Simplicity and complexity of a dripping faucet

Drop formation arises in inkjet printing, arraying, and leaky faucets. Dynamics of dripping are studied in heretofore unexplored ranges of parameters by experiment and computation. Previous studies performed at a moderate Bond number G $\approx $ 0.5 (G=gravitational/surface tension force) and low Ohnesorge number Oh $\approx $ 0.1 (Oh=viscous/surface tension force) show that the dynamics changes from simple period-1 dripping (SD) to complex dripping (CD), where period-n (n$\ge $2) dripping and hysteresis abound, to jetting (J), as Weber number We (inertial/surface tension force) increases. New experiments and computations reveal that lowering G results in a drastic reduction in complexity: when G $\approx $ 0.3 and Oh $\approx $ 0.1, the sole CD response is period-2. Computed phase diagrams in (We, Oh) space reveal that the range of We over which the response is period-2 narrows as Oh increases and ultimately results in a direct transition from SD to J, in accord with experiments. By contrast, new computations at larger Bond number, G $\approx $ 1, with Oh = 0.1 and We = 0.05, predict occurrence of rare period-3 dripping, period-3 intermittence, and chaotic attractors.