Rate Equation and Scaling for Fragmentation with Mass Loss

Boyd F. Edwards, Utah State University
M. Cai
H. Han

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http://pra.aps.org/abstract/PRA/v41/i10/p5755_1

Published by the American Physical Society in "Physical Review A." Publisher PDF is available for download through the link above.

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 x^α and a continuous-mass-loss rate εx^γ,σ=γ-α-1<0 yields a>‘‘recession regime’’ where small particles lose mass continuously without breaking, σ>0 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.