Quasi-universality in the packing of uniform spheres under gravity

Significance Statement

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).

quasi-universality packing uniform spheres under gravity (advances in engineering)

About the author

Prof. XiZhong An received his PhD degree from University of Science and Technology Beijing in 2002, and is currently a professor in School of Metallurgy, Northeastern University. His research interests include particle packing, granular matter, and powder metallurgy. He has published >50 papers. He has received numerous honours and awards including the Science and Technology Progress Award of Chinese Society of Particuology.

About the author

Dr. Kejun Dong is a Senior Lecturer at Centre for Infrastructure Engineering, Western Sydney University. He received BSc and MSc from Hunan University in 1996 and 1999 respectively, and PhD from University of New South Wales in 2007. His research interests include simulation and modelling of particulate systems, particularly in particle packing and flow, and physical separation of particles. He has published about 40 papers in these areas.

About the author

A/Prof. Runyu Yang is an Associate Professor at the School of Materials Science and Engineering, University of New South Wales (UNSW). He received BE and ME from Zhejiang University, and PhD from UNSW. He has strong research interests in powder/particle science and technology, particularly in understanding the behaviour of particles through rigorous modelling and simulation at microscopic and macroscopic levels. He has published over 100 papers.  

About the author

A/Prof. Ruiping Zou is an Associate Professor in the Department of Chemical Engineering, Monash University. She received BE from Northeastern University, ME from University of Wollongong and PhD from UNSW. She is mainly working in particle science and technology, and has published over 120 papers.

About the author

Dr Chuncheng Wang  received his BEng from Yanshan University, and just completed his PhD study in the Department of Chemical Engineering, Monash University. His PhD research is on particle packing, and he has published 4 papers in this area.

About the author

Prof. Aibing Yu is currently Vice-Chancellor’s Professorial Fellow, Pro Vice-Chancellor and President (Suzhou), Monash University. He received BE and ME from Northeastern University, PhD from University of Wollongong, and DSc from UNSW. He mainly works in particle/powder technology and process engineering, and has authored >900 publications. He is a recipient of various prestigious fellowships and awards, including an ARC Federation Fellowship, the Ian Wark Medal and Lecture, and Top 100 Most Influential Engineers in Australia. He is an elected Fellow of Australian Academy of Science, and Australian Academy of Technological Sciences and Engineering.

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
  1. Laboratory for Simulation and Modelling of Particulate Systems, School of Materials Science and Engineering, University of New South Wales, Sydney, Australia
  2. School of Materials and Metallurgy Northeastern University, Shenyang, People’s Republic of China
  3. Laboratory for Simulation and Modelling of Particulate Systems, Department of Chemical Engineering, Monash University, Clayton, Australia
  4. Institute for Infrastructure Engineering, Western Sydney University, Penrith, Australia


Go To Granular Matter


Check Also

3D printing of shape changing composites for constructing flexible paper-based photothermal bilayer actuators