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Related Experiment Videos

Gapped gapless packing structures.

J M Beck1, V A Volpert

  • 1Department of Engineering Sciences and Applied Mathematics, Northwestern University, 2145 N. Sheridan Road, Evanston, IL 60208, USA. jebeck@nwu.edu

Journal of Colloid and Interface Science
|November 1, 2005
PubMed
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This study introduces a new model for random sphere packing, extending the gapless structure concept to non-maximal densities by including voids. The findings reveal a linear relationship between coordination number and packing fraction for various sphere mixtures.

Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Previous models for random sphere packing focused on maximally dense regimes, assuming gapless structures.
  • Characterizing packings away from maximal density requires accounting for void spaces within the structure.

Purpose of the Study:

  • To extend the gapless packing structure concept to include void elements for non-maximal densities.
  • To determine the characteristics of random sphere packings across a range of packing fractions.
  • To investigate the relationship between packing fraction and coordination numbers in monodisperse and bi-disperse systems.

Main Methods:

  • Introduced void spherical elements into the gapless packing model.
  • Utilized specific volume to generate void distributions and coupled integral equations.

Related Experiment Videos

  • Solved integral equations numerically for packing fractions from 0.26 to 0.78.

    • Main Results:

    • Developed a method to determine packing characteristics away from maximal density.
    • Results for monodisperse and bi-disperse packings show good agreement with experimental data.
    • A linear relationship between coordination number and packing fraction was identified for moderate to low densities.

    Conclusions:

    • The extended gapless packing model accurately describes random sphere packings at various densities.
    • Coordination number dependence on packing fraction is invariant to the number distribution of spheres.
    • The study provides insights into maximum and minimum random packing fractions.