Kinetics of catalysis-driven aggregation processes with sequential input of catalyst

We investigate the kinetic behavior of a two-species catalysis-driven aggregation model, in which coagulation of species A occurs only with the help of species B. We suppose the monomers of species B are stable and cannot self-coagulate in reaction processes. Meanwhile, the monomers are continuously injected into the system. The model with a constant rate kernel is investigated by means of the mean-field rate equation. We show that the kinetics of the system depends crucially on the details of the input term. The injection rate of species B is assumed to take the given time-dependent form K(t) similar to t(lambda), and the scaling solution of the cluster size distribution is then investigated analytically. It is found that the cluster size distribution can satisfy the conventional or modified scaling form in most cases.