From ageing to immortality: cluster growth in stirred colloidal solutions

TL;DR

This paper presents a model of cluster growth in stirred colloidal solutions, revealing glassy dynamics, aging, metastability, and the emergence of immortal clusters, with implications for understanding aggregation processes.

Contribution

It introduces a 'winner-takes-all' model for cluster aggregation that captures glassy behavior, aging, and metastability in colloidal solutions, highlighting the formation of immortal clusters.

Findings

Largest cluster always wins in finite assemblies

Model exhibits universal decay law for survival probability

Enhanced glassiness with aging and metastability in finite dimensions

Abstract

This model describes cluster aggregation in a stirred colloidal solution Interacting clusters compete for growth in this 'winner-takes-all' model; for finite assemblies, the largest cluster always wins, i.e. there is a uniform sediment. In mean-field, the model exhibits glassy dynamics, with two well-separated time scales, corresponding to individual and collective behaviour; the survival probability of a cluster eventually falls off according to a universal law $(\ln t)^{-1/2}$. In finite dimensions, the glassiness is enhanced: the dynamics manifests both {\it ageing} and metastability, where pattern formation is manifested in each metastable state by a fraction of {\it immortal} clusters.