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

Robert Whittaker, Simon Cox

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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.
Original languageEnglish
Pages (from-to)385-415
Number of pages31
JournalIMA Journal of Applied Mathematics
Volume84
Issue number2
Early online date14 Jan 2019
DOIs
Publication statusPublished - Apr 2019

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