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

Abstract

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.

LaTeX, 5 pages, replaced with minor changes, accepted for publication in Physical Review Letters

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Cited by in corpus (11)

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• Discrete self-similarity in the formation of satellites for viscous cavity break-up
• Intrinsic conformal order revealed in geometrically confined long-range repulsive particles
• Stability of similarity solutions of viscous thread pinch-off
• Instability and rupture of sheared viscous liquid nanofilms
• Matched asymptotic analysis of self-similar blow-up profiles of the thin film equation