Numerical investigation of the translational motion of bubbles: The comparison of capabilities of the time-resolved and the time-averaged methods

In the present study, the accuracies of two different numerical approaches used to model the translational motion of acoustic cavitational bubble in a standing acoustic field are compared. The less accurate but less computational demanding approach is to decouple the equation of translational motion from the radial oscillation, and solve it by calculating the time-averaged forces exerted on the bubble for one acoustic cycle. The second approach is to solve the coupled ordinary differential equations directly, which provides more accurate results with higher computational effort. The investigations are carried out in the parameter space of the driving frequency, pressure amplitude and equilibrium radius. Results showed that both models are capable to reveal stable equilibrium positions; however, in the case of oscillatory solutions, the difference in terms of translational frequency may be more than three fold, and the amplitude of translational motion obtained by the time-averaged method is roughly 1.5 times higher compared to the time-resolved solution at particular sets of parameters. This observation implies that where the transient behaviour is important, the time-resolved approach is the proper choice for reliable results.     

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.     

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.     

Circular motion of submillimeter-sized acoustic bubbles attached to a boundary by high-speed image analysis

The circular motion of submillimeter-sized bubbles attached to a boundary in an 18.5 kHz ultrasonic field are investigated experimentally by high-speed photography and image analysis. It is found that the vibration of gas bubbles with diameters of 0.2–0.4 mm is between spherical radial vibration and regular surface fluctuation. Different from the circular motion of suspended bubbles in water, the circular motion of gas bubbles attached to a boundary presents some new characteristics. These bubbles attached to a boundary (wandering bubbles) will rotate around a fixed bubble array (holding bubbles). Both the wondering bubbles and holding bubbles are “degas” bubbles. The primary Bjerknes force acting on wandering bubbles in the acoustic wave field and the secondary Bjerknes force between the wandering bubbles and the holding bubbles strongly affects the circular motion. The circling and residence behavior of gas bubbles is described and analyzed in detail, which is helpful to understand and improve industrial applications such as ultrasonic cleaning, sonochemical treatment, aeration and cavitation reduction.     

Interaction of two bubbles with distortion in an acoustic field

Expression of the secondary Bjerknes force of two bubbles is obtained by considering the distrotion of two bubbles. The secondary Bjerknes forces in different acoustic fields are simulated, and the influence factors are analyzed and discussed. It is shown that the distortion of a bubble has an important influence on the interaction of two bubbles. The strength and even the directions of the secondary Bjerknes force of two bubbles with distortion differ considerably from the predictions of the sherical symmetry theory. The results show that when two bubbles oscillated stably in an acoustic field, the secondary Bjerknes force of two bubbles with distortion is several times more than that of two spherical bubbles in the same condition. The secondary Bjerknes force of two bubble with distortion has more interaction distance than that of two spherical bubbles. The secondary Bjerknes force of two bubbles with distortion depends on the distance of two bubbles, the shape mode of two bubbles, the equilibrium radii of two bubbles and the driving acoustic filed. The nonspherical distortion effects of the secondary Bjerknes has an importance on understanding the structure formation of bubbles and evolution process of bubble group in an acoustic field.     

平面行波场中多个粒子受到的声辐射力*

从粒子在行波场中的声散射出发,研究当声场中存在稀疏分布的多个粒子时粒子受到的声辐射力,并且给出了适用于声场中任意位置的粒子声辐射力计算公式。由于声辐射力为非线性力,当声场中存在多个粒子时,直接计算粒子受到的声辐射力非常复杂。结果表明,当声场中存在多个稀疏分布的粒子时,这一多粒子系统可以视为多个单独的双粒子系统的叠加,只需要分别计算各个双粒子系统的声辐射力就可以通过叠加得到声场中任意粒子的声辐射力。这一结果有助于利用声辐射力对微小粒子进行精细操控。     

Nonlinear dynamics and acoustic emissions of interacting cavitation bubbles in viscoelastic tissues

The cavitation-mediated bioeffects are primarily associated with the dynamic behaviors of bubbles in viscoelastic tissues, which involves complex interactions of cavitation bubbles with surrounding bubbles and tissues. The radial and translational motions, as well as the resultant acoustic emissions of two interacting cavitation bubbles in viscoelastic tissues were numerically investigated. Due to the bubble–bubble interactions, a remarkable suppression effect on the small bubble, whereas a slight enhancement effect on the large one were observed within the acoustic exposure parameters and the initial radii of the bubbles examined in this paper. Moreover, as the initial distance between bubbles increases, the strong suppression effect is reduced gradually and it could effectively enhance the nonlinear dynamics of bubbles, exactly as the bifurcation diagrams exhibit a similar mode of successive period doubling to chaos. Correspondingly, the resultant acoustic emissions present a progressive evolution of harmonics, subharmonics, ultraharmonics and broadband components in the frequency spectra. In addition, with the elasticity and/or viscosity of the surrounding medium increasing, both the nonlinear dynamics and translational motions of bubbles were reduced prominently. This study provides a comprehensive insight into the nonlinear behaviors and acoustic emissions of two interacting cavitation bubbles in viscoelastic media, it may contribute to optimizing and monitoring the cavitation-mediated biomedical applications.     

