General solutions and scaling violation for fragmentation with mass loss

Abstract

Explicit solutions of a linear rate equation lead to an improved understanding of fragmentation with discrete and continuous mass loss. Discrete mass loss provides a general expression for the overall mass loss rate which accounts for mass loss in the shattering regime, where runaway fragmentation for small particles produces a phase of zero-mass particles. An explicit solution for the recession regime, where small particles lose large fractions of their mass to surface recession, shows that the total number of particles increases with time until the typical particles become small enough to lose all of their mass (and disappear) rather than to break. A general series solution is presented for fragmentation with continuous and discrete mass loss. A proof that continuous mass loss precludes dynamic scaling is presented.