Particle Survival and Polydispersity in Aggregation

• Published in: arXiv.org
• Main Authors: Hellen, E K O, Salmi, P E, Alava, M J
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 28.11.2001
• Subjects: Agglomeration; Clusters; Decay; Diffusion coefficient; Particle size distribution; Polydispersity; Random walk
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0111522

We study the probability, \(P_S(t)\), of a cluster to remain intact in one-dimensional cluster-cluster aggregation when the cluster diffusion coefficient scales with size as \(D(s) \sim s^\gamma\). \(P_S(t)\) exhibits a stretched exponential decay for \(\gamma < 0\) and the power-laws \(t^{-3/2}\) for \(\gamma=0\), and \(t^{-2/(2-\gamma)}\) for \(0<\gamma<2\). A random walk picture explains the discontinuous and non-monotonic behavior of the exponent. The decay of \(P_S(t)\) determines the polydispersity exponent, \(\tau\), which describes the size distribution for small clusters. Surprisingly, \(\tau(\gamma)\) is a constant \(\tau = 0\) for \(0<\gamma<2\).