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Improving the density of jammed disordered packings using ellipsoids.

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Ellipsoids can pack more densely than spheres, reaching packing fractions up to 0.71. This improved packing density is linked to more particle contacts, impacting granular media and materials science.

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Area of Science:

  • Physics
  • Materials Science
  • Geometry

Background:

  • Packing problems, determining maximum object density, are fundamental in science.
  • Equal spheres achieve a maximum packing fraction of approximately 0.74.
  • Random sphere packings typically reach a lower density of approximately 0.64.

Purpose of the Study:

  • To investigate if ellipsoids can achieve higher random packing densities than spheres.
  • To explore the relationship between particle shape, degrees of freedom, and packing density.
  • To analyze the number of particle contacts required for stable packings.

Main Methods:

  • Experimental packing of ellipsoids.
  • Development of a new simulation algorithm for packing studies.
  • Measurement of particle contacts per particle (Z).

Main Results:

  • Ellipsoids randomly pack more densely than spheres, reaching fractions of 0.68 to 0.71.
  • Packing density approaches 0.74 for specific ellipsoid aspect ratios.
  • Spheroid packings showed approximately 10 contacts per particle, compared to 6 for spheres.

Conclusions:

  • Ellipsoid shape allows for denser random packings than spherical shapes.
  • Increased particle contacts, due to higher degrees of freedom, stabilize denser packings.
  • Findings have implications for granular materials, ceramics, glass formation, and discrete geometry.