Theoretical Analysis of a Dripping Faucet

While previous studies of continuous emission of drops from a faucet have shown the richness of the system's nonlinear response, a theory of dripping has heretofore been lacking. Long-time behavior of dripping is simulated computationally by tracking the formation of up to several hundred drops in a sequence, rather than the usual single drop, at a given flow rate $Q$ and verified by experiments. As $Q$ increases, the system evolves from a period-1 system through a number of period doubling (halving) bifurcations as dripping ultimately gives way to jetting. That hysteresis can occur is also demonstrated.