Forced linear oscillations of microbubbles in blood capillaries

A theoretical investigation of the forced linear oscillations of a gas microbubble in a blood capillary, whose radius is comparable in size to the bubble radius is presented. The natural frequency of oscillation, the thermal and viscous damping coefficients, the amplitude resonance, the energy resonance, as well as the average energy absorbed by the system, bubble plus vessel, have been computed for different kinds of gas microbubbles, containing air, octafluropropane, and perflurobutane as a function of the bubble radius and applied frequency. It has been found that the bubble behavior is isothermal at low frequencies and for small bubbles and between isothermal and adiabatic for larger bubbles and higher frequencies, with the viscous damping dominating over the thermal damping. Furthermore, the width of the energy resonance is strongly dependent on the bubble size and the natural frequency of oscillation is affected by the presence of the vessel wall and position of the bubble in the vessel. Therefore, the presence of the blood vessel affects the way in which the bubble absorbs energy from the ultrasonic field. The motivation of this study lies in the possibility of using gas microbubbles as an aid to therapeutic focused ultrasound treatments.     

气泡线性振动时近海面气泡群的声散射

海洋中的不同成因的气泡群是常见的水下声学目标及声呐混响源,因此对水下气泡群进行声学建模意义重大。利用有效媒质理论描述气泡群内部的相速度及声衰减变化,并考虑到海洋中气泡群往往产生于不同界面附近,进一步利用球面波叠加原理描述海面对气泡群散射声波的再辐射,导出了平海面作用下气泡群声散射截面的一般表达式,建立了其声散射模型,研究了单一尺寸及混合尺寸气泡群的声学特性。数值分析表明,气泡群的谐振频率会随其半径或孔隙率增加而降低;由于海面的存在,气泡群声散射截面会随频率进行周期性变化,且随气泡群远离海面,这一变化逐渐加剧。此外,若气泡的黏滞阻尼项在全部阻尼项中占比较高,气泡群声散射强度会在谐振频率附近存在起伏振荡。该模型可为近海面鱼群、气泡羽流及海底泄漏的甲烷气体的声学建模提供一定的理论基础。     

Spatio-temporal dynamics of an encapsulated gas bubble in an ultrasound field

Coupled equations describing the radial and translational dynamics of an encapsulated gas bubble in an ultrasound field are derived by using the Lagrangian formalism. The equations generalize Church's theory by allowing for the translation motion of the bubble and radiation losses due to the compressibility of the surrounding liquid. The expression given by Church for the inner bubble radius corresponding to the unstrained state of the bubble shell is also refined, assuming that the shell can be of arbitrary thickness and impermeable to gas. Comparative linear analysis of the radial equation is carried out relative to Church's theory. It is shown that there are substantial departures from predictions of Church's theory. The proposed model is applied to evaluate radiation forces exerted on encapsulated bubbles and their translational displacements. It is shown that in the range of relatively high frequencies encapsulated bubbles are able to translate more efficiently than free bubbles of the equivalent size.     

Numerical simulation of gas bubble motion in a flow-through resonator

The problem of gas bubble motion in an acoustic resonator with a fluid flow is solved using numerical methods. It is shown that the distribution of the bubble concentration, which is nonuniform over the resonator length, is formed upon homogeneous introduction of bubbles. The problem on the bubble concentration distribution the along the resonator axis (with fluctuations of the bubble introduction period taken into account) is considered, and the fluctuation parameters are determined at which the periodic structure of the concentration distribution is preserved. The distribution of bubbles with different sizes over the resonator length is determined. It is shown that a resonator with a fluid flow accomplishes bubble selection by size (the average bubble concentration in the resonator increases with an increase in bubble size). The field in the resonator was calculated taking into account the effect of bubbles on sound velocity and damping.     

Flow field around growing and rising vapour bubble by PIV measurement

A study on flow field measurement around growing and rising vapour bubbles by use of PIV technique is presented. Bubbles were generated from single artificial cavities. Experiments have been conducted with saturated boiling of distilled water at atmospheric pressure. In the experiment fluid velocity field surrounding the bubbles was visualized by use of polyamide tracer particles and a sheet of a YAG pulse laser beam. The images were recorded with a cross-correlation CCD-camera. It has been shown that for lower heat flux density bubble growths in an almost quiescent bulk of liquid. For higher heat flux density the train of bubbles creates a vapour column with strong wake effect. Maximum liquid velocity recorded is approximately equal to the terminal velocity of bubble rising in a stagnant liquid.     

