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Journal of Chemical Physics / Volume 131 / Issue 24 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 131, 244104 (2009); http://dx.doi.org/10.1063/1.3276799 (7 pages)

Close packing density of polydisperse hard spheres

Robert S. Farr and Robert D. Groot

Unilever R and D, Olivier van Noortlaan 120, Vlaardingen AT3133, The Netherlands

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(Received 5 November 2009; accepted 2 December 2009; published online 23 December 2009)

The most efficient way to pack equally sized spheres isotropically in three dimensions is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution of a real granular material is never monodisperse. Here we present a simple but accurate approximation for the random close packing density of hard spheres of any size distribution based upon a mapping onto a one-dimensional problem. To test this theory we performed extensive simulations for mixtures of elastic spheres with hydrodynamic friction. The simulations show a general (but weak) dependence of the final (essentially hard sphere) packing density on fluid viscosity and on particle size but this can be eliminated by choosing a specific relation between mass and particle size, making the random close packed volume fraction well defined. Our theory agrees well with the simulations for bidisperse, tridisperse, and log-normal distributions and correctly reproduces the exact limits for large size ratios.

© 2009 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORY
  3. SIMULATION
  4. RESULTS
  5. CONCLUSIONS

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KEYWORDS and PACS

Keywords

density, elasticity, friction, granular materials, hydrodynamics, liquid structure, liquid theory, particle size, statistical mechanics, viscosity

PACS

  • 62.10.+s

    Mechanical properties of liquids

  • 66.20.Cy

    Theory and modeling of viscosity and rheological properties, including computer simulation

  • 61.20.Gy

    Theory and models of liquid structure

  • 61.25.-f

    Studies of specific liquid structures

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3276799

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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