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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.
|Number of pages||31|
|Journal||IMA Journal of Applied Mathematics|
|Early online date||14 Jan 2019|
|Publication status||Published - 01 Apr 2019|
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- Faculty of Business and Physcial Sciences, Department of Mathematics - Professor, Head of Department (Maths)
Person: Teaching And Research
Supporting information for "Stability of a Twisted Plateau Border with Line Tension and Bending Stiffness"
Cox, S., Prifysgol Aberystwyth | Aberystwyth University, 13 Mar 2019
DOI: 10.20391/8ad4a391-b7a5-42e6-b2a5-75c97c091dca, http://facstaff.susqu.edu/brakke/evolver/evolver.html
- 1 Finished
Flow of Gas-Liquid Foams in Narrow Complex Geometries
Engineering and Physical Sciences Research Council
01 Apr 2016 → 31 Mar 2019
Project: Externally funded research