Scaling in the aggregation process with catalysis-driven fragmentation

We propose several aggregation models with catalysis-driven fragmentation, in which two clusters of the same species A bond spontaneously form a large cluster while large A clusters break up only with the help of catalyst B. By means of mean-field rate equations, we obtain the asymptotic solutions of the cluster-mass distributions in several different systems with constant reaction rate kernels. The results show that kinetics of the aggregation process depend strongly on whether or not the catalyst aggregates by itself; meanwhile, whether or not the catalyst is consumed through the catalytic reactions also plays an important role in the kinetic evolution properties. In the system with self-coagulation of catalyst B or with catalyst consumption, the cluster-mass distribution of species A approaches a conventional scaling form; however, when breakup of the catalyst cluster coexists with its self-coagulation, the evolution behaviour of the system falls in a modified scaling regime.