Coalescence of bubbles in a high Reynolds number confined swarm

Abstract

We investigate experimentally the coalescence cascade process for a confined swarm of deformable bubbles immersed in a bidimensional vertical cell filled with water. For different gas volume fractions, air bubbles of size $D_0$ larger than the cell thickness are injected at the bottom of the cell. The bubbles swarms transformation is explored using high-speed visualizations. The time evolution of each bubble in the swarm is determined using a specifically developed algorithm, enabling bubble tracking and coalescence detection. We determine the evolution of the bubble size distribution downstream from the injection point, and show that the stages of the coalescence cascade are characterized by the diameter, $D_{V90}$ , representative of the largest bubbles. The collision frequency of pairs of bubbles of sizes $D_k$ and $D_{k'}$ , $h(D_k, D_{k'})$ , and their coalescence efficiency, $\lambda$ , are obtained from the experiments. The efficiency is nearly constant, independently of the bubble sizes and of the gas volume fraction. Concerning collision frequency, our results reveal the existence of two different coalescence regimes depending on the capability of the bubbles to deform. Models describing $h(D_k, D_{k'})$ for both regimes are provided. They take into account the specific response of the bubble pair, which depends on the reduced diameter $D_p = 2 D_k D_{k'} / (D_k + D_{k'})$ , to the global swarm-induced agitation governed by $D_{V90}$ and the gas volume fraction. In the first regime, occurring for smaller $D_p$ , bubbles are brought together by agitation and rapidly coalesce, while for sufficiently large $D_p$ , both bubbles are able to deform and spend more time adapting mutually their shapes before coalescing.

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