Cavitation mapping by sonochemiluminescence with less bubble displacement induced by acoustic radiation force in a 1.2 MHz HIFU

An acoustic radiation force counterbalanced appliance was employed to map the cavitation distribution in water. The appliance was made up of a focused ultrasound transducer and an aluminum alloy reflector with the exactly same shape. They were centrosymmetry around the focus of the source transducer. Spatial–temporal dynamics of cavitation bubble clouds in the 1.2 MHz ultrasonic field within this appliance were observed in water. And they were mapped by sonochemiluminescence (SCL) recordings and high-speed photography. There were significant differences in spatial distribution and temporal evolution between normal group and counterbalanced group. The reflector could avoid bubble directional displacement induced by acoustic radiation force under certain electric power (⩽50 W). As a result, the SCL intensity in the pre-focal region was larger than that of normal group. In event of high electric power (⩾70 W), most of the bubbles were moving in acoustic streaming. When electric power decreased, bubbles kept stable and showed stripe structure in SCL images. Both stationary bubbles and moving bubbles have been captured, and exhibited analytical potential with respect to bubbles in therapeutic ultrasound.     

自由空间中球形粒子的负向声辐射力

针对一定声场作用下自由空间中的球形粒子,首先分析了声散射过程中的吸收声功率、散射声功率和损失声功率以及三者之间的关系,并通过计算发现了由于参数选取不当导致的负吸收现象。接着从动量守恒定律出发推导了声辐射力的一般表达式,阐释了声辐射力与声能流之间的关系,并从理论和计算两方面验证了负向声辐射力的存在。当负向声辐射力产生时,声波的背向散射被抑制。在此基础上,进一步研究了粒子的偏心特性和流体的黏度这两种常见因素对负向声辐射力的影响。利用球函数的加法公式推导了偏心球的散射系数和声辐射力公式,结果显示偏心距离、粒子的材料等都会显著改变负向声辐射力的产生条件。在低频近似下,由于流体黏度附加的正向声辐射力是否能完全抵消原来的负向声辐射力将决定最终的声辐射力方向。该结果对利用负向声辐射力制成单行波声学镊子来实现对特定粒子的操控有着理论指导意义。     

利用k-Wave计算超声在腹壁组织的声辐射力

随着科学技术的发展,声辐射力在生物医学领域得到了更为广泛的应用,尤其是在弹性成像领域.为了使弹性成像技术更加精准,对声辐射力的预测至关重要.该文基于腹壁组织图像,利用k-Wave对超声波在腹壁组织区域传播时的声场进行数值模拟,获得了其声场分布,进而求得了组织中声辐射力分布情况,同时对面阵换能器的阵元宽度、间距、阵元个数...     

Transition mechanisms of translational motions of bubbles in an ultrasonic field

The translation behaviors of oscillating bubbles are closely related to the polymerizations and dispersions between them, which are crucial for the ultrasonic cavitation effect. In this study, six types of translational motion of bubbles with a wide range of sizes (2–100 μm) in the R₀₁-R₀₂ plane are investigated. Our results demonstrate that in addition (to the 2nd order harmonic), the 1/2 order subharmonic can change the bubble pairs from the three states of the attraction, stable after attraction, and repulsion to that of the repulsion, coalescence, and attraction, respectively. Furthermore, within the range of the main resonance radius and the 1/2 order subharmonic resonance radius, the chaotic bubble pairs with alternating attractive and repulsive forces appear in the region between the coalescence pairs and stable pairs after attraction. Finally, the corresponding physical mechanisms of the chaotic translational motions are also revealed.     

