Packing of Binary Mixtures of Spheres and Irregular Particles

Yerazunis, S.; Bartlett, J. W.; Nissan, A. H.

doi:10.1038/195033a0

Cited by 70 publications

(23 citation statements)

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“…For bimodal dispersions, some prediction models for the maximum volume fraction have been established by Yerazunis et al (1962;1965), Bournonville et al (2004) and Qi and Tanner (2011). The models given by Yerazunis et al (1962Yerazunis et al ( , 1965 and Bournonville et al (2004) have been discussed in our previous paper . Neither of them can give satisfactory estimations in cases in which the maximum volume fraction tends to unity.…”

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confidence: 97%

Random close packing and relative viscosity of multimodal suspensions

Tanner

2011

Rheol Acta

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Multimodal suspensions, consisting of noncolloidal spherical particles and a Newtonian matrix, are considered. A new differential (or multi-scale mean field approach) model for the relative viscosity of multimodal suspensions has been developed. The problem of the random close packing fraction of the solid phase is also investigated. We suppose that the multimodal suspension has a dominant large particle composition and that the smaller particles are embedded in the empty space between the larger particles. The relative viscosity model can therefore be based on the theory of monomodal suspensions. Experimental data of Eveson are compared to the predictions given by using three different models of monomodal suspensions respectively. The Maron-Pierce approach appears to give the best agreement with Eveson's experiments. However, due to experimental uncertainties, we recommend that the Mendoza and Santamaria-Holek (MSH) formula be adopted.

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confidence: 97%

Random close packing and relative viscosity of multimodal suspensions

Tanner

2011

Rheol Acta

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“…The binary mixture is the simplest case in polydisperse packing and was paid particular attention. The polydisperse packings of spheres have been extensively studied [8][9][10][11][12] through experiments, while non-spherical particles were less studied and only a few basic shapes have been considered, such as disks, cylinders and cubes [13][14][15]. The binary mixtures of cylinders and spheres have been investigated in some experiments.…”

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A computational investigation on random packings of sphere-spherocylinder mixtures

Zhao

et al. 2010

Sci. China Phys. Mech. Astron.

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Random packings of binary mixtures of spheres and spherocylinders with the same volume and the same diameter were simulated by a sphere assembly model and relaxation algorithm. Simulation results show that, independently of the component volume fraction, the mixture packing density increases and then decreases with the growth of the aspect ratio of spherocylinders, and the packing density reaches its maximum at the aspect ratio of 0.35. With the same volume particles, results show that the dependence of the mixture packing density on the volume fraction of spherocylinders is approximately linear. With the same diameter particles, the relationship between the mixture packing density and component volume fraction is also roughly linear for short spherocylinders, but when the aspect ratio of spherocylinders is greater than 1.6, the curves turn convex which means the packing of the mixture can be denser than either the sphere or spherocylinder packing alone. To validate the sphere assembly model and relaxation algorithm, binary mixtures of spheres and random packings of spherocylinders were also simulated. Simulation results show the packing densities of sphere mixtures agree with previous prediction models and the results of spherocylinders correspond with the simulation results in literature. packing, binary mixture, sphere, spherocylinder, packing density, aspect ratio PACS: 45.10.Na, 45.70.Cc, 81.05.RmThe sphere and spherocylinder are both important 3D objects and were widely involved in packing investigations and engineering practices. The sphere is the earliest and the most comprehensively studied shape in packing investigations. Weitz [1] listed some important packing densities for identical spheres, where the density is about 0.64 for random close packing and 0.56 for random loose packing. A spherocylinder is a capsule like object which consists of a cylinder and two hemispheres on both sides. The shape of a spherocylinder is usually described by an aspect ratio w = H/D, where H is the height of the cylinder part and D is the diameter. When w = 0, a spherocylinder degenerates to a sphere. The spherocylinder is one of the well-studied non-spherical shapes, since it has a smooth surface and is easy to be described by mathematical functions or a sphere assembly model. In general, the simulation results on the random packing of spherocylinders in literature [2][3][4][5][6][7] are quite consistent, the maximum packing density is around 0.69 ~ 0.7 when w ≈ 0.4.The densest packing has always been an important objective of packing investigations and it is generally measured by the packing density Φ. A mixture of particles with different sizes can give a much higher packing density than mono-sized particles and is widely applied in engineering. The mixture packing density, that is the packing density of the mixture, is dependent on many factors, e.g. the packing density of each component, particle size distribution, volume fraction and particle shape. Among these factors, the influence of particle size distribution ha...

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“…4. The packing fractions of the U3 systems are larger than in U1 and U2, which is due to the different DSDs -with higher fractions of small discs one can ¿ll pores more effectively [18]. The U0 systems exhibit a different trend because of their crystalline regions.…”

Section: Structural Analysesmentioning

confidence: 95%

Microstructural characteristics of planar granular solids

Matsushima¹,

Blumenfeld²

2013

AIP Conference Proceedings

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Abstract. The microstructure of granular materials is the main factor determining their macroscopic behaviour. We study systematically the statistical characteristics of volume elements (called quadrons) of microstructures of mono-and polydisperse planar disc packs granular and report a number of new results. The packs analysed were of different intergranular friction coef¿cients ,μ, contained about 20,000 discs each and were brought to mechanical equilibrium under identical isotropic compression stresses from three different initial states: loose, intermediate and dense. Our ¿ndings are the following. (i) The rattlers volume fraction φ r is not affected by the disc size distribution (DSD). (ii) Excluding the rattlers, we ¿nd that the relation between the packing fraction φ and the mean coordination numberz is independent of the initial state. Together with result (i), this allows us to separate the effects of the DSD and the initial state on the microstructure. (iii) We relate analyticallȳ z, φ and the (normalised) mean quadron volumev . (iv) Combining (iii) and a relation betweenz and the mean cell order,ē, derived from Euler's topological relation, we show that (ii) is a result of the geometrical relation betweenv andē. (v) The probability density function of the quadron volumes, normalised byv , is universal for all the studied systems and it can be ¿t reasonably well by a Γ distribution.

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Packing of Binary Mixtures of Spheres and Irregular Particles

Cited by 70 publications

References 2 publications

Random close packing and relative viscosity of multimodal suspensions

Random close packing and relative viscosity of multimodal suspensions

A computational investigation on random packings of sphere-spherocylinder mixtures

Microstructural characteristics of planar granular solids

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