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Updated: Mar 29, 2026

An Efficient and Flexible Cell Aggregation Method for 3D Spheroid Production
Published on: March 27, 2017
Optimizing packing fraction in granular media composed of overlapping spheres
Leah K Roth1, Heinrich M Jaeger1
1James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637, USA. rothl@uchicago.edu.
Abstract:
What particle shape will generate the highest packing fraction when randomly poured into a container? In order to explore and navigate the enormous search space efficiently, we pair molecular dynamics simulations with artificial evolution. Arbitrary particle shape is represented by a set of overlapping spheres of varying diameter, enabling us to approximate smooth surfaces with a resolution proportional to the number of spheres included. We discover a family of planar triangular particles, whose packing fraction of ϕ ∼ 0.73 is among the highest experimental results for disordered packings of frictionless particles. We investigate how ϕ depends on the arrangement of spheres comprising an individual particle and on the smoothness of the surface. We validate the simulations with experiments using 3D-printed copies of the simplest member of the family, a planar particle consisting of three overlapping spheres with identical radius. Direct experimental comparison with 3D-printed aspherical ellipsoids demonstrates that the triangular particles pack exceedingly well not only in the limit of large system size but also when confined to small containers.
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