Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath

Details Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath

2006-05-14

arxiv.org/abs/physics/0605109v2

Physics

Fluid Dynamics

31 pages, 19 figures accepted: Applied Mathematical Modelling

Scientific paper

The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that drags a thin film out of the bath is set up. From this, a dimension-reduced extended lubrication approximation that includes the meniscus region is derived. This problem constitutes a generalization of the classic drag-out and drag-in problem to the case of axisymmetric flow. The resulting nonlinear fourth-order partial differential equation for the film profile is solved numerically using a finite element scheme. For a range of parameters steady states are found and compared to asymptotic solutions. Patterns of the film profile, as a function of immersion depth and angular velocity are discussed.

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