Getting on geometry’s sweet side

NYU (US)—How many sweets fit into a jar? The answer depends on the shapes and sizes of the sweets, the size of the jar, and how it is filled. Researchers have solved this conundrum by examining it from the candy’s point of view.

To answer the question of how particles pack in general, researchers at New York University made a transparent, fluorescent packing of oil droplets in water, which allowed them to record three-dimensional images and examine the local geometry of each member of the pack.

In other words, what does a packing look like from the grain’s perspective—a “granocentric” view?

Their findings, which appear in the latest issue of the journal Nature, show that packing strongly depends on the size distribution—larger particles pack with more neighbors than do smaller ones. Nevertheless, the average number of contacts per particle always stays the same to preserve mechanical stability.

These experimental clues helped the team, led by physics professor Jasna Brujić, develop a model that successfully captures the geometry, connectivity, and density of the observed sphere packings. This means that starting from a set of particles of known sizes, the density of packing can be determined, making it possible to guess the number of sweets in the jar.

The model also was able to predict experimentally observed trends in density for mixtures of particles of two different sizes with varying ratios.

Packing problems are important in technological settings as well, ranging from oil extraction through porous rocks to grain storage in silos to the compaction of pharmaceutical powders into tablets. The ability to predict the packing of polydisperse particles—a range of sizes in a single system—has significant impact on these and related technologies.

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