Kinetics of fragmentation

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Abstract
A general discussion of the kinetics of continuous, irreversible fragmentation processes is presented. For a linear process, where particle breakup is driven by an external force, the authors develop a scaling theory to describe the evolution of the cluster size distribution. They treat the general case where the breakup rate of a cluster of mass x varies as xlambda . When lambda >0, corresponding to larger clusters more likely to break up, the scaled cluster size distribution, phi (x), decays with the scaled mass, x, as x-2 exp(-axlambda ), as x. For small mass, phi (x) has the log-normal form, exp(-a ln2 x), if the breakup kernel has a small-size cutoff, while phi (x) has a power-law tail in the absence of a cutoff. They also show that a conventional scaling picture applies only for the case lambda >0. For lambda >0, they develop an alternative formulation for the cluster size distribution, in which the typical mass scale is determined by the initial condition. In this regime, they also investigate the nature of a 'shattering' transition, where mass is lost to a 'dust' phase of zero-mass particles. They also study the kinetics of a nonlinear, collision-induced fragmentation process. They analyse the asymptotic behaviour of a simple-minded class of models in which a two-particle collision results in either: (1) both particles splitting into two equal pieces, (2) only the larger particle splitting in two, or (3) only the smaller particle splitting. They map out the kinetics of these models by scaling arguments and by analytic and numerical solutions of the rate equations. Scaling is found to hold for different ranges of homogeneity index for the three models.

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