Fragmentation: Principles versus Mechanisms

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)∼d^{-β}, in that case, with exponent β=D+1-{π^{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.