Kinetics of migration-driven aggregation processes

Abstract

We study the kinetic behavior of the growth of aggregates driven by reversible migration between any two aggregates. For the simple system with the migration rate kernel ${K(k;j)=K}^{\ensuremath{'}}(k;j)\ensuremath{\propto}{\mathrm{kj}}^{\ensuremath{\upsilon}}$ at which the monomers migrate between the aggregates of size k and those of size $j,$ we find that for the $\ensuremath{\upsilon}<~2$ case the evolution of the system always obeys a scaling law. Moreover, the typical aggregate size grows as $\mathrm{exp}{(2\mathrm{IA}}_{0}t)$ in the case of $\ensuremath{\upsilon}=2$ and as ${t}^{1/(2\ensuremath{-}\ensuremath{\upsilon})}$ in the case of $\ensuremath{-}1<\ensuremath{\upsilon}<2.$ In particular, when $\ensuremath{\upsilon}<~\ensuremath{-}2,$ the typical aggregate size always grows as ${t}^{1/3}$ and the aggregate-size distribution approaches a similar scaling form.