The chaotic dripping faucet

We propose a simple model for the chaotic dripping of a faucet in terms of a return map constructed by analyzing the stability of a pendant drop. The return map couples two classical normal forms, an Andronov saddle-node bifurcation, and a Shilnikov homoclinic bifurcation. The former corresponds to the initiation of the instability when the drop volume exceed a critical value set by the balance between surface tension and gravity, while the latter models the global reinjection associated with pinch-off that eventually return the drop to a state close to its original unstable configuration. The results obtained using the return map are consistent with those of numerical simulations of the governing PDEs and prior experiments, and show periodic and quasi-periodic dripping at low and high flow rates, and chaotic behavior at intermediate flow rates.