The Digester

A new equation explains the common pattern in fragment sizes across many materials by combining a statistical selection of messy breaks with a density-change law, and it matches experiments from broken glass and ceramics to smashed sugar cubes and ocean waves.

Emmanuel Villermaux derived an equation that predicts the size distribution of fragments from broken objects.
The theory selects the most probable messy break using maximum entropy and a previously identified law for fragment density change.
The equation matches a wide range of experiments on glass, plates, ceramic tubes, dry spaghetti, smashed sugar cubes and ocean foam.
It does not apply to purely deterministic breakups like uniform droplet formation or to cases with strong fragment interactions or crack healing.
Better fragmentation models could improve ore crushing in mining and help predict rockfalls as climate change increases slope instability.
Open questions include how fragment shapes distribute and what sets the smallest possible fragment size.

Physicist derives universal law for how objects shatter

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