Discrete self-similarity in interfacial hydrodynamics and the formation of iterated structures
File(s)
Published version
Author(s)
Dallaston, Michael C
Fontelos, Marco A
Tseluiko, Dmitri
Kalliadasis, Serafim
Type
Journal Article
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.
Date Issued
2018-01-19
Date Acceptance
2017-11-08
Citation
Physical Review Letters, 2018, 120 (3), pp.034505-1-034505-5
ISSN
0031-9007
Publisher
American Physical Society
Start Page
034505-1
End Page
034505-5
Journal / Book Title
Physical Review Letters
Volume
120
Issue
3
Copyright Statement
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.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Identifier
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.034505
Grant Number
EP/K008595/1
EP/L020564/1
EP/K041134/1
Subjects
physics.flu-dyn
physics.flu-dyn
Notes
LaTeX, 5 pages, replaced with minor changes, accepted for publication in Physical Review Letters
Publication Status
Published
Article Number
034505
Date Publish Online
2018-01-19