Transitional aggregation kinetics in dry and damp environments

We investigate the kinetics of constant-kernel aggregation which is augmented by (a) evaporation of monomers from clusters, which is termed aggregation in a ‘‘dry’’ environment, and (b) continuous cluster growth or condensation, termed aggregation in a ‘‘damp’’ environment. The rate equations for these two processes are analyzed using both exact and 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 competition between evaporation and aggregation leads to several asymptotic outcomes. When the evaporation is weak, the kinetics is similar to that of aggregation with no evaporation, while a steady state is quickly reached in the opposite case. At a critical evaporation rate, a steady state is slowly reached in which the cluster mass distribution decays as ${\mathit{k}}^{\mathrm{-}5/2}$, where k is the mass, while the typical cluster mass, or upper cutoff in the mass distribution, grows with time as ${\mathit{t}}^{2/3}$. For damp aggregation, several cases are considered for the dependence of the cluster growth rate ${\mathit{L}}_{\mathit{k}}$ on k. (i) For ${\mathit{L}}_{\mathit{k}}$ independent of k, the mass distribution attains a conventional scaling form, but with the typical cluster mass growing as t ln t. (ii) When ${\mathit{L}}_{\mathit{k}}$∝k, the typical mass grows exponentially in time, while the mass distribution again scales. (iii) In the intermediate case of ${\mathit{L}}_{\mathit{k}}$∝${\mathit{k}}^{\mathrm{\mu }}$, scaling generally applies, with the typical mass growing as ${\mathit{t}}^{1/\left(1\mathrm{-}\mathrm{\mu }\right)}$. The scaling approach is also adapted to treat diffusion-limited damp aggregation for spatial dimension d⩽2. © 1996 The American Physical Society.