Liquid rope coiling

A thin stream or rope of viscous fluid falling from a sufficient height onto a surface forms a steadily rotating helical coil. Tabletop laboratory experiments in combination with a numerical model for slender liquid ropes reveal that finite-amplitude coiling can occur in four distinct regimes (viscous, gravitational, inertio-gravitational, and inertial) corresponding to different balances among the three principal forces acting on the rope. The model further shows that the onset of coiling has distinct viscous, gravitational, and inertial modes that connect smoothly with the corresponding finite-amplitude regimes. In addition to steady coiling, slender liquid ropes falling onto surfaces can exhibit a remarkable variety of nonstationary behaviors, including propagating spiral waves of air bubbles, supercoiling, the leaping-shampoo (Kaye) effect for non-Newtonian fluids, and the fluid-mechanical sewing machine in which the rope leaves complex stitch patterns on a moving surface