Loughborough University
Browse
Dallaston_PhysRevLett.120.034505.pdf (359.84 kB)

Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures

Download (359.84 kB)
journal contribution
posted on 2017-12-15, 12:06 authored by Michael C. Dallaston, Marco Fontelos, Dmitri TseluikoDmitri Tseluiko, Serafim Kalliadasis
The formation of iterated structures, such as satellite and sub-satellite 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.

Funding

We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the UK through Grants No. EP/K041134/1, EP/K008595/1 and EP/L020564/1 and from the Spanish government through Grant No. MTM2014-57158-R.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Physical Review Letters

Volume

120

Issue

3

Citation

DALLASTON, M.C. ... et al, 2018. Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures. Physical Review Letters, 120(3): paper 034505.

Publisher

American Physical Society

Version

  • VoR (Version of Record)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 Unported Licence (CC BY 4.0) . Full details of this licence are available at: https://creativecommons.org/licenses/by/4.0/

Acceptance date

2017-11-08

Publication date

2018-01-19

Notes

This is an Open Access Article. It is published by American Physical Society under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

ISSN

0031-9007

eISSN

1079-7114

Language

  • en

Article number

034505

Usage metrics

    Loughborough Publications

    Licence

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC