# A lubrication model of coating flows over a curved substrate in space

Article

*Journal of Fluid Mechanics.*454 (1), pp. 235-261. https://doi.org/10.1017/S0022112001007133

Article Title | A lubrication model of coating flows over a curved substrate in space |
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ERA Journal ID | 1294 |

Article Category | Article |

Authors | Roy, R. Valery (Author), Roberts, A. J. (Author) and Simpson, M. E. (Author) |

Journal Title | Journal of Fluid Mechanics |

Journal Citation | 454 (1), pp. 235-261 |

Number of Pages | 27 |

Year | 2002 |

Place of Publication | Cambridge, United Kingdom |

ISSN | 0022-1120 |

1469-7645 | |

Digital Object Identifier (DOI) | https://doi.org/10.1017/S0022112001007133 |

Web Address (URL) | http://ejournals.ebsco.com/direct.asp?ArticleID=3WGLGFA40VM26MHD5W2D> |

Abstract | Consider the three-dimensional flow of a viscous Newtonian fluid upon an arbitrarily curved substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We drive the lubrication model of the dynamics of the film expressed in terms of the film thickness. The comprehensive model accurately includes the effects of the curvature of the substrate, via a physical multiple-scale approach, and gravity and inertia, via more rigorous centre manifold techniques. This new approach theoretically supports the use of the model over a wide range of parameters and provides a sound basis for further development of lubrication models. Numerical simulations exhibit some generic features of the dynamics of such thin fluid films on substrates with complex curvature: we here simulate a film thinning at a corner, the flow around a torus, and draining of a film down a cylinder. The last is more accurate than other lubrication models. The model derived here describes well thin-film dynamics over a wide range of parameter regimes. |

Keywords | lubrication model; Newtonian fluid; curved substrate; coating; curvature; lubrication theory; three-dimensional flow; viscous flow |

ANZSRC Field of Research 2020 | 401207. Fundamental and theoretical fluid dynamics |

401299. Fluid mechanics and thermal engineering not elsewhere classified | |

401706. Numerical modelling and mechanical characterisation | |

Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |

Byline Affiliations | University of Delaware, United States |

Department of Mathematics and Computing |

https://research.usq.edu.au/item/9y52x/a-lubrication-model-of-coating-flows-over-a-curved-substrate-in-space

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