Self-Focussing Dynamics in Monopolarly Charged Suspensions

Abstract

The Smoluchowski equation for irreversible aggregation in suspensions of equally charged particles is studied. Accumulation of charges during the aggregation process leads to a crossover from power law to sub-logarithmic cluster growth at a characteristic time and cluster size. For larger times the suspension is usually called stable, although aggregation still proceeds slowly. In this regime the size distribution evolves towards a {\em universal} scaling form, independent of {\em any} parameter included in the theory. The relative width falls off to a universal value $σ_{\rm r}^{\infty}{\approx}0.2017$ that is much smaller than in the uncharged case. We conjecture that $σ_{\rm r}^{\infty}$ is a lower bound for the asymptotic relative width for all physical systems with irreversible aggregation.