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Fragmentation with, and without mechanism : Are principles enough ?
When it comes to understand how a cohesive object breaks-up, there are two types of temptations : either seek for 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. Microscopic descriptions often overlook the question of the sizes distribution, and the uncontrolled use of conservation principles leads to notorious mistakes (see §11 in JFM 898, P1, 2020).
I will show that an original conservation law coupled with a maximal randomness principle provides new, unifying predictions. I will explain when this principle is likely to apply, and why the fragments sizes distribution is a power law p(d) d^-β in that case, with exponent
β = D + a - 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, will be considered. The discussion is supplemented by an original experiment (https://journals.aps.org/prl/abstract/10.1103/r7xz-5d9c).