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Physics of Fluids / Volume 23 / Issue 12 / ARTICLES / Viscous and Non-Newtonian Flows

Phys. Fluids 23, 123101 (2011); http://dx.doi.org/10.1063/1.3659140 (11 pages)

Dynamic evolution of fingering patterns in a lifted Hele–Shaw cell

Julia Nase1, Didi Derks2, and Anke Lindner1

1PMMH-ESPCI, UMR 7636, CNRS, Universités UPMC and Paris 7, 10 rue Vauquelin, 75005 Paris, France
2Division of Applied Chemistry, Department of Engineering, Osaka University, Osaka 565-0871, Japan

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(Received 1 June 2011; accepted 10 October 2011; published online 7 December 2011)

We present a study on pattern formation in a Newtonian liquid during lifting of a circular Hele–Shaw cell. When a confined layer of oil is subject to such a stretch flow, air penetrates into the liquid from the sides and a fingering instability, a variant of the classical Saffman–Taylor instability, evolves. This setting has the particularity that the finger growth takes place in a conserved volume of liquid and that the dimensionless surface tension, the control parameter which governs the Saffman–Taylor instability, is changing with time. This leads to a constantly evolving pattern, which we investigate with regard to number of fingers and finger amplitude. We distinguish in the pattern at each instant growing fingers and stagnant fingers. Systematically varying the properties of the viscous oil and the geometry of the Hele–Shaw cell, we show that the number of growing fingers is at each moment well described by a simple approach based on linear stability analysis and depends only on the dimensionless surface tension. In contrast, the finger amplitude and consequently the total number of fingers (growing and stagnant fingers) depend also on the cell confinement. We demonstrate that the finger amplitude has a distinct influence on the debonding force. Higher finger amplitude and number of fingers lead to lower forces.

© 2011 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORETICAL CONSIDERATIONS
  3. EXPERIMENTAL
    1. Experimental protocol and conditions
    2. Experimental observations
  4. RESULTS I: PATTERN CHARACTERISTICS
    1. Number of fingers: Growing and stagnant fingers
    2. Influence of system parameters
    3. Discussion
  5. RESULTS II: LIFTING FORCE
  6. CONCLUSION

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KEYWORDS and PACS

Keywords

confined flow, flow control, flow instability, oils, pattern formation, surface tension, viscosity

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3659140

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.
    J. Nase, A. Lindner, and C. Creton, “Pattern formation during deformation of a confined viscoelastic layer: From a viscous liquid to a soft elastic solid,” Phys. Rev. Lett. 101, 074503 (2008).

    D. C. Hong and J. S. Langer, “Analytic theory of the selection mechanism in the Saffman-Taylor problem,” Phys. Rev. Lett. 56, 2032 (1986).

    B. I. Shraiman, “Velocity selection and the Saffman-Taylor problem,” Phys. Rev. Lett. 56, 2028 (1986).

    D. Derks, A. Lindner, C. Creton, and D. Bonn, “Cohesive failure of thin layers of soft model adhesives under tension,” J. Appl. Phys. 93, 1557 (2003)JAPIAU000093000003001557000001.

    R. M. Oliveira and J. A. Miranda, “Stretching of a confined ferrofluid: Influence of viscous stresses and magnetic field,” Phys. Rev. E 73, 036309 (2006).

    A. Lindner, D. Derks, and M. J. Shelley, “Stretch flow of thin layers of Newtonian liquids: Fingering patterns and lifting forces,” Phys. Fluids 17, 072107 (2005)PHFLE6000017000007072107000001.

    M. Tirumkudulu, W. B. Russel, and T. J. Huang, “On the measurement of `tack' for adhesives,” Phys. Fluids 15, 1588 (2003)PHFLE6000015000006001588000001.

    B. A. Francis and R. G. Horn, “Apparatus-specific analysis of fluid adhesion measurements,” J. Appl. Phys. 89, 4167 (2001)JAPIAU000089000007004167000001.


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