Characterisation of the acoustic cavitation cloud by two laser techniques

An experimental investigation of the size and volumetric concentration of acoustic cavitation bubbles is presented. The cavitation bubble cloud is generated at 20 kHz by an immersed horn in a rectangular glass vessel containing bi-distilled water. Two laser techniques, laser diffraction and phase Doppler interferometry, are implemented and compared. These two techniques are based on different measuring principles. The laser diffraction technique analyses the light pattern scattered by the bubbles along a line-of-sight of the experimental vessel (spatial average). The phase Doppler technique is based on the analysis of the light scattered from single bubbles passing through a set of interference fringes formed by the intersection of two laser beams: bubble size and velocity distributions are extracted from a great number of single-bubble events (local and temporal average) but only size distributions are discussed here. Difficulties arising in the application of the laser diffraction technique are discussed: in particular, the fact that the acoustic wave disturbs the light scattering patterns even when there are no cavitation bubbles along the measurement volume. As a consequence, a procedure has been developed to correct the raw data in order to get a significant bubble size distribution. After this data treatment has been applied the results from the two measurement techniques show good agreement. Under the emitter surface, the Sauter mean diameter D(3, 2) is approximately 10 microm by phase Doppler measurement and 7.5 microm by laser diffraction measurement at 179 W. Note that the mean measured diameter is much smaller than the resonance diameter predicted by the linear theory (about 280 microm). The influence of the acoustic power is investigated. Axial and radial profiles of mean bubble diameters and void fraction are also presented.     

Numerical analysis of the effect of bubble distribution on multiple-bubble behavior

Understanding multiple-bubble behavior in a megasonic field is essential for efficient megasonic nanodevice cleaning without pattern damage. In this study, we numerically studied the effects of equilibrium radius and initial void fraction on multiple-bubble behavior and induced pressure. We analyzed the nonspherical collapse, coalescence, and breakup of bubbles in a megasonic field using a compressible, locally homogeneous model of a gas-liquid two-phase medium. Bubbles were simulated with a uniform equilibrium radius or with a bubble size distribution. Our results indicate that the bubble behavior and induced pressure depended mainly on the initial void fraction. For the case of bubbles with uniform equilibrium radius, small bubbles generated high wall pressure at large initial void fractions. When there was a size distribution, bubbles with small equilibrium radii contributed little to the wall pressure because of the damping effect of the oscillation of larger bubbles. Furthermore, the addition of a large bubble suppressed the resonant behavior of the bubbles that induced high wall pressure.     

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.     

Nonlinear oscillation and acoustic scattering of bubbles

The scattered acoustic pressure and scattered cross section of bubbles is studied using the scattered theory of bubbles. The nonlinear oscillations of bubbles and the scattering acoustic fields of a spherical bubble cluster are numerically simulated based on the bubble dynamic and fluid dynamic. The influences of the interaction between bubbles on scattering acoustic field of bubbles are researched. The results of numerical simulation show that the oscillation phases of bubbles are delayed to a certain extent at different positions in the bubble cluster, but the radii of bubbles during oscillation do not differ too much at different positions. Furthermore, directivity of the acoustic scattering of bubbles is obvious. The scattered acoustic pressures of bubbles are different at the different positions inside and outside of the bubble cluster. The scattering acoustic fields of a spherical bubble cluster depend on the driving pressure amplitude, driving frequency, the equilibrium radii of bubbles, bubble number and the radius of the spherical bubble cluster. These theoretical predictions provide a further understanding of physics behind ultrasonic technique and should be useful for guiding ultrasonic application.     

