2013/07/12 by Chen, Yi-chao, Fried, Eliot
#FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft)
paper · doi:10.48550/arxiv.1307.3521
The Euler--Plateau problem, proposed by \citegm, concerns a soap film spanning a flexible loop. The shapes of the film and the loop are determined by the interactions between the two components. In the present work, the Euler--Plateau problem is reformulated to yield a boundary-value problem for a vector field that parameterizes both the spanning surface and the bounding loop. Using the first and second variations of the relevant free-energy functional, detailed bifurcation and stability analyses are performed. For spanning surface with energy density σ and a bounding loop with length 2πR and bending rigidity a, the first bifurcation, during which the spanning surface remains flat but the bounding loop becomes noncircular, occurs at σR3/a=3, confirming a result obtained previously via an energy comparison. Other bifurcation solution branches, including those emanating from the flat circular solution branch to nonplanar solution branches, are also shown to be unstable.