Rate equation and scaling for fragmentation with mass loss

Abstract

A linear rate equation describes fragmentation with continuous and discrete mass loss typified by consumption of porous reactive solids and two-phase heterogeneous solids. For a mass-dependent fragmentation rate ${\mathit{x}}^{\mathrm{\ensuremath{\alpha}}}$ and a continuous-mass-loss rate \ensuremath{\epsilon}${\mathit{x}}^{\ensuremath{\gamma}}$,\ensuremath{\sigma}=\ensuremath{\gamma}-\ensuremath{\alpha}-10 yields a ``recession regime'' where small particles lose mass continuously without breaking, \ensuremath{\sigma}>0 yields a ``fragmentation regime'' where all particles break, and \ensuremath{\sigma}=0 yields scaling for \ensuremath{\alpha}>0. Shattering for \ensuremath{\alpha}0 and \ensuremath{\sigma}\ensuremath{\ge}0 is runaway fragmentation producing an infinte number of particles in a finite time, Exact and asymptotic solutions, exponent relations, and connections with static percolation are found.