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Viscous fingering and dendritic growth under an elastic membrane

Published online by Cambridge University Press:  02 August 2017

Lucie Ducloué Open the ORCID record for Lucie Ducloué [Opens in a new window] ,
Andrew L. Hazel Open the ORCID record for Andrew L. Hazel [Opens in a new window] ,
Draga Pihler-Puzović  and
Anne Juel Open the ORCID record for Anne Juel [Opens in a new window]
Lucie Ducloué
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
Andrew L. Hazel
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK
Draga Pihler-Puzović
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
Anne Juel
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK
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Abstract

We present an experimental investigation of interfacial fingering instabilities in a compliant channel, where the interface can adopt a planar front orthogonal to the direction of propagation over most of the channel width. Finite-length fingers develop on that front, similarly to the previously studied radial configuration with injection of air at constant flow rate (Pihler-Puzović et al., Phys. Rev. Lett., vol. 108 (7), 2012, 074502), but, unlike the radial case, the interface propagates steadily. This allows us to present the first quantification of the nonlinearly saturated fingering pattern and to demonstrate that the morphological features of the fingers are selected in a simple way by the local geometry of the compliant cell. In contrast, the local geometry itself is determined from a complex fluid–solid interaction. Furthermore, we find that changes to the geometry of the channel cross-section lead to a rich variety of possible interfacial patterns.

JFM classification

Interfacial Flows (free surface): Fingering instability Nonlinear Dynamical Systems: Pattern formation

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Type
Rapids
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , R2
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Copyright
© 2017 Cambridge University Press 

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Ducloué et al. supplementary movie 1

Aerial view of an air finger steadily propagating under a latex membrane (b=210 μm) topping a partially occluded channel. The fingers regularly split, maintaining a constant average width and length. Block dimensions: 30 mm wide and 900 μm high; h = 150 μm. The video has been slowed down four times.

Download Ducloué et al. supplementary movie 1(Video)
Video 906.1 KB

Ducloué et al. supplementary movie 2

Side view of an air finger propagating under a thin (b = 100 μm) silicone membrane. The transparent membrane has been dusted with fine powder to make the laser line visible (bright line). The straight section of interface propagating on the block does not undergo fingering. Block dimensions: 30 mm wide and 900 μm high; h = 150 μm. The video has been slowed down twice.

Download Ducloué et al. supplementary movie 2(Video)
Video 3.6 MB