Self-Focussing Dynamics in Monopolarly Charged Suspensions

TL;DR

This paper investigates how charge accumulation affects aggregation dynamics in suspensions, revealing a universal scaling behavior and a lower bound for size distribution width in charged particle systems.

Contribution

It introduces a detailed analysis of charge effects on aggregation, showing a universal size distribution and a lower bound for the relative width in charged suspensions.

Findings

Charge accumulation causes a crossover in growth behavior.

The size distribution approaches a universal form.

The relative width converges to a lower bound of approximately 0.2017.

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