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Instability of radially spreading extensional flows. Part 1. Experimental analysis

Published online by Cambridge University Press:  25 October 2019

Roiy Sayag Open the ORCID record for Roiy Sayag [Opens in a new window]  and
M. Grae Worster
Roiy Sayag*
Affiliation:
Department of Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 8499000, Israel Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 8410501, Israel
M. Grae Worster
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

We present laboratory experiments that show that fingering patterns can emerge when circular interfaces of strain-rate-softening fluids displace less viscous fluids in extensionally dominated flows. The fingers were separated by regions in which the fluid appeared to be torn apart. Initially, the interface had a large dominant wavenumber, but some of the fingers progressively merged so that the number of fingers gradually declined in time. We find that the transition rate to a lower wavenumber during this cascade is faster the larger is the discharge flux of the displacing fluid. At late times, depending on the discharge flux, the pattern either converged into an integer wavenumber or varied stochastically within a finite range of wavenumbers, implying convergence to a fractional wavenumber. In that stage of the evolution we find that the average wavenumber declines with the discharge flux of the displacing fluid.

JFM classification

Complex Fluids: Complex Fluids Instability: Instability Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 881 , 25 December 2019 , pp. 722 - 738
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Copyright
© 2019 Cambridge University Press 

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Sayag et al. supplementary movie 1

Movie of experiment with source flux Q = 3.9 g/cm^3

Download Sayag et al. supplementary movie 1(Video)
Video 3.3 MB

Sayag et al. supplementary movie 2

Movie of experiment with source flux Q = 2.64 g/cm^3

Download Sayag et al. supplementary movie 2(Video)
Video 4.8 MB

Sayag et al. supplementary movie 3

Movie of experiment with source flux Q = 1.36 g/cm^3

Download Sayag et al. supplementary movie 3(Video)
Video 2.8 MB