Similarity solutions of a Becker-Doring system with time-dependent monomer input

We formulate the Becker-Doring equations for cluster growth in the presence of a time-dependent source of monomer input. In the case of size-independent aggregation and fragmentation rate coefficients we find similarity solutions which are approached in the large time limit. The form of the solutions depends on the rate of monomer input and whether fragmentation is present in the model; four distinct types of solution are found.