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Fluctuation-induced spreading of size distribution in condensation kinetics

J. Chem. Phys. 131, 164514 (2009); doi:10.1063/1.3254384

Published 30 October 2009

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V. G. Dubrovskii
St.-Petersburg Physics and Technology Centre for Research and Education, Russian Academy of Sciences, Khlopina 8/3, 194021 St.-Petersburg, Russia and Ioffe Physical Technical Institute, Russian Academy of Sciences, Politekhnicheskaya 26, 194021 St.-Petersburg, Russia
One of the major results of condensation theory is the time independence of the size distribution shape (in terms of a certain invariant size) at the stage of regular growth of particles. This property follows directly from the simplified Zeldovich equation in the continuous form, where the fluctuation term is neglected. We show that the time invariance is broken by the fluctuation-induced spreading of the size spectrum. We first analyze the linear kinetic equations for the distributions pi(t) with the growth rates of the form ialpha. Exact solutions demonstrate the increase in dispersion with time as sqrt(t) at alpha=0 and the time-independent dispersion at alpha=1. From the asymptotic analysis of the continuous Zeldovich equation with fractional alpha, it is shown that the distribution spreading always occurs at alpha<1/2. We then study the general case of homogeneous condensation in an open system with pumping. Asymptotical solutions for the size distribution have the form of a diffusionlike Gaussian. In the case of constant material influx, the spectrum width increases with mean size z as sqrt(z) irrespective of alpha. We present a diagram of different growth scenarios and show that the time spreading occurs in the majority of condensing systems. Some numerical estimates for the effect of spectrum spreading are also presented. ©2009 American Institute of Physics
History: Received 19 August 2009; accepted 5 October 2009; published 30 October 2009
Permalink: http://link.aip.org/link/?JCPSA6/131/164514/1
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KEYWORDS and PACS

Keywords
PACS
  • 64.70.fm
    Thermodynamics studies of evaporation and condensation
  • 66.10.C-
    Diffusion and thermal diffusion in liquids
  • YEAR: 2009

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ISSN:
0021-9606 (print)   1089-7690 (online)
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