TRANSITIONAL AGGREGATION KINETICS IN DRY AND DAMP ENVIRONMENTS

We investigate the kinetics of constant-kernel aggregation which is au gmented by (a) evaporation of monomers from clusters, which is termed aggregation in a ''dry'' environment, and (b) continuous cluster growt h or condensation, termed aggregation in a ''damp'' environment. The r ate equations for these two processes are analyzed using both exact an d asymptotic methods. In dry aggregation, mass conserving evaporation is treated, in which the monomers which evaporate remain in the system and continue to be reactive. For this reaction process, the competiti on between evaporation and aggregation leads to several asymptotic out comes. When the evaporation is weak, the kinetics is similar to that o f aggregation with no evaporation, while a steady state is quickly rea ched in the opposite case. At a critical evaporation rate, a steady st ate is slowly reached in which the cluster mass distribution decays as k(-5/2), where k is the mass, while the typical cluster mass, or uppe r cutoff in the mass distribution, grows with time as t(2/3). For damp aggregation, several cases are considered for the dependence of the c luster growth rate L(k) on k. (i) For L(k) independent of k, the mass distribution attains a conventional scaling form, but with the typical cluster mass growing as t In t. (ii) When L(k) proportional to k, the typical mass grows exponentially in time, while the mass distribution again scales. (iii) In the intermediate case of L(k) proportional to k(mu), scaling generally applies, with the typical mass growing as t(1 /(1-mu)). The scaling approach is also adapted to treat diffusion-limi ted damp aggregation for spatial dimension d less than or equal to 2.