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Cell shape analysis of jammed ellipsoid packings

In particulate systems with short-range interactions, such as granular matter or simple fluids, the local structure plays a pivotal role in determining the macroscopic physical properties. Many studies on packing phenomena have focused on sphere packings, the simplest convex object. However, spheres are only the simplest model with obvious differences to the possible anisotropic shapes found in nature, like sand or stones. The study of aspherical particle packings offers the possibility to assess the effect of the particle shape. In this work jammed static configurations of ellipsoids, obtained by tomographic imaging of frictional particles and by discrete element method simulations of frictional and frictionless particles with and without gravity are analyzed. The pore space of the packings is assigned to the particles by using a Set Voroni construction [1]. The distribution of the local packing fractions (aka inverse volumes of the Voronoi cells) in the packings shows the same simple scaling behavior as found in sphere packs and is independent on the aspect ratio. The average cell shape, analyzed by anisotropy indices based on Minkowski tensors [2], is very similar in dense and loose sphere packings.
In contrast, the shape of the cells differs substantially in dense and loose ellipsoid packings.
This non-universality has implications for our understanding of jamming of aspherical particles.

[1] Schaller et.al., Phil. Mag., 93:3993-4017 (2013)
[2] Schröder-Turk et.al., NJP, 15:083028 (2013)

Author(s):

Fabian Schaller    
Institut für Theoretische Physik, Universität Erlangen-Nürnberg
Germany

Sebastian Kapfer    
Institut für Theoretische Physik, Universität Erlangen-Nürnberg
Germany

Matthias Schröter    
Max Planck Institute for Dynamics and Self-Organization, Göttingen
Germany

Gary Delaney    
CSIRO, Clayton South, Victoria
Australia

Gerd Schröder-Turk    
Institut für Theoretische Physik, Universität Erlangen-Nürnberg
Germany