The equation that describes fragmentation kinetics, such as that which occurs in cluster breakup and polymer chain degradation (depolymerisation), is solved for models where the rate of breakup depends upon the size of the object breaking up. The resulting dynamic scaling behaviour is investigated. Both discrete and continuous models are considered.

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Large-scale computer simulations of cluster-cluster aggregation of particles undergoing Brownian motion have been performed to investigate the kinetic properties of the coagulation process. It is shown that the mean-field approach of the Smoluchowski equation accurately describes the kinetics if the fractal geometry of the clusters is taken into account. The kinetic rate kernels that enter into that equation are deduced explicitly from the simulations.

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