Air entrainment by plunging jets and droplet trains
Transportation of air into the liquid phase in the form of bubbles is a well-known phenomenon. This ubiquitous and complex process facilitates the transfer of oxygen and other gases when a breaking wave plunges into the ocean, which is essential for sustaining aquatic life. In industries, air entrainment is crucial for applications such as fermentation and the degradation of organic pollutants.
At a fundamental level, one can examine the air-entrainment mechanism by considering a simple case of a plunging jet impacting the surface of a pool. This impact generates a bubble-laden jet flow beneath the surface, known as a bubble cloud. The height of this cloud, referred to as the bubble cloud depth, is critical because it directly influences factors such as the volume of the two-phase region and the gas mixing efficiency in various chemical processes. The study begins with experimental investigations of bubble clouds formed by single circular plunging jets. The results demonstrate that, at a constant impact momentum of the jet, increasing either the impact diameter or the jet fall height-to-diameter ratio reduces the bubble cloud depth. Systematic measurements of the local void fraction using phase detection probes confirm that this reduction is directly related to an increased air content within the cloud. Furthermore, a simple momentum balance model, incorporating only inertia and buoyancy forces, accurately predicts the bubble cloud depth without requiring any fitting parameters. In addition, a Froude number which is based on bubble terminal velocity, cloud depth, and net void fraction, is introduced to delineate the threshold between inertia-dominated and buoyancy-dominated bubble clouds.
The study then examines bubble clouds generated by closely spaced twin and triple identical jets to simulate air entrainment by fragmented plunging jets. In these cases, individual bubble clouds overlap and merge after reaching a certain pre-interaction depth, forming a unified structure analogous to that of a single plunging jet but slightly longer for a constant impact momentum. Experiments are further extended to even more closely packed multiple identical jets in a hexagonal arrangement to mimic large fragmented jets. Just below the interface, an inverted dome structure is formed, surrounded by air fingers, which generates a distinct bubble cloud without revealing a pre-interaction depth. The study describes this structure and the mechanism by which bubbles are shed from it. Interestingly, the net air flux does not scale with the number of jets but is proportional to the diameter of the multi-jet configuration. In all cases, the mean bubble size in a bubble cloud increases with depth, likely primarily driven by the coalescence of bubbles, as suggested by high-speed visualization and Weber number analysis. Finally, a more realistic scenario of bubble clouds formed by stream of droplets is explored. In this case, an unusually high void fraction, up to 70%, is observed, which decreases with depth. The creation of the foamy region is associated with the repetitive formation and collapse of the air cavity entrained by droplets. By adjusting the impact momentum to account for droplet frequency, it is shown that the momentum balance accurately predicts the cloud depth in this scenario as well.
Contact Nathanaël Machicoane for more information or to schedule a discussion with the seminar speaker.