Stability of a Twisted Plateau Border with Line Tension and Bending Stiffness

Whittaker, Robert and Cox, Simon (2019) Stability of a Twisted Plateau Border with Line Tension and Bending Stiffness. IMA Journal of Applied Mathematics, 84 (2). pp. 835-415. ISSN 0272-4960

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Abstract

The stability of a Plateau border between three soap films is considered, taking into account the effects of line tension and bending stiffness in the border. A simple geometry is considered, in which the border initially lies in equilibrium along the axis of a circular cylinder, with three equally-spaced films radiating outwards to meet the inside wall of the cylinder. The films are pinned at the two ends of the cylinder with a fixed relative twist, so the initial film surfaces are helicoids. The stability of this system to small perturbations, involving both the films and the border, is investigated as a function of the cylinder aspect ratio, twist angle, film surface tension, border line tension, and border bending stiffness. Analytically, the stability problem is reduced to finding the first occurrence of a zero eigenvalue of an infinite matrix, which is then estimated numerically. The results from this calculation are in good agreement with full numerical simulations.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: LivePure Connector
Date Deposited: 13 Feb 2019 14:30
Last Modified: 15 May 2020 00:08
URI: https://ueaeprints.uea.ac.uk/id/eprint/69922
DOI: 10.1093/imamat/hxy063

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