An accurate and comprehensive model of thin fluid flows with inertia on curved substrates

Roberts, A. J. and Li, Zhenquan (2006) An accurate and comprehensive model of thin fluid flows with inertia on curved substrates. Journal of Fluid Mechanics, 553 (1). pp. 33-73. ISSN 1469-7645

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Abstract

Consider the three-dimensional flow of a viscous Newtonian fluid upon a curved two-dimensional substrate when the fluid film is thin, as occurs in many draining, coating and biological flows. We derive a comprehensive model of the dynamics of the film, the model being expressed in terms of the film thickness n and the average lateral velocity Pu. Centre manifold theory assures us that the model accurately and systematically includes the effects of the curvature of substrate, gravitational body force, fluid inertia and dissipation. The model resolves wavelike phenomena in the dynamics of viscous fluid flows over arbitrarily curved substrates such as cylinders, tubes and spheres. We briefly illustrate its use in simulating drop formation on cylindrical fibres, wave transitions, three-dimensional instabilities, Faraday waves, viscous hydraulic jumps, flow vortices in a compound channel and flow down and up a step. These models are the most complete models for thin-film flow of a Newtonian fluid; many other thin-film models can be obtained by different restrictions and truncations of the model derived here.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: This is the author's version, deposited in accordance with the publisher's policy.
Depositing User: epEditor USQ
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 00:31
Last Modified: 02 Jul 2013 22:35
Uncontrolled Keywords: viscous fluid flows; flow over curved surfaces; thin-film flow
Fields of Research (FOR2008): 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
09 Engineering > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics
01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI: doi: 10.1017/S0022112006008640
URI: http://eprints.usq.edu.au/id/eprint/887

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