The Chaotic Dripping Faucet: Investigation of Chaotic Behavior in Water Droplet Formation

The dripping faucet experiment seeks to provide a simple example of a system that exhibits predictable dynamics that transition to an unpredictable, chaotic behavior under certain conditions. The time between water drops falling from a nozzle, is measured with a straightforward experimental setup using a photodiode and a laser. The period, or time between falling drops, is dependent on the flow rate of the water through the nozzle. The photodiode records a drop as the drop breaks the beam of light passing between the diode and laser. The photodiode is interfaced to a computer through an analog to digital converter. The data are analyzed and visualized to characterize the nonlinear dynamics of the system. The dynamics exhibit perioddoubling and chaotic behavior. A model is provided for the system, and simulation results are used to interpret the experimentally derived data. The experimental and simulation data are found to follow understood period-doubling and chaotic behavior, however additional modeling and experimentation remains to fully understand the system.