WIAS Preprint No. 1418, (2009)

Self-similar rupture of viscous thin films in the strong-slip regime



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

We consider rupture of thin viscous films in the strong-slip regime with small Reynolds numbers. Numerical simulations indicate that near the rupture point viscosity and van-der-Waals forces are dominant and that there are self-similar solutions of the second kind. For a corresponding simplified model we rigorously analyse self-similar behaviour. There exists a one-parameter family of self-similar solutions and we establish necessary and sufficient conditions for convergence to any self-similar solution in a certain parameter regime. We also present a conjecture on the domains of attraction of all self-similar solutions which is supported by numerical simulations.

Appeared in

  • Nonlinearity, 23 (2010) pp. 409--427.

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