WIAS Preprint No. 1074, (2005)

Thin film dynamics on vertically rotating disks


  • Afanasiev, Konstantin
  • Münch, Andreas
  • Wagner, Barbara

2010 Mathematics Subject Classification

  • 76A20 76D27 65M60 41A60

2008 Physics and Astronomy Classification Scheme

  • 47.85.mf 47.32.Ef


  • Lubrication theory, FEM, matched asymptotic expansions, rotating flow, free boundary flow


The axisymmetric flow of a thin liquid film subject to surface tension, gravity and centrifugal forces is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. This problem constitutes a generalization of the classic Landau-Levich drag-out problem to axisymmetric flow. A generalized lubrication model that includes the meniscus region connecting the thin film to the bath is derived. The resulting nonlinear fourth-order partial differential equation is solved numerically using a finite element scheme. For a range of parameters steady states are found. While the solutions for the height profile of the film near the drag-out region show excellent agreement with the asymptotic solutions to the corresponding classic Landau-Levich problem, they show novel patterns away from the meniscus region. The implications for possible industrial applications are discussed.

Appeared in

  • Appl. Math. Modelling, 32 (2008) pp. 1894-1911.

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