Dallaston_PhysRevLett.120.034505.pdf (359.84 kB)
Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures
journal contribution
posted on 2017-12-15, 12:06 authored by Michael C. Dallaston, Marco Fontelos, Dmitri TseluikoDmitri Tseluiko, Serafim KalliadasisThe 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 LettersVolume
120Issue
3Citation
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 SocietyVersion
- 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
2017-11-08Publication date
2018-01-19Notes
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
0031-9007eISSN
1079-7114Publisher version
Language
- en