The packing of uniform spheres has been extensively studied due to its unique role in basic scientific research and wide industrial applications. Packing fraction or density, which is the fraction of space occupied by particles, or its equivalent such as porosity (=1-packing fraction), is a commonly used macroscopic parameter to characterise a packing. On the other hand, many parameters are also proposed to describe packing structures at the microscopic level. Thus an important question arises: is there a one-to-one correlation between a macroscopic parameter such as packing fraction and the microscopic, structural parameters? While there is some evidence supporting the existence of this correlation under certain conditions, which is sometimes referred to as the “quasi-universality”, this problem has not been systematically and comprehensively investigated yet.
This article presents a relatively thorough investigation of this quasi-universality problem by examining a large database generated under different packing conditions. Packings of mono-sized spheres which are mechanically stable under gravity are formed by means of the discrete element method. The packings cover a wide range of packing fractions from 0.2 to 0.74, as a result of different inter-particle and particle-fluid interactions. The packing structures are analysed in terms of coordination number, radial distribution function, Voronoi and Delaunay tessellation.
As illustrated in Figure below, for the packings with similar densities, the mean values and distributions of these properties are comparable. When the mean values of the properties are plotted against packing faction, they respectively collapse into one single curve.
The results clearly demonstrate that the quasi-universality is valid for the packing of spheres formed with the gravity as the driving force. They thus justify the wide use of a single macroscopic parameter such as packing fraction or porosity as a primary state parameter in the modelling of many complicated structural properties. This finding also provides a base for the future study to establish some unified correlations for estimating different structural properties, which should have wide applications in engineering practice.
Figure: Comparisons of the distributions of coordination number (left top), radial distribution (right top) and local (Voronoi) pore size (left bottom), for Groups a-f of packing fractions 0.280, 0.370, 0.550, 0.610, 0.634 and 0.740; and the mean values (black symbols) and standard deviations (red symbols) of a few representative structural properties such a coordination number (CN), face number and area of a Voronoi polyhedron as a function of packing fraction (right bottom).
CITATION: Z. An1,2, K. J. Dong1,4, R. Y. Yang1, R. P. Zou1,3, C. C. Wang1,3, A. B. Yu1,3. Quasi-universality in the packing of uniform spheres under gravity. Granular Matter, 2016, 18:6.Show Affiliations
- Laboratory for Simulation and Modelling of Particulate Systems, School of Materials Science and Engineering, University of New South Wales, Sydney, Australia
- School of Materials and Metallurgy Northeastern University, Shenyang, People’s Republic of China
- Laboratory for Simulation and Modelling of Particulate Systems, Department of Chemical Engineering, Monash University, Clayton, Australia
- Institute for Infrastructure Engineering, Western Sydney University, Penrith, Australia
Go To Granular Matter