An assessment of the mathematical models for estimating the coordination number of the packing of multisized particles

Abstract Coordination number (CN) is an important microscopic parameter in describing the packing of particles. There are a few mathematical models proposed in the literature to calculate the CN of a particle mixture. However, they have not been comprehensively assessed as the experimental data are limited. In this paper, the applicability of three models, respectively proposed by Dodds, Ouchiyama & Tanaka, and Suzuki & Oshima, is assessed against the results recently generated by means of discrete element method. The results indicate that the model of Ouchiyama & Tanaka differ from the simulated CNs significantly, thus not recommended. The other two models produce similar results, but the Dodds model is probably more reasonable. In particular, these two models are able to estimate the variation trend of the average CN for various particle size distributions but their predictability reduces with the increase of particle size difference. The Dodds model becomes numerically unsolvable when the small-to-large size ratio is smaller than 0.154. Therefore, modification of the existing models or development of a new model is required in future studies for better prediction of the CN of the packings of multisized particles.

[1]  Yixiang Gan,et al.  X-ray tomography investigations of mono-sized sphere packing structures in cylindrical containers , 2017 .

[2]  M. Clusel,et al.  A ‘granocentric’ model for random packing of jammed emulsions , 2009, Nature.

[3]  P. D. Foote,et al.  Packing of Homogeneous Spheres , 1929 .

[4]  T. Aste,et al.  Local and global relations between the number of contacts and density in monodisperse sphere packs , 2006, 0709.3141.

[5]  Toshio Oshima,et al.  Estimation of the Co-ordination number in a Multi-Component Mixture of Spheres , 1983 .

[6]  A. Yu,et al.  Discrete particle simulation of particulate systems: Theoretical developments , 2007 .

[7]  Aibing Yu,et al.  A simulation study of the effects of dynamic variables on the packing of spheres , 2001 .

[8]  Runyu Yang,et al.  Effect of material properties on the packing of fine particles , 2003 .

[9]  J. L. Finney,et al.  Fine structure in randomly packed, dense clusters of hard spheres , 1976 .

[10]  Runyu Yang,et al.  Discrete particle simulation of particulate systems: A review of major applications and findings , 2008 .

[11]  K. Shinohara,et al.  A particle-scale index in the quantification of mixing of particles , 2012 .

[12]  J. Dodds,et al.  The porosity and contact points in multicomponent random sphere packings calculated by a simple statistical geometric model , 1980 .

[13]  Paul Zulli,et al.  Particle scale study of heat transfer in packed and bubbling fluidized beds , 2009 .

[14]  Masanobu Oda,et al.  CO-ORDINATION NUMBER AND ITS RELATION TO SHEAR STRENGTH OF GRANULAR MATERIAL , 1977 .

[15]  S. Patlazhan.  Porosity and microstructure of polydisperse random packing of hard spheres , 1993 .

[16]  Clarke,et al.  Structural changes accompanying densification of random hard-sphere packings. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Paul Zulli,et al.  Evaluation of effective thermal conductivity from the structure of a packed bed , 1999 .

[18]  Runyu Yang,et al.  Critical states and phase diagram in the packing of uniform spheres , 2009 .

[19]  Runyu Yang,et al.  Computer simulation of the packing of fine particles , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[20]  Aibing Yu,et al.  Evaluation of effective thermal conductivity in random packed bed: Heat transfer through fluid voids and effect of packing structure , 2020, Powder Technology.

[21]  G. D. Scott,et al.  Packing of Spheres: Packing of Equal Spheres , 1960, Nature.

[22]  R. Zou,et al.  Radical tessellation of the packing of spheres with a log-normal size distribution. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  M. J. Powell.  Computer-simulated random packing of spheres , 1980 .

[24]  A. Yu,et al.  Quasi-universality in the packing of uniform spheres under gravity , 2016 .

[25]  W. Zhou,et al.  Strong contacts, connectivity and fabric anisotropy in granular materials: A 3D perspective , 2020 .

[26]  N. Ouchiyama,et al.  Porosity estimation from particle size distribution , 1986 .

[27]  N. Ouchiyama,et al.  Predicting the densest packings of ternary and quaternary mixtures of solid particles , 1989 .

[28]  J. D. BERNAL,et al.  Packing of Spheres: Co-ordination of Randomly Packed Spheres , 1960, Nature.

[29]  N. Ouchiyama,et al.  Estimation of the Average Number of Contacts between Randomly Mixed Solid Particles , 1980 .

[30]  Paul Zulli,et al.  Coordination Number of Ternary Mixtures of Spheres† , 2003 .

[31]  J. Dodds.  Simplest statistical geometric model of the simplest version of the multicomponent random packing problem , 1975, Nature.

[32]  Y. Gan,et al.  Modes of wall induced granular crystallisation in vibrational packing , 2018, Granular Matter.

[33]  G. T. Nolan,et al.  Computer simulation of random packing of hard spheres , 1992 .

[34]  Runyu Yang,et al.  Numerical study of the packing of wet coarse uniform spheres , 2003 .

[35]  M. Clusel,et al.  Model for random packing of polydisperse frictionless spheres , 2010 .

[36]  Randall M. German,et al.  Particle packing characteristics , 1989 .

[37]  Luc Oger,et al.  Properties of disordered sphere packings I. Geometric structure: Statistical model, numerical simulations and experimental results , 1986 .

[38]  Tatsuo Tanaka,et al.  A new experimental method to specify the diffusing component in a reacting particulate packing , 1990 .

[39]  J. Goodling,et al.  Co-ordination number distribution of spherical particles in a packed cylindrical bed , 1985 .

[40]  N. Standish,et al.  A study of particle size distributions , 1990 .

[41]  J. Vicente,et al.  3d tomography analysis of the packing structure of spherical particles in slender prismatic containers , 2019 .

[42]  Aibing Yu,et al.  Dynamic simulation of the centripetal packing of mono-sized spheres , 1999 .

[43]  Michitaka Suzuki,et al.  Co-ordination number of a multi-component randomly packed bed of spheres with size distribution , 1985 .

[44]  Charles H. Bennett,et al.  Serially Deposited Amorphous Aggregates of Hard Spheres , 1972 .

[45]  Paul Zulli,et al.  Coordination number of binary mixtures of spheres , 1998 .

[46]  Tatsuo Tanaka,et al.  Porosity estimation for random packings of spherical particles , 1984 .

[47]  Aibing Yu,et al.  Prediction of the porosity of multi-component mixtures of cohesive and non-cohesive particles , 2011 .

[48]  Shuixiang Li,et al.  Structural universality in disordered packings with size and shape polydispersity. , 2020, Soft matter.

[49]  E. M. Tory,et al.  Anisotropy in Simulated Random Packing of Equal Spheres , 1968, Nature.

[50]  Aibing Yu,et al.  Coordination Number of the Packing of Ternary Mixtures of Spheres: DEM Simulations versus Measurements , 2011 .

[51]  Runyu Yang,et al.  Settling of particles in liquids: Effects of material properties , 2012 .

[52]  Chuan-Yu Wu,et al.  Unified size-density and size-topology relations in random packings of dry adhesive polydisperse spheres. , 2018, Physical review. E.

[53]  Aibing Yu,et al.  Prediction of the Porosity of Particle Mixtures , 1998 .

[54]  Aibing Yu,et al.  Particle Scale Evaluation of the Effective Thermal Conductivity from the Structure of a Packed Bed: Radiation Heat Transfer , 2013 .

[55]  H. Scott Fogler,et al.  Modeling flow in disordered packed beds from pore‐scale fluid mechanics , 1997 .