Pulsation, translation and P1 deformation of two aspherical bubbles in liquid

The oscillations of non-spherical bubbles in liquid

In this paper, the interaction between non-spherical bubbles is studied using a high-speed camera, and the effects of the interaction on the temperature within the bubble and the velocity of the surrounding fluid are theoretically investigated. It is found that the mean radius and the mean wall velocity of the middle bubble in three-bubble system are slightly greater than those in two-bubble system when the initial parameters are consistent. The acoustic response of the middle bubble presented a leftward shift of resonance peak and an increase of resonance peaks with increasing sound pressure. Two patterns of interactions were found in the three-bubble system: steady oscillations with slight non-spherical shape deformation, and a strong coupled state that tends to coalesce. In both patterns, the largest bubble should impose more constraints on the middle bubble, and the middle bubble was observed to be ejected towards the largest. The interacting pattern of bubbles depends on many factors, such as bubble spacing, initial radii of bubbles, acoustic frequency and intensity, which also affect the shape deformation of bubbles. Non-spherical shape deformation decreases the internal gas temperature and disturbs the flow field distribution, all of which are close to cavitation activities. Predictions of the three-bubble model are in good agreement with experimental observations, and can be used to explain bubble behaviors in chained multi-bubble systems in inertial cavitation field.

Theoretical study on the movements of bubbles

The radial and translational motions of multiple interacting spherical bubbles are obtained using classical Newton mechanics. It is seen that bubbles not only move in straight line, but also in circular motion. The tracks of the bubbles show that the interactions among them include attractive, repulsive and dynamic equilibrium. There are three types of straight line corresponding to attraction, coexistence of attraction and repulsion and dynamic equilibrium, and two types of circular movement corresponding to attraction and dynamic equilibrium. The results can provide an explanation for cavitation chain and profile in cavitation field.

Refined secondary Bjerknes force equation for double bubbles with pulsation, translation, and deformation

The secondary Bjerknes force (SBF) is the time-averaged interaction between two bubbles driven in a sound field. We derived a refined formula for the interaction force, incorporating the radial vibration and translational and deformational motions of the bubble. The coupling of pulsation, translation, and deformation enhances the interaction between bubbles but also weakens their stability, making it easier for bubbles to merge or break during motion. The effects of the coupling mode on the magnitude and direction of SBFs coupled with pulsation, translation, and deformation were numerically analyzed and studied. Under certain sound-field conditions, the SBF increased with increasing pressure amplitude, initial radius, and initial velocity, while decreased as the distance increased. In addition, the SBF irregularly increased with increasing frequency.

Multi-bubble scattering acoustic fields in viscoelastic tissues under dual-frequency ultrasound

Bubbles are widely used in the medical field due to their strong acoustic scattering properties, and the interaction between bubbles affects the scattering acoustic field caused by the bubble cluster. In this study, the dynamic equations of bubbles oscillating in viscoelastic tissues are solved numerically. The effect of bubble interaction on the scattered acoustic pressure under dual-frequency ultrasound is analyzed. In addition, the frequency spectra of the scattered acoustic waves due to the bubbles with and without considering the interaction are compared. The results show that the suppression or enlargement of the scattered sound pressure caused by the interaction between bubbles is related to the bubble radius and the incident frequency. Moreover, when the incident frequency is equal to the resonant frequency of the bubble with equilibrium radius R0, the effect of resonant bubbles is stronger than that of non-resonant bubbles. Meanwhile, for the multi-bubble system with a small bubble number density, the total response of the bubble cluster can be approximated as an algebraic sum of the dynamical behavior of individual bubbles.

The left-right symmetrical and asymmetrical deformations in a three-bubble system

This paper studies the simplest system that can possess left-right symmetrical and asymmetrical surroundings, three bubbles in a line. Assuming that the deformations are small, the surfaces of bubbles are described by a combination of the first three Legendre polynomials, that is, spherical symmetrical mode P₀, L-R antisymmetrical mode P₁, and symmetrical mode P₂. A dynamical model is built to describe aspherical oscillations of central and two side bubbles. It is found that when three identical bubbles are separated uniformly, the central bubble only has a P₂ component and P₁ component tends to zero, while two side bubbles have both P₁ and P₂ components. When three identical bubbles are separated by different distances, they can be degenerated into a two-bubble system and a free bubble. The bubble deformations contain both P₁ and P₂ components in the two-bubble system, while both aspherical components P₁ and P₂ of the free bubble tend to zero. If side bubbles are different in ambient radii but located symmetrically on the left and right of the central bubble, the side bubble pulsated more strongly plays an important role on the deformation of the central one.