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Driven Brownian coagulation of polymers
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Krapivsky, Pavel L. and Connaughton, Colm (2012) Driven Brownian coagulation of polymers. Journal of Chemical Physics, Vol.136 (No.20). Article:204901. doi:10.1063/1.4718833 ISSN 1089-7690.
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Official URL: http://dx.doi.org/10.1063/1.4718833
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, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| 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 | ||||
| Official Date: | 22 May 2012 | ||||
| Dates: |
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| Volume: | Vol.136 | ||||
| Number: | No.20 | ||||
| Page Range: | Article:204901 | ||||
| DOI: | 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: |
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