Spatio-temporal dynamics in a train of rising bubbles

Abstract

It has been suggested that rising bubbles in dense fluids resemble an inverted dripping faucet and that they undergo analogues period-doubling bifurcations to chaos. We present experimental results that demonstrate that this analogy is weak because the dominant source of instability in the bubble train is inherently different — mutual interactions between spatially separated bubbles as opposed to nozzle dynamics. Unlike the dripping faucet, the initial instability in a bubble train develops at a location far from the injection nozzle and progresses toward the nozzle with increasing gas flow. From qualitative and rigorous quantitative observations, we conclude that rising-bubble dynamics are best described as ‘small-box spatio-temporal chaos’ with a flow instability. Such dynamics can superficially appear to be simple temporal chaos when considering spatially localized measurements. We show similarity between our experimental results and a bubble-interaction model that accounts for drag and coalescence effects without considering any nozzle dynamics.