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.

Multiple Bubble Removal Strategies to Promote Oxygen Evolution Reaction: Mechanistic Understandings from Orientation, Rotation, and Sonication Perspectives.

Bubble coverage of catalytically active sites is one of the well-known bottlenecks to the kinetics of the oxygen evolution reaction (OER). Herein, various bubble removal approaches (electrode orientation, rotating, and sonication) were considered for the OER performance evaluation of a state-of-the-art Ir-based electrocatalyst. Key parameters, such as catalyst mass loss, activity, overpotential, and charge- and mass-transfer mechanisms, were analyzed. First, it was suggested that a suitable orientation of the working electrode facilitates coalescence and sliding bubble effects on the catalyst surface, leading to better electrochemical performance than those of the traditional rotating disk electrode (RDE) configuration. Then, the convection and secondary Bjerknes force were explained as the responsible phenomena in improving the OER activity in the RDE and sonication methods. Finally, simultaneous implementation of the methods enhanced the catalyst mass activity up to 164% and provided fast charge-transfer kinetics and low double-layer capacitance, which eventually led to a 22% reduction in overpotential, while the catalyst loss slightly increased from 1.93 to 3.88%.

Dynamics of three cavitation bubbles with pulsation and symmetric deformation.

A new system of dynamical equations was obtained by using the perturbation and potential flow theory to couple the pulsation and surface deformation of the second-order Legendre polynomials (P2) of three bubbles in a line. The feasibility and effectiveness of the model were verified by simulating the radial oscillations, surface deformation with P2, and shape evolution of three bubbles. The spherical radial pulsation and surface deformation of the three bubbles exhibit periodic behavior. The maximum secondary Bjerknes forces (SBFs) on the three bubbles are found not to depend on the system's resonance frequency. Within a stable region, the SBFs of the three bubbles increase with increasing sound pressure amplitude but decrease with increasing distance between the bubbles. The primary Bjerknes force (PBF) on a bubble is significantly higher than the SBF on it.

Structure of bubble cluster adjacent to the water surface in the ultrasonic field.

The generation and evolution of bubble clusters in ultrasound fields were studied using high-speed photography. The transition of a spherical bubble cluster to a layer-like bubble cluster was demonstrated in detail. At a distance of half a wavelength to the water surface, the rising spherical cluster oscillated strongly and its equilibrium size grew. The speed was about 0.4 m/s and had a tendency to decrease. A jet caused by the last collapse of the spherical cluster rushed to the water surface, creating a bulge on the surface. Subsequently, due to the primary acoustic field, bubbles accumulated again below the bulge, and a layer-like bubble cluster gradually formed. The effects of acoustic frequency and intensity on the layer-like cluster were considered. It was found that the clusters located at a distance-to-wavelength ratio of about 0.08 to 0.13, very close to the water surface. The flickering bubble clusters were easy to be observed at 28 kHz and 40 kHz, while the accumulation of bubbles and their flicker were relatively weak at 80 kHz. The higher the frequency, the shorter the wavelength, the closer the structure to the water surface. However, at 80 kHz, the cavitation threshold is supposed to be higher and the resonance size of the bubbles is smaller, so the bubble oscillations and their interactions were weaker, and the phenomenon was different from the cases of 28 kHz and 40 kHz. Multiple structures mainly exist at 40 kHz. The formation and evolution of the layer-like cluster are closely dependent on the adequate supply of bubble nuclei from the water surface and the surrounding liquid. A Y-shaped bifurcation was used to model the branch streamers, which provided a path of bubbles accumulate into the clusters. The secondary Bjerknes forces between bubbles were adapted to analyze the interactions, and the results proved that it plays an important role in the appearance and evolution of the substructures.

Interactions of bubbles in acoustic Lichtenberg figure.

