When it comes to understanding how a cohesive object breaks up, there are two types of temptations: either seek detailed mechanisms (capillary instabilities for liquids, cracks, propagation in brittle solids...), or rely on a general principle to infer the multiplicity of the fragments’ sizes. Here we show that an original conservation law coupled with a maximal randomness principle provides new, unifying predictions. We explain when this principle is likely to apply, and why the fragment’s size distribution is a power law $p(d)\sim d^{-\beta }$, in that case, with exponent $\beta =D+1-\{{\pi }^{D/2}/[2^D(D/2)!]\},$ a function of the dimensionality of the breaking object $D$. Examples including crushed and grinned brittle materials like solid bars, plates, and shells; or cubes and spheroids; but also liquid drops and bubbles; exploding liquid shells; plastic debris in the ocean; and remnants from the cavemen industry are considered. The discussion is supplemented by an original experiment.

Close

PrevNext

View figure in article

• Irreversible processes
• Nonequilibrium statistical mechanics
• Stochastic thermodynamics