular level in terms of the local densities and packing fractions of the surface and fluid particles as well as the topology of the formed molecular clusters and networks.