非球形效应对强声场中次Bjerknes力的影响

考虑了非球形气泡在声场中的形状振动,推导了非球形气泡和球形气泡之间的次Bjerknes力方程,数值模拟了声场中非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡之间的次Bjerknes力,并对非球形气泡和球形气泡之间的次Bjerknes力的影响因素进行了分析讨论.研究结果表明:当驱动声压振幅大于非球形气泡的Black阈值且又能使得非球形气泡稳定振动时,在第一个声驱动周期内,非球形气泡和球形气泡之间的次Bjerknes力和两个球形气泡的次Bjerknes力方向差异较大,在大小上是两个球形气泡次Bjerkens力的数倍,且有着更长的作用距离.非球形气泡和球形气泡之间的次Bjerknes力取决于非球形气泡的形状模态、两个气泡初始半径的比值、驱动声压振幅、气泡间距和两个气泡的相对位置.     

Resonance frequency of microbubbles: effect of viscosity

The transmitted frequency at which a gas bubble of millimeter or submillimeter size oscillates resonantly in a low-viscosity liquid is approximately equal to the undamped natural frequency (referred to as the Minnaert frequency if surface tension effects are disregarded). Based on a theoretical analysis of bubble oscillation, this paper shows that such an approximation cannot be validated for microbubbles used in contrast-enhanced ultrasound imaging. The contrast-agent microbubbles represent either encapsulated bubbles of size less than 10 microm or free (nonencapsulated) bubbles of submicron size. The resonance frequency of the microbubbles deviates significantly from the undamped natural frequency over the whole range of microbubble sizes due to the increased viscous damping coefficient. The difference between these two frequencies is shown to have a tremendous impact on the resonant backscatter by the microbubbles. In particular, the first and second harmonics of the backscattered signal from the microbubbles are characterized by their own resonance frequencies, equal to neither the microbubble resonance frequency nor the undamped natural frequency.     

Bubbles in an acoustic field: an overview

Acoustic cavitation is the fundamental process responsible for the initiation of most of the sonochemical reactions in liquids. Acoustic cavitation originates from the interaction between sound waves and bubbles. In an acoustic field, bubbles can undergo growth by rectified diffusion, bubble-bubble coalescence, bubble dissolution or bubble collapse leading to the generation of primary radicals and other secondary chemical reactions. Surface active solutes have been used in association with a number of experimental techniques in order to isolate and understand these activities. A strobe technique has been used for monitoring the growth of a single bubble by rectified diffusion. Multibubble sonoluminescence has been used for monitoring the growth of the bubbles as well as coalescence between bubbles. The extent of bubble coalescence has also been monitored using a newly developed capillary technique. An overview of the various experimental results has been presented in order to highlight the complexities involved in acoustic cavitation processes, which on the other hand arise from a simple, mechanical interaction between sound waves and bubbles.     

三探头单纤光导探针测量二维气泡速度的实验研究

1前言气液两相流广泛存在于动力、化工等工业过程中，到目前为止，人们已开发了大量的实验测定方法，用于研究气液两相流空泡份额等。但是对气泡速度的测量研究并不多，主要原因在于气泡速度测量的困难性。近几年人们尝试使用激光多普勒测速技术、颗粒轨迹测速技术等测量气泡速度，这些测量方法不仅系统复杂，而且还有相应的限制条件，适用范围有限。利用相关测速技术可以测量一维气泡速度，其原理是：设距离为L的上、下游两个测点的传感器在时间间隔T内测得的随机气泡信号为X（t）和Y（t），而且X（t）和Y（t）为平稳和各态遍历，则相关…     

A dual passive cavitation detector for localized detection of lithotripsy-induced cavitation in vitro

