Soap-film dynamics and topological transitions under continuous deformation∗

The response of a soap film to the continuous deformation of its wire boundary is considered, with particular attention to the topological transitions that can occur at critical stages of the deformation process. Two well-known examples that have been studied by both theory and experiment are the catenoid suspended between circular wires in parallel planes, and the Möbius-strip soap film spanning a wire that is twisted and folded back on itself. In this latter case, we have shown in previous publications that, when the wire is unfolded, the soap film undergoes a topological transition through a boundary singularity to a two-sided film, with a corresponding jump in the linking number between the axis of the wire and the Plateau boundary on its surface. Here, we review this particular aspect of the problem, and propose a simplified model experiment through which the slipping adjustment of a Plateau border on a solid surface may be investigated.