Importance of Surface Tension: Minimal Surfaces
From a mathematical point of view, soap films are considered as minimal surfaces. See for instance the approximate numerical method for minimal surfaces form finding at Stretched grid method. Surface tension, which measures the energy needed to create a surface indeed acts as a physical surface minimizer: since energy is proportional to the soap film surface, the film deforms to minimize its surface and, thus its energy.
Depending on the support of the soap film, the latter then naturally takes the minimal surface. On a flat support, the soap film is usually flat. But, on more complicate support, it takes the minimal achievable surface.
Read more about this topic: Soap Film
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