Dripping-Jetting Transitions in a Dripping Faucet

Fascinating dynamics is known to result when the flow rate $Q$ at which water drips from a faucet varies. Starting with simple (period-1) dripping, the system transitions as $Q$ increases to complex dripping, where it exhibits period-$n$ ($n=2,4,\dots$) and chaotic responses, and then jets once $Q$ exceeds a threshold. New experiments and simulations show that high viscosity ($\mu$) liquids, e.g., syrup, transition directly from simple dripping to jetting as $Q$ increases. Phase diagrams showing transitions between simple and complex dripping and jetting in $(Q,\mu )$ space are developed. Values of $Q$ for transition from dripping to jetting are estimated from scaling arguments and shown to accord well with simulations.