Physics
Soap films
Minimal surfaces on wire frames and the physics of soap bubbles.
What happens
A soap film stretched between two rings takes the shape of least area, the catenoid. Pull the rings apart with the slider: the neck thins, turns metastable and finally snaps into two flat disks, the Goldschmidt solution. Dip the rings again to rebuild the film; the chart compares the neck with theory.
Equations used in the module
Equations E = 2γA; H = 0 Δp = 2γ(1/R₁+1/R₂) r(z) = a cosh(z/a); R = a cosh(h/(2a)) h/R ≤ 1.32549 Δx_i ∝ −∂A/∂x_i
