Bubble coalescence in confined inertial swarms

For processes using bubbly flows, prediction of the bubble sizes results is important since the size distribution governs the mass, momentum, and energy transfers at the interfaces. Considering isothermal dispersed gas-liquid flows, main changes in the size distribution are due to coalescence and breakup processes. The evolution of sizes of a population is often modeled by means of a Boltzmann-type partial integro-differential conservation equation, usually called the Population Balance Equation (PBE). When the only changes in the population are caused by coalescence, the kernels of the source and sink terms in the PBE depend on the collision frequency and the collision efficiency in giving rise to coalescence, for the different sizes present in the distribution. Commonly, these terms have been modeled for turbulent flows, establishing an analogy with the gas kinetic theory. In contrast, the purpose of this work is to determine the frequency and efficiency from bubble coalescence experiments performed in different swarms of bubbles at high-Reynolds numbers that are injected at the bottom of a planar vertical thin-gap cell filled with water at rest. This confined configuration favours the bubbles tracking and the direct observation of collision and coalescence events.

We present an experimental investigation of the coalescence cascade process for different injected gas volume fractions, which drives the evolution of the bubble size distribution along the vertical direction. We found that the stages of the coalescence cascade can be described by a characteristic diameter, representative of the largest bubbles in the distribution. In addition, the collision frequency of pairs of bubbles of different sizes and their coalescence efficiency are then obtained from the experiments. Our results reveal the existence of two different coalescence regimes depending on the capability of the bubbles to deform. Models describing the coalescence frequency for both regimes are provided, which are able to reproduce the experimental results. They consider the specific response of the bubble pair, which depends on the deformability of both bubbles, to the agitation induced by the swarm, governed by the distribution characteristic diameter and the gas volume fraction.