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 ${\sigma }_{\mathrm{r}}^{\infty }\approx 0.2017$ that is much smaller than in the uncharged case. We conjecture that ${\sigma }_{\mathrm{r}}^{\infty }$ is a lower bound for the asymptotic relative width for all physical systems with irreversible aggregation.

4 pages, 4 figures, minor changes

Cited by in corpus (1)

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