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Shape of an elastic loop strongly bent by surface tension: Experiments and comparison with theory
Phys. Rev. E 86, 026119 – Published 30 August, 2012
DOI: https://doi.org/10.1103/PhysRevE.86.026119
Abstract
When a very flexible wire is dipped into a soapy solution, it collapses onto itself. We consider the regions of high curvature where the wire folds back onto itself, enclosing a capillary film. The shapes of these end loops are measured in experiments using soap films and compared to a known similarity solution. The sizes of these structures provide a simple and reliable way to measure surface tension.
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References (18)
- A. Love, A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944).
- L. Giomi and L. Mahadevan, Proc. R. Soc. London, Ser. A 468, 1851 (2012).
- A. E. Cohen and L. Mahadevan, Proc. Natl. Acad. Sci. USA 100, 12141 (2003).
- J. Bico, B. Roman, L. Moulin, and A. Boudaoud, Nature (London) 432, 690 (2004).
- J. E. Flaherty, J. B. Keller, and S. I. Rubinow, SIAM J. Appl. Math. 23, 446 (1972).
- J. Plateau, Mém. Acad. Roy. Belgique 29, 1 (1849).
- M. Lévy, J. Math. Pure Appl. 10, 5 (1884).
- G. F. Carrier, J. Math. Phys. 26, 94 (1947).
- A. J. Adams, J. Math. Phys. 49, 032902 (2008).
- I. Tadjbakhsh and F. Odeh, J. Math. Anal. Appl. 18, 59 (1967).
- P. A. Djondjorov, V. M. Vassilev, and I. M. Mladenov, Int. J. Mech. Sci. 53, 355 (2011).
- H.-Y. Kim and L. Mahadevan, J. Fluid Mech. 548, 141 (2004).
- C. Py, P. Reverdy, L. Doppler, J. Bico, B. Roman, and C. N. Baroud, Phys. Rev. Lett. 98, 156103 (2007).
- K. Holmberg, B. Jonsson, B. Kronberg, and B. Lindman, Surfactants and Polymers in Aqueous Solution (Wiley, Chichester, 2007).
- S. Antman, J. Math. Anal. Appl. 21, 132 (1968).
- R. Burridge and J. B. Keller, SIAM Rev. 20, 31 (1978).
- C. Majidi, Mech. Res. Commun. 34, 85 (2007).
- Computer code wolfram mathematica (Wolfram Research, Inc., Champaign, IL, 2011).