Kinetics of fragmentation
نویسنده
چکیده
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, we develop a scaling theory to describe the evolution of the cluster size distribution. We treat the general case where the breakup rate of a cluster of mass x varies as xi. When I > 0, corresponding to larger clusters more likely to break up, the scaled cluster size distribution, $(x), decays with the scaled mass, x, as x-* exp(-ax”), as x -+ 00. For small mass, $(x) has the log-normal form, exp(-a In2 x), if the breakup kernel has a small-size cutoff, while $(x) has a power-law tail in the absence of a cutoff. We also show that a conventional scaling picture applies only for the case I > 0. For I < 0, we develop an alternative formulation for the cluster size distribution, in which the typical mass scale is determined by the initial condition. In this regime, we also investigate the nature of a ‘shattering’ transition, where mass is lost to a ‘dust’ phase of zero-mass particles. We also study the kinetics of a nonlinear, collision-induced fragmentation process. We analyse the asymptotic behaviours 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. We 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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تاریخ انتشار 1989