Theoretical and experimental study of the stability of a soap film spanning a flexible loop

A variational approach is used to study the stability of a soap film spanning a flexible loop. The film is modeled as a fluid surface endowed with constant tension and the loop is modeled as an inextensible and unshearable elastic rod that resists not only bending but also twisting about the tangent to its centerline. The first and second variations of the underlying energy functional are derived, leading to governing equilibrium equations and energetically based stability conditions. The latter conditions are applied to explore the effect of subjecting flat circular configurations to planar and transverse perturbations. Both the areal stretching and the lineal twisting prove to compete against the lineal bending to destabilize such a configuration. Experiments are performed to study post-buckled configurations and to assess the validity of the theoretical predictions.