Analysis of the Shape Hysteresis of a Soap Film Supported by Two Circular Rings

Abstract

The behavior of a minimal surface supported by two circular coaxial rings is analyzed by increasing (decreasing) distance between rings. The assumption on metastability of certain configurations of the minimal surface is confirmed. This makes it possible to explain hysteresis of a soap film taking on different configurations observed experimentally. The effectiveness of applying analytical methods of the theory of flows of Non-Newtonian fluids through porous media to the problem of describing minimal surfaces on rings is demonstrated.