The distortion of a horizontal soap film due to the impact of a falling sphere. (12th October 2019) - Chen, C.-H.; Perera, A.; Jackson, P.; Hallmark, B.; Davidson, J.F.
Graphical abstract: Highlights: A small sphere falls through a horizontal soap film: the film detaches at angle ψ . The sphere may bounce, or pass through the film before rupturing it. There is film rupture when the angle of detachment, ψ, is about 150°. Prediction of film shape assumes zero pressure difference across the film. The film surface area is shown to be minimal, taking the shape of a catenoid. Abstract: A horizontal soap film is established in vertical tube a few centimetres in diameter. A metal sphere, 1–2 mm diameter, is dropped onto the film, whose distortion is observed by means of a high speed camera. The film wraps partly around the sphere, detaching at a circle which moves up the sphere as it falls. The shape of the film at successive radii, bigger than the radius of contact, was predicted from theory relying on the proposition that if both sides of the film are open to atmosphere, there can be no pressure difference across it. The pressure difference across a film is proportional to (surface tension)/(radius of curvature); hence it follows that the radii of curvature in two planes, perpendicular to each other and to the film surface, must be equal and opposite. This proposition gives equations predicting the shape, in reasonable agreement with experiment. This theory is compared with the theory of catenoids, first studied by Euler in 1744. Catenoid theory gives exactly the same results as the 'radius of curvature' theory presented here. A simple energy conservation argument shows that the two theories are compatible and agree with a published photograph of a soap film catenoid.