A solvable two-species catalysis-driven aggregation model

We study the kinetics of a two-species catalysis-driven aggregation system, in which an irreversible aggregation between any two clusters of one species occurs only with the catalytic action of another species. By means of a generalized mean-field rate equation, we obtain the asymptotic solutions of the cluster mass distributions in a simple process with a constant rate kernel. For the case without any consumption of the catalyst, the cluster mass distribution of either species always approaches a conventional scaling law. However, the evolution behaviour of the system in the case with catalyst consumption is complicated and depends crucially on the relative data of the initial concentrations of the two species.