Granular Matter

, Volume 10, Issue 4, pp 329–334 | Cite as

Characterization of voids in spherical particle systems by Delaunay empty spheres

  • S. RémondEmail author
  • J. L. Gallias
  • A. Mizrahi


The pore space of mono-sized spherical particle systems of increasing density is characterized by Delaunay empty spheres. Periodic packings of densities ranging from 0.57 up to 0.70 are generated numerically by symmetric vibration. The Voronoi diagrams of these packings are then computed with an algorithm based on the research of Delaunay empty spheres. The voids distribution and the tortuosity of packings as a function of density are studied. As the density increases, the voids distribution becomes more narrow. For partly ordered packings of high density, the voids distribution presents two peaks corresponding to the size of Delaunay empty spheres of perturbed fcc or hcp packings. The tortuosity of disordered packings decreases slowly with density. However, when the system becomes partly ordered, a large increase in tortuosity is observed.


Packing Delaunay empty sphere Voronoi diagram Voids distribution Tortuosity 


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© Springer-Verlag 2008

Authors and Affiliations

  1. 1.L2MGC, EA 4114Université de Cergy-PontoiseCergy-Pontoise CedexFrance
  2. 2.Département de MathématiquesUniversité de Cergy-PontoiseCergy-Pontoise CedexFrance

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