Coiling of viscous jets

A stream of viscous fluid falling from a sufficient height onto a surface forms a series of regular coils. I use a numerical model for a deformable fluid thread to predict the coiling frequency as a function of the thread's radius, the flow rate, the fall height, and the fluid viscosity. Three distinct modes of coiling can occur: viscous (e.g. toothpaste), gravitational (honey falling from a moderate height) and inertial (honey falling from a great height). When inertia is significant, three states of steady coiling with different frequencies can exist over a range of fall heights. The numerically predicted coiling frequencies agree well with experimental measurements in the inertial coiling regime.