Random-close packing limits for monodisperse and polydisperse hard spheres

Baranau, Vasili; Tallarek, Ulrich

doi:10.1039/c3sm52959b

Cited by 172 publications

(132 citation statements)

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“…This subject has been investigated by many authors. [12][13][14][15][16][17][18] Two main group of techniques are based on the so-called random sequential addition process, 19 or on the Lubachevsky-Stillinger compression algorithm. 20 The technique applied in this paper is similar to the Lubachevsky-Stillinger algorithm which was originally proposed for two-dimensional discs.…”

Section: Introductionmentioning

confidence: 99%

Generation of random microstructures and prediction of sound velocity and absorption for open foams with spherical pores

Zieliński¹

2015

The Journal of the Acoustical Society of America

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This paper proposes and discusses an approach for the design and quality inspection of the morphology dedicated for sound absorbing foams, using a relatively simple technique for a random generation of periodic microstructures representative for open-cell foams with spherical pores. The design is controlled by a few parameters, namely, the total open porosity and the average pore size, as well as the standard deviation of pore size. These design parameters are set up exactly and independently, however, the setting of the standard deviation of pore sizes requires some number of pores in the representative volume element (RVE); this number is a procedure parameter. Another pore structure parameter which may be indirectly affected is the average size of windows linking the pores, however, it is in fact weakly controlled by the maximal pore-penetration factor, and moreover, it depends on the porosity and pore size. The proposed methodology for testing microstructure-designs of sound absorbing porous media applies the multi-scale modeling where some important transport parameters-responsible for sound propagation in a porous medium-are calculated from microstructure using the generated RVE, in order to estimate the sound velocity and absorption of such a designed material.

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Section: Introductionmentioning

confidence: 99%

Generation of random microstructures and prediction of sound velocity and absorption for open foams with spherical pores

Zieliński¹

2015

The Journal of the Acoustical Society of America

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“…In figure 5 this boundary is indicated by a solid magenta line. The pressure of a hard sphere gas diverges at the so called Glass Close Packing (GCP) point with φ GCP ≈ 0.65 [20,21,23]. From which follows that the system runs out of nonoverlapping configurations and S HS goes to zero.…”

Section: Granular Physics Happens At Volume Fractions Inaccessible Tomentioning

confidence: 99%

“…This excludes both packings crystallizing in FCC and HCP configurations at volume fractions above φ g ≈ 0.65 [15][16][17][18][19][20][21] 1 and the "tunneled crystal" packings at φ g = 0.49 [22]. Neither of these two configurations are extensive, i.e.…”

Section: Granular Physics Happens At Volume Fractions Inaccessible Tomentioning

confidence: 99%

“…The exact value of φ g of a frictionless packing at zero pressure does depend on the preparation history [20,21,28,51]. However, the scaling laws of these packings are normally studied by preparing pressure free packings with a given protocol and then increasing φ g by compressing this packing [7,26].…”

Section: The Volume Fraction Of Frictional Particles Is Controlled Bymentioning

confidence: 99%

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A local view on the role of friction and shape

Schröter

2017

EPJ Web Conf.

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Abstract. Leibniz said "Naturam cognosci per analogiam": nature is understood by making analogies. This statement describes a seminal epistemological principle. But one has to be aware of its limitations: quantum mechanics for example at some point had to push Bohr's model of the atom aside to make progress. This article claims that the physics of granular packings has to move beyond the analogy of frictionless spheres, towards local models of contact formation.On earth solid assemblies of granular particles are by far the most frequent phase of granular matter; we encounter granular packings everywhere from our kitchen cabinet to civil engineering textbooks. In order to make their handling, transport, and storage more efficient, we strive for a theory that predicts their mechanical properties, such as shear and bulk modulus or yield stress, starting from a few state variables only. Efforts to develop such a theory often start by modeling granular packings as an assembly of frictionless spheres. This is a rather unsuitable starting point, for a number of reasons:1. All granular particles are frictional. 2. Frictional particles have lower isostatic numbers than frictionless particles. 3. Granular physics happens at volume fractions inaccessible to frictionless particles. 4. The volume fraction of soft particles can be changed by compression. The volume fraction of frictional particles is changed by changing their geometry. 5. Friction is one reason for history dependence in granular systems. 6. Real world granular media are rarely spherical.Shape adds complexity, e.g. to history dependence.These six theses are also the outline for the following sections. They are intended to provoke discussions with a sizeable subgroup of the theoretically or numerically working scientists. Many experimentalists, applied scientist, and engineers might find them, at least in part, well-known. For simplicity, we will discuss in the following only monodisperse spheres; except for section 6.

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“…However the study of these geometries can be relevant for other problems such as solid heterogeneous materials or multiphase dispersed flows. To recreate more realistic granular and consolidated porous media, many algorithms have been proposed (see [18,19] and references therein). In this work an extended version of the Jodrey-Tory algorithm [20] has been used, that consists in a post-processing iterative greedy-type moves to displace overlapping or detached grains.…”

Section: Random Arrangementsmentioning

confidence: 99%

On the predictivity of pore-scale simulations: Estimating uncertainties with multilevel Monte Carlo

Icardi

Boccardo

Tempone

2016

Advances in Water Resources

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A fast method with tunable accuracy is proposed to estimate errors and uncertainties in porescale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another "equivalent" sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an opensource code [1], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics.

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Random-close packing limits for monodisperse and polydisperse hard spheres

Cited by 172 publications

References 64 publications

Generation of random microstructures and prediction of sound velocity and absorption for open foams with spherical pores

Generation of random microstructures and prediction of sound velocity and absorption for open foams with spherical pores

A local view on the role of friction and shape

On the predictivity of pore-scale simulations: Estimating uncertainties with multilevel Monte Carlo

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