WIAS Preprint No. 1069, (2005)

Lubrication models with small to large slip lengths



Authors

  • Münch, Andreas
  • Wagner, Barbara
  • Witelski, Thomas P.

2010 Mathematics Subject Classification

  • 76A2 76D27

2008 Physics and Astronomy Classification Scheme

  • 97.10.Gz 97.30.Qt

Keywords

  • lubrication models, matched asymptotics, stability analysis, Navier slip condition, dewetting films

Abstract

A set of lubrication models for the thin film flow of incompressible fluids on solid substrates is derived and studied.The models are obtained as asymptotic limits of the Navier-Stokes equations with the Navier-slip boundary condition for different orders of magnitude for the slip-length parameter. Specifically, the influence of slip on the dewetting behavior of fluids on hydrophobic substrates is investigated here. Matched asymptotics are used to describe the dynamic profiles for dewetting films and comparison is given with computational simulations. The motion of the dewetting front shows transitions from being nearly linear in time for no-slip to $t^2/3$ as the slip is increased. For much larger slip lengths the front motion appears to become linear again. Correspondingly, the dewetting profiles undergo a transition from oscillatory to monotone decay into the uniform film layer for large slip.Increasing the slip further, to very large values, is associated with an increasing degree of asymmetry in the structure of the dewetting ridge profile.

Appeared in

  • J. Engrg. Math., 53 (2005) pp. 359-383.

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