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Discrete Self-Similarity in Interfacial Hydrodynamics and the Formation of Iterated Structures

Michael C. Dallaston, Marco A. Fontelos, Dmitri Tseluiko, and Serafim Kalliadasis
Phys. Rev. Lett. 120, 034505 – Published 19 January 2018
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Abstract

The formation of iterated structures, such as satellite and subsatellite drops, filaments, and bubbles, is a common feature in interfacial hydrodynamics. Here we undertake a computational and theoretical study of their origin in the case of thin films of viscous fluids that are destabilized by long-range molecular or other forces. We demonstrate that iterated structures appear as a consequence of discrete self-similarity, where certain patterns repeat themselves, subject to rescaling, periodically in a logarithmic time scale. The result is an infinite sequence of ridges and filaments with similarity properties. The character of these discretely self-similar solutions as the result of a Hopf bifurcation from ordinarily self-similar solutions is also described.

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  • Received 3 January 2017

DOI:https://doi.org/10.1103/PhysRevLett.120.034505

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsFluid Dynamics

Authors & Affiliations

Michael C. Dallaston1,*, Marco A. Fontelos2, Dmitri Tseluiko3, and Serafim Kalliadasis4,†

  • 1School of Computing, Electronics, and Mathematics, and Flow Measurement and Fluid Mechanics Research Center, Coventry University, Coventry CV1 5FB, United Kingdom
  • 2Instituto de Ciencias Matemáticas, C/Nicolás Cabrera, Madrid 28049, Spain
  • 3Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
  • 4Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom

  • *At Imperial College London while undertaking work reported herein.
  • Author to whom correspondence should be addressed. s.kalliadasis@imperial.ac.uk

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Vol. 120, Iss. 3 — 19 January 2018

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