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

K. Afanasiev·A. Münch·B. Wagner
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Abstract

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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K. Afanasiev, A. Münch, B. Wagner. 2007-06-02. Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath. https://arxiv.org/abs/physics/0605109

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