Bubble Interactions in Polydisperse Swarms of Confined Inertial Bubbles : Coalescence and Agitation
For processes involving bubbly flows, whether in environmental or industrial systems, predicting the bubble size distribution is crucial, as it governs the transfer of mass, momentum, and energy at the interfaces. Moreover, it controls the agitation induced in the liquid, which strongly influences the mixing process, particularly when bubbles rise in a quiescent fluid. In this context, we present a comprehensive experimental study focused on the interactions and collective dynamics of polydisperse swarms of bubbles rising at large Reynolds numbers in water otherwise at rest, and confined in a narrow gap between two vertical walls. This bubbly flow in a thin-gap cell represents a quasi-2D bubble column, where bubbles of size D rise in a planar cell of width w (of the order of magnitude of the capillary length but smaller than D). Besides enabling to shed light on several mechanisms involved in the complexity of 3D bubbly flows (by taking advantage of the restrictions in the degrees of freedom of the bubbles) and providing a comprehensive description of the flows, inertial bubbly flows in thin-gap cells combine the good mixing properties of large-scale bubble reactors and the efficient mass transfer of confined Taylor flows. Thus, they further provide new possibilities of applications, such as recently developed photo-chemical-reactors and photo-bio-reactors.
The evolution of sizes of a population is often modelled 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. The purpose of the present work is to directly determine the frequency and efficiency from bubble coalescence experiments performed in different swarms of bubbles at high-Reynolds number that are injected at the bottom of a planar vertical thin-gap cell filled with water at rest. The change rate of the population of bubbles is determined analysing the evolution of the size distribution by means of high-speed visualizations registered at various downstream location of the cell. It was 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. A nearly constant value of efficiency was found, while two different coalescence regimes were observed depending on the size of the colliding bubbles and on their capability to mutually adapt their shapes. Models describing the coalescence frequency for both regimes are provided, which consider the specific response of the bubble pair to the agitation induced by the swarm, governed by the distribution characteristic diameter and the gas volume fraction.
In addition, we conducted a detailed study of bubble kinematics at the different stages of the polydisperse swarm evolution, based on well converged velocity data of bubbles of different sizes. A Bubble Tracking Algorithm (BTA) was specifically developed to detect all the bubbles in the swarm and to follow their motion as they rise. Statistical information about the bubble-bubble interaction processes was also extracted from the results. Notably, due to hydrodynamic interactions, the probability density function (p.d.f.) of the vertical velocity component for bubbles in the swarm differs significantly from the p.d.f. of terminal velocities for isolated bubbles of equivalent sizes. A detailed analysis of the conditional statistics reveals that the tails observed in the vertical velocity p.d.f. for different bubble classes are directly related to interactions with the wakes of other bubbles in the population, even when such interactions do not ultimately result in collisions. Scaling laws for the vertical velocity fluctuations are proposed based on the overall agitation induced in the liquid by the entire distribution of bubbles, which increases both with the presence of larger bubbles (resulting from coalescence) and with the gas volume fraction.
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