Catalysis-driven aggregate growth

We propose two-species catalysis-driven aggregation models in which coagulation of one species occurs only in the presence of another species (the catalyst). By means of generalized Smoluchovski rate equations, we study the kinetics of the system with the rate kernel KA(i; j; l) ∝ lυ, at which two A clusters of size i and j bond together under the catalytic action of a B cluster of size l. The results show that the cluster mass distribution of species A obeys a conventional scaling law in the υ ≥ 0 case while it may satisfy the modified scaling form in other cases. Moreover, it is found that the scaling exponents are nonuniversal and dependent on the value of index υ in most cases. On the other hand, we also investigate the scaling behaviour of the mutually catalysis-driven aggregate growth. For the system with the rate kernel KA(i; j; l) ∝ lυ1 and KB(i; j; l) ∝ lυ2, its kinetics depends crucially on the values of the indices υ1 and υ2. Either species scales according to the conventional or modified form in most cases; while the system may undergo a gelation transition in some special cases