Stability of a twisted Plateau border with line tension and bending stiffness

Authors Organisations
Type Article
Original languageEnglish
Article numberhxy063
Number of pages29
JournalIMA Journal of Applied Mathematics
Volume82
Issue number2
Early online date14 Jan 2019
DOI
Publication statusPublished - 01 Apr 2019
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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.