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