Unraveling the Duel: Inertial vs buoyancy dominated bubble clouds formed by plunging jets

The impact of a plunging jet on a liquid entrains air beneath the surface, forming a bubble cloud, a common phenomenon observed in nature and various industrial applications. The depth of the bubble cloud (H) is an essential parameter to model in various applications and is strongly influenced by the void fraction (Φ), as previously demonstrated by a force balance model (PRL 124, 194503, 2020). Bubble clouds can thereby be classified into two categories, namely inertial or buoyancy-dominated clouds. This study presents novel void fraction measurements in bubble clouds formed from injectors ranging from 2.7 mm to 10 mm in diameter, elucidating the scaling laws for cloud size. A Froude number based on the bubble terminal velocity, H and the net void fraction is introduced to provide a criterion for the threshold between inertial and buoyancy-dominated clouds. Furthermore, the measured radial profile of Φ, following a Gaussian distribution, is employed to model the buoyancy force acting on the cloud, enabling the prediction of H through the force balance model. Remarkably, this approach shows a good match even with measured H from past studies. The model is extended to the more practical scenario of clouds formed by closely packed multi-injectors.