Bubble size distribution in acoustic droplet vaporization via dissolution using an ultrasound wide-beam method

Performance and efficiency of numerous cavitation enhanced applications in a wide range of areas depend on the cavitation bubble size distribution. Therefore, cavitation bubble size estimation would be beneficial for biological and industrial applications that rely on cavitation. In this study, an acoustic method using a wide beam with low pressure is proposed to acquire the time intensity curve of the dissolution process for the cavitation bubble population and then determine the bubble size distribution. Dissolution of the cavitation bubbles in saline and in phase-shift nanodroplet emulsion diluted with undegassed or degassed saline was obtained to quantify the effects of pulse duration (PD) and acoustic power (AP) or peak negative pressure (PNP) of focused ultrasound on the size distribution of induced cavitation bubbles. It was found that an increase of PD will induce large bubbles while AP had only a little effect on the mean bubble size in saline. It was also recognized that longer PD and higher PNP increases the proportions of large and small bubbles, respectively, in suspensions of phase-shift nanodroplet emulsions. Moreover, degassing of the suspension tended to bring about smaller mean bubble size than the undegassed suspension. In addition, condensation of cavitation bubble produced in diluted suspension of phase-shift nanodroplet emulsion was involved in the calculation to discuss the effect of bubble condensation in the bubble size estimation in acoustic droplet vaporization. It was shown that calculation without considering the condensation might underestimate the mean bubble size and the calculation with considering the condensation might have more influence over the size distribution of small bubbles, but less effect on that of large bubbles. Without or with considering bubble condensation, the accessible minimum bubble radius was 0.4 or 1.7 μm and the step size was 0.3 μm. This acoustic technique provides an approach to estimate the size distribution of cavitation bubble population in opaque media and might be a promising tool for applications where it is desirable to tune the ultrasound parameters to control the size distribution of cavitation bubbles.     

Incubation pit analysis and calculation of the hydrodynamic impact pressure from the implosion of an acoustic cavitation bubble

An experimental study to evaluate cavitation bubble dynamics is conducted. The aim is to predict the magnitude and statistical distribution of hydrodynamic impact pressure generated from the implosion of various individual acoustic cavitation bubbles near to a rigid boundary, considering geometrical features of the pitted area.A steel sample was subjected to cavitation impacts by an ultrasonic transducer with a 5 mm diameter probe. The pitted surface was then examined using high-precision 3D optical interferometer techniques. Only the incubation period where surface is plastically deformed without material loss is taken into account. The exposure time was adjusted in the range of 3–60 s to avoid pit overlapping and a special procedure for pit analysis and characterisation was then followed. Moreover, a high-speed camera device was deployed to capture the implosion mechanisms of cavitation bubbles near to the surface.The geometrical characteristics of single incubation pits as well as pit clusters were studied and their deformation patterns were compared. Consequently, a reverse engineering approach was applied in order the hydrodynamic impact pressure from the implosion of an individual cavitation bubble to be determined. The characteristic parameters of the cavitation implosion process such as hydrodynamic impact pressure and liquid micro-jet impact velocity as well as the hydrodynamic severity of the cavitation impacts were quantified. It was found that the length of the hypotenuse of the orthographic projections from the center of the pit, which basically represents the deformed area of the pit, increases with the hydrodynamic impact aggressiveness in a linear rate. Majority of the hydrodynamic impacts were in the range of 0.4–1 GPa while the corresponding micro-jet velocities were found to be in the range of 200–700 m/s. Outcomes of this study, contribute to further understanding the cavitation intensity from the implosion of acoustically generated bubbles and could certainly represent a significant step towards developing more accurate cavitation models.     

Effects of surface tension on the dynamics of a single micro bubble near a rigid wall in an ultrasonic field

Acoustic cavitation is a very important hydrodynamic phenomenon, and is often implicated in a myriad of industrial, medical, and daily living applications. In these applications, the effect mechanism of liquid surface tension on improving the efficiency of acoustic cavitation is a crucial concern for researchers. In this study, the effects of liquid surface tension on the dynamics of an ultrasonic driven bubble near a rigid wall, which could be the main mechanism of efficiency improvement in the applications of acoustic cavitation, were investigated at the microscale level. A synchronous high-speed microscopic imaging method was used to clearly record the temporary evolution of single acoustic cavitation bubble in the liquids with different surface tension. Meanwhile, the bubble dynamic characteristics, such as the position and time of bubble collapse, the size and stability of the bubbles, the speed of bubble boundaries and the micro-jets, were analyzed and compared. In the case of the single bubbles near a rigid wall, it was found that low surface tension reduces the stability of the bubbles in the liquid medium. Meanwhile, the bubbles collapse earlier and farther from the rigid wall in the liquids with lower surface tension. In addition, the surface tension has no significant influence on the speed of the first micro-jet, but it can substantially increase the speed of second and the third micro-jets after the first collapse of the bubble. These effects of liquid surface tension on the bubble dynamics can explain the mechanism of surfactants in numerous fields of acoustic cavitation for facilitating its optimization and application.     

