Eur. Phys. J. Plus (2013) 128: 108
https://doi.org/10.1140/epjp/i2013-13108-y

Regular Article

Perturbative stability of catenoidal soap films

¹ Department of Physics, Indian Institute of Technology, 721 302, Kharagpur, India
² Department of Physics and Centre for Theoretical Studies, Indian Institute of Technology, 721 302, Kharagpur, India

^* e-mail: soumyajana.physics@gmail.com

Received: 16 February 2013
Revised: 16 August 2013
Accepted: 3 September 2013
Published online: 19 September 2013

Abstract

The perturbative stability of catenoidal soap films formed between parallel, equal radii, coaxial rings is studied using analytical and semi-analytical methods. Using a theorem on the nature of eigenvalues for a class of Sturm-Liouville operators, we show that, for the given boundary conditions, azimuthally asymmetric perturbations are stable, while symmetric perturbations lead to an instability --a result demonstrated in Ben Amar et al. (Eur. Phys. J. B 3, 197 (1998)) using numerics and experiment. Further, we show how to obtain the lowest real eigenvalue of perturbations, using the semi-analytical Asymptotic Iteration Method (AIM). Conclusions using AIM support the analytically obtained result as well as the results by Ben Amar et al.. Finally, we compute the eigenfunctions and show, pictorially, how the perturbed soap film evolves in time.