The evolution of acoustic Lichtenberg figure (ALF) in ultrasound fields is studied using high-speed photography. It is observed that bubbles travel along the branch to the aggregation region of an ALF, promoting the possibility of large bubble or small cluster formation. Large bubbles move away from the aggregation region while surrounding bubbles are attracted into this structure, and a bubble transportation cycle arises in the cavitation field. A simplified model consisting of a spherical cluster and a chain of bubbles is developed to explain this phenomenon. The interaction of the two units is analyzed using a modified expression for the secondary Bjerknes force in this system. The model reveals that clusters can attract bubbles on the chain within a distance of 2 mm, leading to a bubble transportation process from the chain to the bubble cluster. Many factors can affect this process, including the acoustic pressure, frequency, bubble density, and separation distance. The larger the bubble in the cluster, the broader the attraction region. Therefore, the presence of large bubbles might enhance the process in this system. Local disturbances in bubble density could destroy the ALF structure. The predictions of the model are in good agreement with the experimental phenomena.

Modulation of the secondary Bjerknes force in multi-bubble systems.

The behaviours of insonated bubble clusters are regulated by the secondary Bjerknes force between bubble pairs. While the force has been investigated extensively for two-bubble systems, the modulation of the force by nearby bubbles remains unclear. This problem is investigated in this paper by theoretical analyses and numerical simulations of a three bubble system. For weak oscillations, the third bubble is found to have strong effects when its radius is close to the resonant radius. The equilibrium distance between the bubble pair is reduced when the radius of the third bubble is smaller than the resonant threshold, and increased when it is larger. For strong oscillations of bubbles with radii of a few microns, the third bubble reduces the magnitude of the force, hence increasing the equilibrium distance. The modulation effects depend strongly on the relative sizes of the bubbles. Stronger effects can be produced when the third bubble is placed closer to the smaller bubble in the bubble pair. The findings highlight the need for a more accurate parametrization of the secondary Bjerknes force in the simulation and manipulation of bubble clusters.

The secondary Bjerknes force between two oscillating bubbles in Kelvin-Voigt-type viscoelastic fluids driven by harmonic ultrasonic pressure.

The interaction between two small bubbles experiencing transient cavitation in a nonlinear Kelvin-Voigt fluid is investigated. The time-delay effect in the interaction is incorporated in the coupled Keller-Miksis model. The refined model predicts that bubbles with radii smaller than 2µm will be repelled by large bubbles, in contrast to predictions from previous models. The matching pressure needed to obtain same level of transient cavitation in different Kelvin-Voigt fluids is shown to depend mainly on the shear modulus and is insensitive to other parameters, which makes it a useful parameter to correlate the results. When the radii of the bubbles fall between 4µm and 6µm, the secondary Bjerknes force obtained with matching pressures shows only weak dependence on the shear modulus. For the pressure amplitudes investigated, equilibrium distances can be found between two bubbles when the equilibrium radius of one of the bubbles is in a narrow range around 2 µm. The equilibrium distance decreases when the shear modulus is increased. A simple relation between the two quantities is established.

[The effect of secondary Bjerknes force in sonoporation on cell by ultrasound-mediated microbubbles].

In sonoporation, the cell membrane is broken-up temporarily by ultrasound mediated microbubbles, which is promoting drug or gene into the cell. In current literatures, there are numerous studies of single microbubble dynamics in sonoporation. However till now, little studies have been focused on the sonoporation incidence caused by more than one microbubble. In this article, the dynamic model of two adjacent microbubbles in stable cavitation has been introduced. By the model, the forces including secondary Bjerknes force on cell membrane given by microbubbles and their effects on sonoporation have been numerically studied. According to the experimental parameters, we numerically studied (1) effects of the ultrasound and microbubble parameters on the secondary Bjerknes forces; (2) the forces exerted on cell membrane by microbubble, including the secondary Bjerknes force; (3) the sonoporation possibility caused by those forces produced by microbubble. In this article, the ultrasound and microbubbles' parameters range were found to produce sonoporation by two adjacent microbubbles. Furthermore, it is the first time to found that the microbubbles' parameters are more important than ultrasound parameters on sonoporation.

