Journal
PHYSICAL REVIEW LETTERS
Volume 120, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.120.034505
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Funding
- Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom [EP/K041134/1, EP/K008595/1, EP/L020564/1]
- Spanish government [MTM2014-57158-R]
- EPSRC [EP/K008595/1, EP/K041134/1, EP/L020564/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K008595/1, EP/L020564/1, EP/K041134/1] Funding Source: researchfish
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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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