Krapivsky, Pavel L. and Connaughton, Colm. (2012) Driven Brownian coagulation of polymers. Journal of Chemical Physics, Vol.136 (No.20). Article:204901. ISSN 1089-7690

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Abstract

We present an analysis of the mean-field kinetics of Brownian coagulation of droplets and polymers driven by input of monomers which aims to characterize the long time behavior of the cluster size distribution as a function of the inverse fractal dimension, a, of the aggregates. We find that two types of long time behavior are possible. For 0 <= a < 1/2 the size distribution reaches a stationary state with a power law distribution of cluster sizes having exponent 3/2. The amplitude of this stationary state is determined exactly as a function of a. For 1/2 < a <= 1, the cluster size distribution never reaches a stationary state. Instead a bimodal distribution is formed in which a narrow population of small clusters near the monomer scale is separated by a gap (where the cluster size distribution is effectively zero) from a population of large clusters which continue to grow for all time by absorbing small clusters. The marginal case, a=1/2, is difficult to analyze definitively, but we argue that the cluster size distribution becomes stationary and there is a logarithmic correction to the algebraic tail.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Centre for Complexity Science Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Brownian movements, Coagulation -- Mathematical models
Journal or Publication Title:	Journal of Chemical Physics
Publisher:	American Institute of Physics
ISSN:	1089-7690
Date:	22 May 2012
Volume:	Vol.136
Number:	No.20
Page Range:	Article:204901
Identification Number:	10.1063/1.4718833
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Boston University, University of Warwick
Related URLs:	Other Repository
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URI:	http://wrap.warwick.ac.uk/id/eprint/44640

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