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Lubrication models with small to large slip lengths

Publication ,  Journal Article
Münch, A; Wagner, B; Witelski, TP
Published in: Journal of Engineering Mathematics
December 1, 2005

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 t2/3 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. © Springer 2005.

Duke Scholars

Published In

Journal of Engineering Mathematics

DOI

EISSN

1573-2703

ISSN

0022-0833

Publication Date

December 1, 2005

Volume

53

Issue

3-4

Start / End Page

359 / 383

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0913 Mechanical Engineering
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Münch, A., Wagner, B., & Witelski, T. P. (2005). Lubrication models with small to large slip lengths. Journal of Engineering Mathematics, 53(3–4), 359–383. https://doi.org/10.1007/s10665-005-9020-3
Münch, A., B. Wagner, and T. P. Witelski. “Lubrication models with small to large slip lengths.” Journal of Engineering Mathematics 53, no. 3–4 (December 1, 2005): 359–83. https://doi.org/10.1007/s10665-005-9020-3.
Münch A, Wagner B, Witelski TP. Lubrication models with small to large slip lengths. Journal of Engineering Mathematics. 2005 Dec 1;53(3–4):359–83.
Münch, A., et al. “Lubrication models with small to large slip lengths.” Journal of Engineering Mathematics, vol. 53, no. 3–4, Dec. 2005, pp. 359–83. Scopus, doi:10.1007/s10665-005-9020-3.
Münch A, Wagner B, Witelski TP. Lubrication models with small to large slip lengths. Journal of Engineering Mathematics. 2005 Dec 1;53(3–4):359–383.
Journal cover image

Published In

Journal of Engineering Mathematics

DOI

EISSN

1573-2703

ISSN

0022-0833

Publication Date

December 1, 2005

Volume

53

Issue

3-4

Start / End Page

359 / 383

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0913 Mechanical Engineering
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics