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Self-similar dynamics of air film entrained by a solid disk in confined space: A simple prototype of topological transitions

Hana Nakazato, Yuki Yamagishi, and Ko Okumura
Phys. Rev. Fluids 3, 054004 – Published 17 May 2018
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Abstract

In hydrodynamic topological transitions, one mass of fluid breaks into two or two merge into one. For example, in honey-drop formation when honey is dripping from a spoon, honey is extended to separate into two masses as the liquid neck bridging them thins down to the micron scale. At the moment when the topology changes due to the breakup, physical observables such as surface curvature locally diverge. Such singular dynamics has widely attracted physicists, revealing universality in self-similar dynamics, which shares much in common with critical phenomena in thermodynamics. Many experimental examples have been found, including an electric spout and vibration-induced jet eruption. However, only a few cases have been physically understood on the basis of equations that govern the singular dynamics and even in such a case the physical understanding is mathematically complicated, inevitably involving delicate numerical calculations. Here we study the breakup of air film entrained by a solid disk into viscous liquid in a confined space, which leads to formation, thinning, and breakup of the neck of air. As a result, we unexpectedly find that equations governing the neck dynamics can be solved analytically by virtue of two remarkable experimental features: Only a single length scale linearly dependent on time remains near the singularity and two universal scaling functions describing the singular neck shape and velocity field are both analytic. The present solvable case would be essential for a better understanding of the singular dynamics and will help reveal the physics of unresolved examples intimately related to daily-life phenomena and diverse practical applications.

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  • Received 8 December 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.054004

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsFluid DynamicsStatistical Physics & ThermodynamicsPolymers & Soft Matter

Authors & Affiliations

Hana Nakazato, Yuki Yamagishi, and Ko Okumura*

  • Department of Physics and Soft Matter Center, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan

  • *okumura@phys.ocha.ac.jp

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Vol. 3, Iss. 5 — May 2018

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