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 xα and a continuous-mass-loss rate εxγ,σ=γ-α-1\u3c0 yields a ‘‘recession regime’’ where small particles lose mass continuously without breaking, σ\u3e0 yields a ‘‘fragmentation regime’’ where all particles break, and σ=0 yields scaling for α\u3e0. Shattering for α\u3c0 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