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Physics of Fluids / Volume 15 / Issue 6 / ARTICLES

Phys. Fluids 15, 1702 (2003); doi:10.1063/1.1568340 (9 pages)

Interfacial hoop stress and instability of viscoelastic free surface flows

Michael D. Graham

Department of Chemical Engineering, University of Wisconsin-Madison, 1415 Engineering Drive, Madison, Wisconsin 53706-1691

(Received 29 July 2002; accepted 24 February 2003; published online 6 May 2003)

Viscoelasticity can dramatically exacerbate free surface flow instabilities. It is shown here that this destabilization arises, at least in part, from the combination of large tangential tension and curvature along a concave free surface. Tension and curvature generically lead to an unstable stress gradient at the free surface; a perturbation that locally thickens a fluid layer leads to a local accumulation of hoop stress, which drives further thickening of the layer. A simple theory based in this observation captures several features of experimental observations of coating flows, specifically the correlation between destabilization and extensional viscosity and the increase in wavenumber with viscoelasticity. In a particular model situation, instability of flow with a concave free surface can be reduced to a viscoelastic Rayleigh-Taylor problem, which is amenable to analytical treatment. In this situation the growth rate can be very large, because the stored elastic energy cannot balance the surface work associated with interface deformation. Application of the theory to the instability of filament stretching flow yields a prediction of the Weissenberg number below which instability does not occur that agrees well with experimental observations. © 2003 American Institute of Physics.  

© 2003 American Institute of Physics

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KEYWORDS and PACS

Keywords

surface tension, non-Newtonian flow, Rayleigh-Taylor instability, perturbation theory, coatings

PACS

  • 47.50.-d

    Non-Newtonian fluid flows

  • 47.20.Dr

    Surface-tension-driven instability

  • 68.03.Cd

    Surface tension and related phenomena

  • 47.15.Fe

    Stability of laminar flows

ARTICLE DATA

Permalink
http://link.aip.org/link/doi/10.1063/1.1568340

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.
    K. R. Shull, C. M. Flanigan, and A. J. Crosby, "Fingering instabilities of confined elastic layers in tension," Phys. Rev. Lett. 84, 3057 (2000).

    L. Schwartz, "Stability of Hele-Shaw flows: The wetting layer effect," Phys. Fluids 29, 3086 (1986)PFLDAS000029000009003086000001.

    Y. L. Joo and E. S. G. Shaqfeh, "Viscoelastic Poiseuille flow through a curved channel: A new elastic instability," Phys. Fluids A 3, 1691 (1991)PFADEB000003000007001691000001.

    P. Pakdel and G. H. McKinley, "Elastic instability and curved streamlines," Phys. Rev. Lett. 77, 2459 (1996).


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