A passive cavitation detector (PCD) identifies cavitation events by sensing acoustic emissions generated by the collapse of bubbles. In this work, a dual passive cavitation detector (dual PCD), consisting of a pair of orthogonal confocal receivers, is described for use in shock wave lithotripsy. Cavitation events are detected by both receivers and can be localized to within 5 mm by the nature of the small intersecting volume of the focal areas of the two receivers in association with a coincidence detection algorithm. A calibration technique, based on the impulse response of the transducer, was employed to estimate radiated pressures at collapse near the bubble. Results are presented for the in vitro cavitation fields of both a clinical and a research electrohydraulic lithotripter. The measured lifetime of the primary growth-and-collapse of the cavitation bubbles increased from 180 to 420 microseconds as the power setting was increased from 12 to 24 kV. The measured lifetime compared well with calculations based on the Gilmore-Akulichev formulation for bubble dynamics. The radiated acoustic pressure 10 mm from the collapsing cavitation bubble was measured to vary from 4 to 16 MPa with increasing power setting; although the trends agreed with calculations, the predicted values were four times larger than measured values. The axial length of the cavitation field correlated well with the 6-dB region of the acoustic field. However, the width of the cavitation field (10 mm) was significantly narrower than the acoustic field (25 mm) as bubbles appeared to be drawn to the acoustic axis during the collapse. The dual PCD also detected signals from "rebounds," secondary and tertiary growth-and-collapse cycles. The measured rebound time did not agree with calculations from the single-bubble model. The rebounds could be fitted to a Rayleigh collapse model by considering the entire bubble cloud as an effective single bubble. The results from the dual PCD agreed well with images from high-speed photography. The results indicate that single-bubble theory is sufficient to model lithotripsy cavitation dynamics up to time of the main collapse, but that upon collapse bubble cloud dynamics becomes important.     

Regimes of bubble volume oscillations in a pipe

The effect of an acoustically driven bubble on the acoustics of a liquid-filled pipe is theoretically analyzed and the dimensionless groups of the problem are identified. The different regimes of bubble volume oscillations are predicted theoretically with these dimensionless groups. Three main regimes can be identified: (1) For small bubbles and weak driving, the effect of the bubble oscillations on the acoustic field can be neglected. (2) For larger bubbles and still small driving, the bubble affects the acoustic field, but due to the small driving, a linear theory is sufficient. (3) For large bubbles and large driving, the two-way coupling between the bubble and the flow dynamics requires the solution of the full nonlinear problem. The developed theory is then applied to an air bubble in a channel of an inkjet printhead. A numerical model is developed to test the predictions of the theoretical analysis. The Rayleigh-Plesset equation is extended to include the influence of the bubble volume oscillations on the acoustic field and vice versa. This modified Rayleigh-Plesset equation is coupled to a channel acoustics calculation and a Navier-Stokes solver for the flow in the nozzle. The numerical simulations indeed confirm the predictions of the theoretical analysis.     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

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.     

混响场中用相关传声器识别声源直达声的近似工程法

本文研究了在混响场中用相关传声器识别主声源直达声的近似工程法，包括理论及实验技术。采用该方法对一个置于混响声污染下的恒定声源进行了直达声测量，并将测量结果与该恒定声源的消声室测量结果进行了比较，结果表明：相关传声器近似工程法在很大程度上能减少混响声对主要源声压测量的干扰，从而能在混响声场中获取一定精度的主声源声压级。     

The characterization of acoustic cavitation bubbles - an overview

Acoustic cavitation, in simple terms, is the growth and collapse of preexisting microbubbles under the influence of an ultrasonic field in liquids. The cavitation bubbles can be characterized by the dynamics of oscillations and the maximum temperatures and pressures reached when they collapse. These aspects can be studied both experimentally and theoretically for a single bubble system. However, in a multibubble system, the formation of bubble streamers and clusters makes it difficult to characterize the cumulative properties of these bubbles. In this overview, some recently developed experimental procedures for the characterization of acoustic cavitation bubbles have been discussed.     

Investigation of noninertial cavitation produced by an ultrasonic horn

This paper reports on noninertial cavitation that occurs beyond the zone close to the horn tip to which the inertial cavitation is confined. The noninertial cavitation is characterized by collating the data from a range of measurements of bubbles trapped on a solid surface in this noninertial zone. Specifically, the electrochemical measurement of mass transfer to an electrode is compared with high-speed video of the bubble oscillation. This gas bubble is shown to be a "noninertial" event by electrochemical surface erosion measurements and "ring-down" experiments showing the activity and motion of the bubble as the sound excitation was terminated. These measurements enable characterization of the complex environment produced below an operating ultrasonic horn outside of the region where inertial collapse can be detected. The extent to which solid boundaries in the liquid cause the frequencies and shapes of oscillatory modes on the bubble wall to differ from their free field values is discussed.