Universal elements of fragmentation

Abstract

A fragmentation theory is proposed that explains the universal asymptotic behavior of the fragment-size distribution in the large-size range, based on simple physical principles. The basic principles of the theory are the total mass conservation in a fragmentation process and a balance condition for the energy expended in increasing the surface of fragments during their breakup. A flux-based approach is used that makes it possible to supplement the basic principles and develop a minimal theory of fragmentation. Such a supplementary principle is that of decreasing fragment-volume flux with increasing energy expended in fragmentation. It is shown that the behavior of the decreasing flux is directly related to the form of a power-law fragment-size distribution. The minimal theory is used to find universal asymptotic fragment-size distributions and to develop a natural physical classification of fragmentation models. A more general, nonlinear theory of strong fragmentation is also developed. It is demonstrated that solutions to a nonlinear kinetic equation consistent with both basic principles approach a universal asymptotic size distribution. Agreement between the predicted asymptotic fragment-size distributions and experimental observations is discussed.