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Physics of Fluids / Volume 24 / Issue 2 / ARTICLES / Interfacial Flows

Phys. Fluids 24, 022105 (2012); http://dx.doi.org/10.1063/1.3682001 (18 pages)

Thin films flowing down inverted substrates: Three-dimensional flow

T.-S. Lin1, L. Kondic1, and A. Filippov2

1Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
2Houston, Texas, USA

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(Received 19 September 2011; accepted 17 January 2012; published online 14 February 2012)

We study contact line induced instabilities for a thin film of fluid under destabilizing gravitational force in three-dimensional setting. In the previous work [T.-S. Lin and L. Kondic, Phys. Fluids 22, 052105 (2010)], we considered two-dimensional flow, finding formation of surface waves whose properties within the implemented long-wave model depend on a single parameter, D = (3Ca)1/3cotα, where Ca is the capillary number and α is the inclination angle. In the present work we consider fully 3D setting and discuss the influence of the additional dimension on stability properties of the flow. In particular, we concentrate on the coupling between the surface instabilities and the transverse (fingering) instabilities of the film front. We furthermore consider these instabilities in the setting where fluid viscosity varies in the transverse direction. It is found that the flow pattern strongly depends on the inclination angle and the viscosity gradient.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. PROBLEM FORMULATION
  3. INVERTED RIVULET
    1. Inverted infinite rivulet
    2. Inverted rivulet with a front
      1. Initial and boundary conditions
      2. Results
  4. INVERTED FILM WITH A FRONT
    1. Linear stability analysis in the transverse direction
    2. Fully 3D simulations
      1. Remark
        1. The width of a finger
    3. Rayleigh-Taylor instability of inverted film
  5. INVERTED FILM OF VARIABLE VISCOSITY WITH A FRONT
  6. CONCLUSIONS

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KEYWORDS and PACS

Keywords

capillarity, film flow, flow instability, liquid films, pattern formation, surface waves (fluid), viscosity

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3682001

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.
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    J. A. Diez and L. Kondic, “Contact line instabilities of thin liquid films,” Phys. Rev. Lett. 86, 632 (2001).

    L. Kondic and J. A. Diez, “Contact line instabilities of thin film flows: Constant flux configuration,” Phys. Fluids 13, 3168 (2001)PHFLE6000013000011003168000001.

    J. R. de Bruyn, “Growth of fingers at a driven three–phase contact line,” Phys. Rev. A 46, 4500 (1992).

    S. V. Alekseenko, D. M. Markovich, and S. I. Shtork, “Wave flow of rivulets on the outer surface of an inclined cylinder,” Phys. Fluids 8, 3288 (1996)PHFLE6000008000012003288000001.

    M. Mavromoustaki, O. K. Matar, and R. V. Craster, “Shock-wave solutions in two-layer channel flow. I. One-dimensional flows,” Phys. Fluids 22, 112102 (2010)PHFLE6000022000011112102000001.

    B. R. Duffy and S. K. Wilson, “A rivulet of perfectly wetting fluid with temperature-dependent viscosity draining down a uniformly heated or cooled slowly varying substrate,” Phys. Fluids 15, 3236 (2003)PHFLE6000015000010003236000001.


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