Leaky Tap Behavior Described by a Simple Discrete Mapping

Abstract

The complex variety of phenomena associated with the dynamical behavior of a dripping faucet is reproduced with a simple map deduced from a one-dimensional analog mass-on-spring simulation, which has a dependence on a reduced number of parameters. It is analyzed how the dynamics of the real tap depends on the flow rate and on the geometrical parameters of the tip. Experimental bifurcation diagrams and attractors illustrate the adherence of the mapping to the real dynamics. The enormous simplifications in reducing the actual physical system to a simple oscillator mapping allows to us to investigate more deeply the parameter space and to understand the most important dynamical mechanisms of the leaky tap.

Temporal dynamics of a jökulhlaup system

“…The drop sequence becomes chaotic at high supply rates (Shaw, 1984; Martien and others, 1985), and models of such behaviour (e.g. D’Innocenzo and others, 2006) have considered the fluid mechanics of drop formation and detachment, analogous to flood initiation.…”

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

“…To account for the droplet detachment superimposed with the pressure oscillations in the fluid column a massspring model was proposed. 13,15,18,25,[35][36][37][38] As governing parameters the spring constant, the transient evolution of the droplet mass, and gravity as driving force are used. Extensions of the model account for the dispersed phase density ρ disp , surface tension σ , and geometrical properties.…”

“…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.…”