  A variational model 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 elastic rod resistant to both bending and
twist. The first and second energy variations of the underlying energy
functional are derived, leading to governing equilibrium equations and
stability criteria. The latter criteria are employed to explore the stability
of flat circular configurations with respect to planar and transverse
perturbations. Experiments are performed to study post-buckled configurations
and to explore the validity of the theoretical predictions. Imparting a twist
to the bounding loop destabilizes flat circular loops which are short-enough to
be stable when twist-free. Nevertheless, when the circular disk is perturbed
merely radially or merely transversely, the stability condition is indifferent
to twist. By the equilibrium equations, the twisting angle of a planar
equilibrium configuration should be distributed uniformly along the loop. The
stability criteria guarantee that this uniformity is preserved after buckling.
The stability with respect to increasing the surface tension of the film or the
length of the loop is sensitive to the cross-sectional thickness of the
bounding loop. However, stability with respect to increasing the total twist is
indifferent to that thickness.
