November 28, 2025 by Paul Arnold, Phys.org
Collected at: https://phys.org/news/2025-11-universal-law-shatter-bottles.html
When a plate drops or a glass smashes, you’re annoyed by the mess and the cost of replacing them. But for some physicists, the broken pieces are a source of fascination: Why does everything break into such a huge variety of sizes? Now, Emmanuel Villermaux at Aix-Marseille University in France and the University Institute of France has come up with a simple, elegant law for how objects shatter, whether they are brittle solids, liquid drops, or exploding bubbles.
Scientists have long suspected that there was something universal about fragmentation. If you count how many fragments fall into each size range and make a graph of that distribution, it would have the same shape regardless of the object that shattered.
A formula for fragmentation
Villermaux’s starting point was the massive chaos of a shattering event. He argued that, in the majority of cases, the most likely outcome would always be the messiest and most irregular one, a principle he called maximal randomness. This is nature choosing the path of least resistance.
However, because it is generally known that chaos must obey physical limits, he introduced a conservation law that his team had previously discovered. This law acts as an invisible rule that ensures the overall scale of the fragments (how many large pieces and how many small pieces) cannot change randomly as the object breaks. To come up with his universal fragmentation law, he combined both maximal randomness and the conservation law.
“A kinematic constraint applied to a maximal randomness principle infers both the power law shape of the fragment size distribution and the value of its dimensionality-dependent exponent,” Villermaux wrote in his paper published in the journal Physical Review Letters.
Testing the new law
By linking these two principles, he was able to mathematically predict the universal size pattern of the fragments. He showed that the law perfectly matched large amounts of fragmentation data collected over decades from a variety of objects, including brittle solids and liquids. And he tested it in an original experiment by crushing single sugar cubes and correctly predicted the specific size pattern based on the cube’s three-dimensional shape.
However, this universal law doesn’t explain every breakage. The rule works best when an object shatters randomly, such as when a glass tumbler suddenly hits the floor. But it doesn’t work well if the material is too soft, like some plastics, or if the breakup is too orderly, such as when surface tension causes a stream of water to break into droplets of the same size.
More information: Emmanuel Villermaux, Fragmentation: Principles versus Mechanisms, Physical Review Letters (2025). DOI: 10.1103/r7xz-5d9c
Journal information: Physical Review Letters
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