Fragmentation, the way objects break into pieces, has long intrigued scientists. Researchers have observed that broken objects tend to produce fragments in a wide range of sizes, and the distribution of those sizes often follows a consistent pattern, regardless of the material.

Building on this understanding, Emmanuel Villermaux of Aix-Marseille University and the University Institute of France has formulated a straightforward and elegant law describing how objects shatter. His approach applies to a wide variety of cases, including brittle solids, liquid drops, and exploding bubbles. 

By providing a unified framework, the law helps explain the underlying principles behind how materials break across different contexts.

Why broken objects follow patterns in chaos

Villermaux began by examining the extreme disorder created during a shattering event. He proposed that in most cases, the outcome would naturally be the messiest and most irregular configuration, a principle he described as maximal randomness – essentially, nature following the path of least resistance.

At the same time, Villermaux recognized that even chaotic events are bound by physical limits. To account for this, he applied a conservation law that his team had previously discovered, ensuring that the apparent randomness of fragmentation still adheres to predictable physical constraints.

The law functions as an invisible framework, ensuring that the overall balance of fragments – how many are large versus small – remains constrained even as an object breaks. To develop his universal fragmentation law, Villermaux combined the principle of maximal randomness with the conservation law. 

This approach allows the predictable distribution of fragment sizes to emerge naturally, providing a unifying explanation for how materials shatter across a wide range of contexts, from brittle solids to liquid drops and exploding bubbles, Phys.org reported.

Uncovering predictable patterns in chaotic shattering

By combining the principles of maximal randomness and the conservation law, Villermaux was able to mathematically predict a universal pattern for fragment sizes. His model aligns closely with decades of experimental data, covering a wide range of materials from brittle solids to liquids. The results show that despite the apparent chaos of shattering, underlying physical laws govern the way fragments form, creating predictable distributions across different types of objects.

To validate his theory, Villermaux conducted a creative experiment by crushing individual sugar cubes. He was able to accurately predict the resulting fragment sizes, demonstrating that the pattern of breakage closely reflected the cube’s three-dimensional shape. 

The universal law has its limits – it works best when objects break in a random, chaotic way, such as when a glass tumbler falls and shatters on the floor. However, the law is less accurate for very soft materials, like some plastics, which tend to deform rather than fragment. 

It also struggles to predict breakage when the process is highly ordered, such as a stream of water splitting into evenly sized droplets under the influence of surface tension. These exceptions show that while the law captures many natural shattering events, certain materials and conditions follow different rules.