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

Roy, R. Valery and Roberts, A. J. and Simpson, M. E. (2002) A lubrication model of coating flows over a curved substrate in space. Journal of Fluid Mechanics, 454 (1). pp. 235-261. ISSN 0022-1120


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.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published version deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 01:18
Last Modified: 02 Jul 2013 22:48
Uncontrolled Keywords: lubrication model; Newtonian fluid; curved substrate; coating; curvature; lubrication theory; three-dimensional flow; viscous flow
Fields of Research : 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
09 Engineering > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: 10.1017/S0022112001007133
URI: http://eprints.usq.edu.au/id/eprint/2974

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