Scaling description for the growth of condensation patterns on surfaces

Jean Louis Viovy, Daniel Beysens, and Charles M. Knobler
Phys. Rev. A 37, 4965 – Published 1 June 1988
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Abstract

The growth of a droplet pattern condensing on a surface (e.g., breath figures) is analyzed for the case of arbitrary dimensionality. The growth of a droplet occurs through a two-step process: (i) continuous growth by condensation on its surface and/or on the substrate and (ii) coalescence with neighboring droplets. As long as the one-droplet growth remains scale invariant, the growth of the entire pattern is shown to be self-similar in time and very general growth laws can be deduced, whose exponents are functions only of the dimensionality of the space of the droplets, and of the condensing substrate. In particular, for the case of three-dimensional droplets condensing on a plane substrate (breath figures), the growth exponent of a single droplet should be (1/3, whereas the exponent corresponding to a mean droplet, averaged over the pattern, should be unity. Comparison with experiment is performed and possible deviations from the predictions are considered.

  • Received 21 October 1987

DOI:https://doi.org/10.1103/PhysRevA.37.4965

©1988 American Physical Society

Authors & Affiliations

Jean Louis Viovy

  • Ecole Supérieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI), rue Vauquelin, 75231 Paris Cedex 05, France

Daniel Beysens

  • Service de Physique du Solide et de Résonance Magnétique (SPSRM), Centre d’Etudes Nucléaires de Saclay, 91191 Gif-sur-Yvette Cedex, France

Charles M. Knobler

  • Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024

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Issue

Vol. 37, Iss. 12 — June 1988

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