Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/50933
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Type: | Journal article |
Title: | A lubrication model of coating flows over a curved substrate in space |
Author: | Roy, R. Roberts, A. Simpson, M. |
Citation: | Journal of Fluid Mechanics, 2002; 454:235-261 |
Publisher: | Cambridge Univ Press |
Issue Date: | 2002 |
ISSN: | 0022-1120 1469-7645 |
Statement of Responsibility: | R. Valéry Roy, A. J. Roberts and M. E. Simpson |
Abstract: | <jats:p>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.</jats:p> |
Rights: | Copyright © 2002 Cambridge University Press |
DOI: | 10.1017/S0022112001007133 |
Published version: | http://dx.doi.org/10.1017/s0022112001007133 |
Appears in Collections: | Aurora harvest 5 Mathematical Sciences publications |
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hdl_50933.pdf | Published version | 629.11 kB | Adobe PDF | View/Open |
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