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Thin-film flows on rotating noncircular cylinders with large curvature variations

Chance Parrish1, Marcio S. Carvalho2, and Satish Kumar1,*

  • 1Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 2Department of Mechanical Engineering, Pontificia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Rio de Janeiro 22451-900, Brazil

  • *Corresponding author: kumar030@umn.edu
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Phys. Rev. Fluids 7, 054002 – Published 17 May, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.054002

Abstract

The coating of rotating objects with varying surface curvature is an important manufacturing step for a wide variety of products. To efficiently examine the flow of liquid coatings on such objects, we develop a lubrication-theory-based model for flow on 2D cross sections of rotating noncircular cylinders whose variations in the radius of curvature are comparable to the characteristic cylinder radius. Good quantitative agreement is found between model predictions and Galerkin finite-element method simulations when the coating thickness is small, whereas qualitative agreement is found for thicker coatings. Encouraged by this agreement, we conduct a parametric study to examine coating behavior on rotating elliptical cylinders. Four regimes of coating behavior are found spanning gravity-dominated and surface-tension-dominated regimes. The parameter space yielding smooth coatings on elliptical cylinders is small, suggesting the need for additional steps such as the addition of surfactant to widen this coating window.

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Phys. Rev. Fluids 7, 054002– Published 17 May, 2022
  • Received 23 June 2021
  • Accepted 5 April 2022
Article part of CHORUS
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