In this work, we established a novel theory for the dynamics of oscillating bubbles such as cavitation bubbles, underwater explosion bubbles, and air bubbles. For the first time, we proposed bubble dynamics equations that can simultaneously take into consideration the effects of boundaries, bubble interaction, ambient flow field, gravity, bubble migration, fluid compressibility, viscosity, and surface tension while maintaining a unified and elegant mathematical form. The present theory unifies different classical bubble equations such as the Rayleigh-Plesset equation, the Gilmore equation, and the Keller-Miksis equation. Furthermore, we validated the theory with experimental data of bubbles with a variety in scales, sources, boundaries, and ambient conditions and showed the advantages of our theory over the classical theoretical models, followed by a discussion on the applicability of the present theory based on a comparison to simulation results with different numerical methods. Finally, as a demonstration of the potential of our theory, we modeled the complex multi-cycle bubble interaction with wide ranges of energy and phase differences and gained new physical insights into inter-bubble energy transfer and coupling of bubble-induced pressure waves.

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Vertically neutral collapse of a pulsating bubble occurs when the boundaries above or below the bubble balance the buoyancy effect over a pulsation. In this study, the vertically neutral collapse of a bubble near a vertical rigid wall below the free surface is investigated. The boundary integral method (BIM) is employed to model the bubble dynamics with an open-domain free surface. Moreover, this method is validated against several buoyant bubble experiments. Bubble dynamics in such conditions are associated with three dimensionless parameters: the bubble-free surface distance $\gamma _{{f}}$ , bubble–wall distance $\gamma _{{w}}$ and buoyancy parameter $\delta$ . We derive the Kelvin impulse of a spherical bubble and the algebraic relationship for vertically neutral collapse, which proves to be accurate for predicting vertically neutral collapse when the bubble is relatively far from the boundaries. Four patterns of the vertically neutral collapse of the bubble for different $\gamma _{{w}}$ and $\gamma _{{f}}$ are identified: (i) formally downward jet; (ii) annular collapse; (iii) horizontal jet; and (iv) weak jet. Despite the downward jet shape, the ‘formally downward jet’ is in the vertically neutral collapse state in terms of the profile of toroidal bubbles and the orientation of local high-pressure zones around the bubble at jet impact. A bulge with a high curvature above the bubble in the ‘annular collapse’ pattern is formed during bubble collapse under two local high-pressure zones at the left and right extremities of the bubble. The ‘horizontal jet’ pattern has the greatest potential to attack the wall, and the power laws of the moment of the jet impact, jet velocity and bubble displacement with respect to the theoretical Kelvin impulse are discussed. In particular, we quantitatively illustrate the role of the free surface on bubble migration towards the wall through the variational power-law exponents of the bubble displacement with respect to $\gamma _{{w}}$ .

The dynamics of a buoyant pulsating bubble near two crossed perpendicular rigid boundaries (a horizontal and a vertical wall) are studied using the boundary element method combined with the method of mirror images. The Kelvin impulse and the elastic mesh velocity method are used to calculate the direction and volume of the liquid jet generated during bubble collapse. The numerical results show good agreement with experiments. An increase in buoyancy causes a local high-pressure zone at the root of the jet to move toward the bottom of the bubble, causing the jet to rotate upward toward the vertical wall. At a certain position, with the change in buoyancy, the dimensionless bubble volume at the instant of jet impact reaches a minimum when the jet direction is horizontal, with a peak in the dimensionless jet velocity occurring. A comprehensive parametric study of jet characteristics, including jet direction, velocity, and relative volume (the volume ratio of the jet to the bubble at the instant of jet impact), is carried out in terms of buoyancy and the standoff distances to the two walls. The Blake criterion can be used to judge whether a bubble jet is pointing obliquely upward or downward, provided that it deviates significantly from the horizontal direction. Depending on the buoyancy, the jet characteristics at different standoff distances are found to exhibit three distinct patterns of behavior. Finally, we discuss the changes in the jet velocity and relative volume as the buoyancy is varied.