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

Robert J. Whittaker, Simon Cox

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

131 Wedi eu Llwytho i Lawr (Pure)

Crynodeb

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.
Iaith wreiddiolSaesneg
Rhif yr erthyglhxy063
Tudalennau (o-i)385-415
Nifer y tudalennau31
CyfnodolynIMA Journal of Applied Mathematics
Cyfrol84
Rhif cyhoeddi2
Dyddiad ar-lein cynnar14 Ion 2019
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 01 Ebr 2019

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