Buckling of liquid columns

Under appropriate conditions, a column of viscous liquid falling onto a rigid surface undergoes a buckling instability. Here we show experimentally and theoretically that liquid buckling exhibits a hitherto unsuspected complexity involving three different modes—viscous, gravitational, and inertial—depending on how the viscous forces that resist bending of the column are balanced. We also find that the nonlinear evolution of the buckling exhibits a surprising multistability with three distinct states: steady stagnation flow, "liquid rope coiling," and a new state in which the column simultaneously folds periodically and rotates about a vertical axis. The transitions among these states are subcritical, leading to a complex phase diagram in which different combinations of states coexist in different regions of the parameter space.