Picture of the low-dimensional structure in chaotic dripping faucets

Abstract

Chaotic dynamics of the dripping faucet was investigated both experimentally and theoretically. We measured continuous change in drop position and velocity using a high-speed camera. Continuous trajectories of a low-dimensional chaotic attractor were reconstructed from these data, which was not previously obtained but predicted in our fluid dynamic simulation. From the simulation, we further obtained an approximate potential function with only two variables, the drop mass and its position of the center of mass. The potential landscape helps one to understand intuitively how the dripping dynamics can exhibit low-dimensional chaos.Comment: 8 pages, 3 figure

Hydrodynamical models for the chaotic dripping faucet

“…Let X be a state variable characterizing the drop in a potential determined by the gravitational and surface energies as shown in figure 9. Giving a physical interpretation of X is tricky; it can be related to the centre of gravity of the drop, as used for example by Kiyono et al (2003), but only indirectly because different shapes can have the same centre of gravity. A better interpretation of X relates it to the projection of the complete shape on a spatial mode of the drop and indicates the location of the drop relative to its stationary solutions as shown in figure 9 in the spirit of the qualitative behaviour of dynamical systems.…”

Nonlinear Dynamics of a Flow-Focusing Bubble Generator: An Inverted Dripping Faucet

“…Reports on bubbling from a nozzle describe period-2, period-3, and period-4 attractors, and transitions to chaos-a behavior similar to that of a dripping faucet [5,13,14,[16][17][18]. The study by Nguyen et al [8] suggests, however, that the cause of the instability in a system in which a nozzle injects a train of bubbles into an ambient fluid (a system we refer to as a ''vertical nozzle'') is different from the cause of bifurcations in the dripping faucet.…”

“…Systems as simple as a leaky faucet [5,[13][14][15][16][17][18], or a pressurized nozzle releasing gas into a tank of fluid [6,8,[19][20][21][22] provide archetypal examples of nonlinear dynamics. The behavior of these systems changes dramatically as a control parameter (typically the rate of flow of the fluid that is dispersed) increases above a critical value, and one observes that a series of identical droplets (or bubbles) is replaced by repeating sequences of two, four, or, in general, a number of fluid segments of different sizes.…”

Periodic dripping dynamics in a co-flowing liquid-liquid system

“…17,18,22 These theoretical approaches allow to model the experimental dripping patterns, but they are inadequate in describing complex drop formation dynamics such as periodic dripping and chaotic dripping as well as the transition from dripping to jetting. Chaotic dripping into air at high Bond-numbers was investigated experimentally and theoretically by Kiyono et al 40 Steady dripping from asymmetrical tips was investigated by D'Innocenzo et al; 38,41 these authors did not observe droplet groups and trains, but noticed fluid oscillations.…”