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Simulation of a Soap Film Möbius Strip Transformation

Part of: Thin bodies, structures Incompressible viscous fluids

Published online by Cambridge University Press:  07 September 2017

Yongsam Kim ,
Ming-Chih Lai  and
Yunchang Seol
Yongsam Kim*
Affiliation:
Department of Mathematics, Chung-Ang University, Dongjakgu Heukseokdong, Seoul 156-756, Korea
Ming-Chih Lai*
Affiliation:
Department of Applied Mathematics, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 300, Taiwan
Yunchang Seol*
Affiliation:
National Center for Theoretical Sciences, No. 1, Sec. 4, Road. Roosevelt, National Taiwan University, Taipei 10617, Taiwan
*
*Corresponding author. Email addresses:kimy@cau.ac.kr (Y. Kim), mclai@math.nctu.edu.tw (M.-C. Lai), ycseol@ntu.edu.tw (Y. Seol)
*Corresponding author. Email addresses:kimy@cau.ac.kr (Y. Kim), mclai@math.nctu.edu.tw (M.-C. Lai), ycseol@ntu.edu.tw (Y. Seol)
*Corresponding author. Email addresses:kimy@cau.ac.kr (Y. Kim), mclai@math.nctu.edu.tw (M.-C. Lai), ycseol@ntu.edu.tw (Y. Seol)
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Abstract

If the closed wire frame of a soap film having the shape of a Möbius strip is pulled apart and gradually deformed into a planar circle, the soap film transforms into a two-sided orientable surface. In the presence of a finite-time twist singularity, which changes the linking number of the film's Plateau border and the centreline of the wire, the topological transformation involves the collapse of the film toward the wire. In contrast to experimental studies of this process reported elsewhere, we use a numerical approach based on the immersed boundary method, which treats the soap film as a massless membrane in a Navier-Stokes fluid. In addition to known effects, we discover vibrating motions of the film arising after the topological change is completed, similar to the vibration of a circular membrane.

Keywords

Möbius stripminimal surfacetwist singularitytopological changeNavier-Stokes equationimmersed boundary method

MSC classification

Secondary: 68U20: Simulation 74K35: Thin films 76D05: Navier-Stokes equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 3 , August 2017 , pp. 615 - 628
Copyright
Copyright © Global-Science Press 2017 

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