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Register a new userA new setup for giant soap films characterization
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Artists, using an empirical knowledge, manage to generate and play with giant soap films and bubbles. Until now, scientific studies of soap films generated at a controlled velocity and without any feeding from the top, studied films of a few square centimeters. The present work aims to present a new setup to generate and characterize giant soap films (2~m $times$ 0.7~m). Our setup is enclosed in a humidity-controlled box of 2.2~m high, 1~m long and 0.75~m large. Soap films are entrained by a fishing line withdrawn out of a bubbling solution at various velocities. We measure the maximum height of the generated soap films, as well as their lifetime, thanks to an automatic detection. This is allowed by light-sensitive resistors collecting the light reflected on the soap films and ensures robust statistical measurements. In the meantime, thickness measurements are performed with a UV-VIS-spectrometer, allowing us to map the soap films thickness over time.
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We develop a general framework for the description of instabilities on soap films using the Bjorling representation of minimal surfaces. The construction is naturally geometric and the instability has the interpretation as being specified by its amplitude and transverse gradient along any curve lying in the minimal surface. When the amplitude vanishes, the curve forms part of the boundary to a critically stable domain, while when the gradient vanishes the Jacobi field is maximal along the curve. In the latter case, we show that the Jacobi field is maximally localised if its amplitude is taken to be the lowest eigenfunction of a one-dimensional Schrodinger operator. We present examples for the helicoid, catenoid, circular helicoids and planar Enneper minimal surfaces, and emphasise that the geometric nature of the Bjorling representation allows direct connection with instabilities observed in soap films.
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