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Physics of Fluids / Volume 21 / Issue 9 / LETTERS

Phys. Fluids 21, 091702 (2009); http://dx.doi.org/10.1063/1.3231847 (4 pages)

Multiple-timescale asymptotic analysis of transient coating flows

C. M. Groh and M. A. Kelmanson

Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

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(Received 12 June 2009; accepted 27 August 2009; published online 22 September 2009)

New stability results for the widely studied paradigm “rotating cylinder coating flow” problem are found using a novel multiple-timescale asymptotic approach that is not only fully automated within an algebraic-manipulator platform, but also more widely applicable to diverse evolution equations, particularly those arising in thin-film flow on spatially periodic topographies. Hitherto undiscovered contributions to the capillary decay and gravitational drift in the Fourier modes comprising the coating-film thickness on the cylinder are found, the main discovery being the formal derivation of the functional form of a time-dependent decay rate that has previously been speculated only partially and heuristically. The new asymptotic approach admits analysis of the solution on a geometric progression of increasingly slow timescales, the slowest timescale being a priori dictated in the automated procedure. Theoretical results are in excellent agreement with those obtained from spectrally accurate numerical integrations of the evolution equation for the film thickness. The extent to which the predictions of prior related asymptotic studies are improved upon is quantified.

© 2009 American Institute of Physics

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KEYWORDS and PACS

Keywords

capillarity, coatings, film flow, gravity, surface tension

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3231847

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    A. Oron, S. H. Davis, and S. G. Bankoff, “Long-scale evolution of thin liquid films,” Rev. Mod. Phys. 69, 931 (1997).

    P. L. Evans, L. W. Schwarz, and R. V. Roy, “Steady and unsteady solutions for coating flow on a rotating horizontal cylinder: Two-dimensional theoretical and numerical modeling,” Phys. Fluids 16, 2742 (2004)PHFLE6000016000008002742000001.

    E. S. Benilov and S. B. G. O'Brien, “Inertial instability of a liquid film inside a rotating horizontal cylinder,” Phys. Fluids 17, 052106 (2005)PHFLE6000017000005052106000001.

    P. L. Evans, L. W. Schwarz, and R. V. Roy, “Three-dimensional solutions for coating flow on a rotating horizontal cylinder: Theory and experiment,” Phys. Fluids 17, 072102 (2005)PHFLE6000017000007072102000001.


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