Experimental investigation of conical bubble structure and acoustic flow structure in ultrasonic field

The objective of this paper is to investigate the transient conical bubble structure (CBS) and acoustic flow structure in ultrasonic field. In the experiment, the high-speed video and particle image velocimetry (PIV) techniques are used to measure the acoustic cavitation patterns, as well as the flow velocity and vorticity fields. Results are presented for a high power ultrasound with a frequency of 18 kHz, and the range of the input power is from 50 W to 250 W. The results of the experiment show the input power significantly affects the structures of CBS, with the increase of input power, the cavity region of CBS and the velocity of bubbles increase evidently. For the transient motion of bubbles on radiating surface, two different types could be classified, namely the formation, aggregation and coalescence of cavitation bubbles, and the aggregation, shrink, expansion and collapse of bubble cluster. Furthermore, the thickness of turbulent boundary layer near the sonotrode region is found to be much thicker, and the turbulent intensities are much higher for relatively higher input power. The vorticity distribution is prominently affected by the spatial position and input power.     

Contactless and non-invasive delivery of micro-particles lying on a non-customized rigid surface by using acoustic radiation force

In the existing acoustic micro-particle delivery methods, the micro-particles always lie and slide on the surface of platform in the whole delivery process. To avoid the damage and contamination of micro-particles caused by the sliding motion, this paper deals with a novel approach to trap micro-particles from non-customized rigid surfaces and freely manipulate them. The delivery process contains three procedures: detaching, transporting, and landing. Hence, the micro-particles no longer lie on the surface, but are levitated in the fluid, during the long range transporting procedure. It is very meaningful especially for the fragile and easily contaminated targets. To quantitatively analyze the delivery process, a theoretical model to calculate the acoustic radiation force exerting upon a micro-particle near the boundary in half space is built. An experimental device is also developed to validate the delivery method. A 100 μm diameter micro-silica bead adopted as the delivery target is detached from the upper surface of an aluminum platform and levitated in the fluid. Then, it is transported along the designated path with high precision in horizontal plane. The maximum deviation is only about 3.3 μm. During the horizontal transportation, the levitation of the micro-silica bead is stable, the maximum fluctuation is less than 1 μm. The proposed method may extend the application of acoustic radiation force and provide a promising tool for microstructure or cell manipulation.     

Mechanism of the quasi-zero axial acoustic radiation force experienced by elastic and viscoelastic spheres in the field of a quasi-Gaussian beam and particle tweezing

The present analysis investigates the (axial) acoustic radiation force induced by a quasi-Gaussian beam centered on an elastic and a viscoelastic (polymer-type) sphere in a nonviscous fluid. The quasi-Gaussian beam is an exact solution of the source free Helmholtz wave equation and is characterized by an arbitrary waist w₀ and a diffraction convergence length known as the Rayleigh range z_R. Examples are found where the radiation force unexpectedly approaches closely to zero at some of the elastic sphere’s resonance frequencies for kw₀ ? 1 (where this range is of particular interest in describing strongly focused or divergent beams), which may produce particle immobilization along the axial direction. Moreover, the (quasi)vanishing behavior of the radiation force is found to be correlated with conditions giving extinction of the backscattering by the quasi-Gaussian beam. Furthermore, the mechanism for the quasi-zero force is studied theoretically by analyzing the contributions of the kinetic, potential and momentum flux energy densities and their density functions. It is found that all the components vanish simultaneously at the selected ka values for the nulls. However, for a viscoelastic sphere, acoustic absorption degrades the quasi-zero radiation force.     

Study on the radial vibration and acoustic field of an isotropic circular ring radiator

Based on the exact analytical theory, the radial vibration of an isotropic circular ring is studied and its electro-mechanical equivalent circuit is obtained. By means of the equivalent circuit model, the resonance frequency equation is derived; the relationship between the radial resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions, the material property is analyzed. For comparison, numerical method is used to simulate the radial vibration of isotropic circular rings. The resonance frequency and the radial vibrational displacement distribution are obtained, and the radial radiation acoustic field of the circular ring in radial vibration is simulated. It is illustrated that the radial resonance frequencies from the analytical method and the numerical method are in good agreement when the height is much less than the radius. When the height becomes large relative to the radius, the frequency deviation from the two methods becomes large. The reason is that the exact analytical theory is limited to thin circular ring whose height must be much less than its radius.