illustris

A ball chain is siphoning out of a beaker like a fountain jet when its loose end experiences gravity as soon as it extends beyond the rim of the beaker. This phenomenon is known as Mould effect, reported by Steve Mould in 2013. The physics has been described by Biggins and Warner in 2014 (Proc. R. Soc. A 470:20130689 , YouTube video). The fountain height is proportional to the distance between the beaker and the floor, the velocity of the falling chain. The essential force which pushes the chain upwards was believed to be a result from restricted chain flexibility, its beads cannot be bent at any angle to each other (picture below). Several beads next to the point where the chain is lifted are acting like a stiff rod (symbolized as rectangular in the sketch below). Lifting one end would lead to rotation around the rod's center of mass. Consequently, the opposite end is pushing on the underlying, unyielding chain reservoir which propels the beads upwards. Therefore the fountain effect is not observed with flexibel chains, e.g. ball chains with longer and flexible spacer between the beads. Nevertheless, other 1D objects consisting of aligned rigid building blocks linked by flexible joints will behave like the bead chain shown in the slow motion movie. Biggins and Warner demonstrated that with macaroni on a string. However, in 2016 an article from Rogério Martins unraveled mechanistic details in the uncoiling of a ball chain from 2D arrays. The chain dynamics increases with the number of twists, each of them creating a whip like backlash. Indeed, the chain fountain height is more pronounced if the chain in the beaker is laid more randomly (more twists).

Below are videos inspired by the chain fountain. The upper ones illustrate the difference between a semi-rigid (left) and a flexibel (right) ball chain, the latter would not show self-sustained siphoning (vide supra). Below two "human" chains are shown, the one on the right illustrates the necessary balance of flexibility and rigidity for a chain fountain. This natural phenomenon is a paradox: it's rooted in the chain segments' restricted mobility whereas the chain's movement gives the impression of freedom. In a human context, captivity rather than freedom is connoted with chains. This is addressed on the page l'homme enchaȋné.

Pause/Play the GROK animated pictures with an (un)hovering mouse.