The effect of secondary Bjerknes force in sonoporation on cell by ultrasound-mediated microbubbles / 生物医学工程学杂志

In sonoporation, the cell membrane is broken-up temporarily by ultrasound mediated microbubbles, which is promoting drug or gene into the cell. In current literatures, there are numerous studies of single microbubble dynamics in sonoporation. However till now, little studies have been focused on the sonoporation incidence caused by more than one microbubble. In this article, the dynamic model of two adjacent microbubbles in stable cavitation has been introduced. By the model, the forces including secondary Bjerknes force on cell membrane given by microbubbles and their effects on sonoporation have been numerically studied. According to the experimental parameters, we numerically studied (1) effects of the ultrasound and microbubble parameters on the secondary Bjerknes forces; (2) the forces exerted on cell membrane by microbubble, including the secondary Bjerknes force; (3) the sonoporation possibility caused by those forces produced by microbubble. In this article, the ultrasound and microbubbles' parameters range were found to produce sonoporation by two adjacent microbubbles. Furthermore, it is the first time to found that the microbubbles' parameters are more important than ultrasound parameters on sonoporation.

Experiment and modeling of translational dynamics of an oscillating bubble cluster in a stationary sound field.

Translational motion of an oscillating bubble cluster under sound irradiation is studied experimentally and is modeled in the framework of the classical approach of Bjerknes. An experimental technique is proposed to observe bubble cluster formation and its translational dynamics interacting with wall boundaries due to the secondary Bjerknes force. The translational motion observed in the experiment is modeled by extending the classical theory of Bjerknes on a single bubble; a bubble cluster is treated as a single bubble. The extended Bjerknes theory is shown to allow us to predict the overall trajectory of the cluster translating toward a wall of finite acoustic impedance by tuning acoustic energy loss at the wall. The drag force turns out to be unimportant for the translation of a millimeter-sized cluster that we observed.

The secondary Bjerknes force between two gas bubbles under dual-frequency acoustic excitation.

The secondary Bjerknes force is one of the essential mechanisms of mutual interactions between bubbles oscillating in a sound field. The dual-frequency acoustic excitation has been applied in several fields such as sonochemistry, biomedicine and material engineering. In this paper, the secondary Bjerknes force under dual-frequency excitation is investigated both analytically and numerically within a large parameter zone. The unique characteristics (i.e., the complicated patterns of the parameter zone for sign change and the combination resonances) of the secondary Bjerknes force under dual-frequency excitation are revealed. Moreover, the influence of several parameters (e.g., the pressure amplitude, the bubble distance and the phase difference between sound waves) on the secondary Bjerknes force is also investigated numerically.

Influence of acoustic pressure and bubble sizes on the coalescence of two contacting bubbles in an acoustic field.

In this study, the coalescence time between two contacting sub-resonance size bubbles was measured experimentally under an acoustic pressure ranging from 10kPa to 120kPa, driven at a frequency of 22.4kHz. The coalescence time obtained under sonication was much longer compared to that calculated by the film drainage theory for a free bubble surface without surfactants. It was found that under the influence of an acoustic field, the coalescence time could be probabilistic in nature, exhibiting upper and lower limits of coalescence times which are prolonged when both the maximum surface approach velocity and secondary Bjerknes force increases. The size of the two contacting bubbles is also important. For a given acoustic pressure, bubbles having a larger average size and size difference were observed to exhibit longer coalescence times. This could be caused by the phase difference between the volume oscillations of the two bubbles, which in turn affects the minimum film thickness reached between the bubbles and the film drainage time. These results will have important implications for developing film drainage theory to account for the effect of bubble translational and volumetric oscillations, bubble surface fluctuations and microstreaming.

Experimental and theoretical analysis of secondary Bjerknes forces between two bubbles in a standing wave.

Bubbles in an acoustic field are affected by forces such as primary and secondary Bjerknes forces, which have been shown to be influenced by acoustic pressure, frequency, bubble size and separation distance between bubbles. However, such studies are predominantly theoretical, and are mostly focused on the sign reversal of the secondary Bjerknes force. This study provides experimental data on the effect of a range of bubble sizes (8-30 µm), distances (⩽0.2 mm), acoustic pressures (20-40 kPa) and frequencies (40-100 kHz) on the relative acceleration of two approaching bubbles. Under these conditions, only variations in the magnitude of the attractive force were observed. Using coupled equations of radial and translational motions, the acceleration and secondary Bjerknes force were calculated and compared to the experimental data. The variations in the magnitude of the secondary Bjerknes forces were explained by simulating bubble radius and coupled volume oscillation as a function of time.