Rate equation and scaling for fragmentation with mass loss

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 ${\mathit{x}}^{\mathrm{\alpha }}$ and a continuous-mass-loss rate ε${\mathit{x}}^{\gamma }$,σ=γ-α-10 yields a ‘‘fragmentation regime’’ where all particles break, and σ=0 yields scaling for α>0. Shattering for α<0 and σ≥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.