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Discrete self-similarity in thin film equations and the formation of iterated structures

Banff International Research Station for Mathematical Innovation and Discovery

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. Joint work with M. Dallaston, D. Tseluiko and S. Kalliadasis.

Mathematics; Fluid mechanics; Approximations and expansions; Fluid dynamics

video/mp4

Author affiliation: ICMAT

2019-10-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72105

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/