WIAS Preprint No. 1417, (2009)

Thin film rupture for large slip



Authors

  • Peschka, Dirk
    ORCID: 0000-0002-3047-1140
  • Münch, Andreas
  • Niethammer, Barbara

2010 Mathematics Subject Classification

  • 76A20 35B40 76D08 60G18

Keywords

  • Asymptotic behavior of solutions, Thin fluid films, Lubrication theory, Self-similar processes

Abstract

This paper studies the rupture of thin liquid films on hydrophobic substrates, assuming large slip at the liquidsolid interface. Using a recently developed em strong slip lubrication model, it is shown that the rupture passes through up to three self-similar regimes with different dominant balances and different scaling exponents. For one of these regimes the similarity is of second kind, and the similarity exponent is determined by solving a boundary value problem for a nonlinear ODE. For this regime we also prove finite-time rupture.

Appeared in

  • J. Engrg. Math., 66 (2010) pp. 33--51.

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