Coarsening of unstable thin films subject to gravity

M. B. Gratton and T. P. Witelski
Phys. Rev. E 77, 016301 – Published 4 January 2008

Abstract

Thin films of viscous fluids coating hydrophobic substrates are unstable to dewetting instabilities, and long-time evolution leads to the formation of an array of near-equilibrium droplets connected by ultrathin fluid layers. In the absence of gravity, previous use of lubrication theory has shown that coarsening dynamics will ensue—the system will evolve by successively eliminating small drops to yield fewer larger drops. While gravity has only a weak influence on the initial thin film, we show that it has a significant influence on the later stages of the coarsening dynamics, dramatically slowing the rate of coarsening for large drops. Small drops are relatively unaffected, but as coarsening progresses, these aggregate into larger drops whose shape and dynamics are dominated by gravity. The change in the mean drop shape causes a corresponding gradual transition from power-law coarsening to a logarithmic behavior.

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  • Received 9 July 2007

DOI:https://doi.org/10.1103/PhysRevE.77.016301

©2008 American Physical Society

Authors & Affiliations

M. B. Gratton*

  • Department of Mathematics, Duke University, Box 90320, Durham, North Carolina 27708-0320, USA

T. P. Witelski

  • Oxford Centre for Industrial and Applied Mathematics, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, United Kingdom

  • *mgratton@math.duke.edu
  • witelski@maths.ox.ac.uk

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Vol. 77, Iss. 1 — January 2008

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