Bubble levitation and translation under single-bubble sonoluminescence conditions

Bubble levitation in an acoustic standing wave is re-examined for conditions relevant to single-bubble sonoluminescence. Unlike a previous examination [Matula et al., J. Acoust. Soc. Am. 102, 1522-1527 (1997)], the stable parameter space [Pa,R0] is accounted for in this realization. Forces such as the added mass force and drag are included, and the results are compared with a simple force balance that equates the Bjerknes force to the buoyancy force. Under normal sonoluminescence conditions, the comparison is quite favorable. A more complete accounting of the forces shows that a stably levitated bubble does undergo periodic translational motion. The asymmetries associated with translational motion are hypothesized to generate instabilities in the spherical shape of the bubble. A reduction in gravity results in reduced translational motion. It is hypothesized that such conditions may lead to increased light output from sonoluminescing bubbles.     

声驻波场中空化泡的动力学特性

以水为工作介质, 考虑了液体的可压缩性, 研究了驻波声场中空化泡的运动特性, 模拟了驻波场中各位置处空化泡的运动状态以及相关参数对各位置处空化泡在主Bjerknes力作用下运动方向的影响. 结果表明: 驻波声场中, 空化泡的运动状态分为三个区域, 即在声压波腹附近空化泡做稳态空化, 在偏离波腹处空化泡做瞬态空化, 在声压波节附近, 空化泡在主Bjerknes 力作用下, 一直向声压波节处移动, 显示不发生空化现象; 驻波场中声压幅值增加有利于空化的发生, 但声压幅值增加到一定上限时, 压力波腹区域将排斥空化泡, 并驱赶空化泡向压力波节移动, 不利于空化现象的发生; 当声频率小于初始空化泡的共振频率时, 声频率越高, 由于主Bjerknes 力的作用将有更多的空化泡向声压波节移动, 不利于空化的发生, 尤其是驻波场液面的高度不应是声波波长的1/4; 当声频率一定时, 空化泡初始半径越大越有利于空化现象的发生, 但当空化泡的初始半径超过声频率的共振半径时, 由于主Bjerknes力的作用将有更多的空化泡向声压波节移动, 不利于空化的发生.     

Oscillation and Migration of Bubbles within Ultrasonic Field

The oscillation and migration of bubbles within an intensive ultrasonic field are important issues concerning acoustic cavitation in liquids.We establish a selection map of bubble oscillation mode related to initial bubble radius and driving sound pressure under 20 kHz ultrasound and analyze the individual-bubble migration induced by the combined effects of pressure gradient and acoustic streaming.Our results indicate that the pressure threshold of stable and transient cavitation decreases with the increasing initial bubble radius.At the pressure antinode,the Bjerknes force dominates the bubble migration, resulting in the large bubbles gathering toward antinode center,whereas small bubbles escape from antinode.By contrast,at the pressure node,the bubble migration is primarily controlled by acoustic streaming,which effectively weakens the bubble adhesion on the container walls,thereby enhancing the cavitation effect in the whole liquid.     

Collective bubble dynamics near a surface in a weak acoustic standing wave field

The transport of bubbles to a neighboring surface is very important in surface chemistry, bioengineering, and ultrasonic cleaning, etc. This paper proposes a multi-bubble transport method by using an acoustic standing wave field and establishes a model that explains the multi-bubble translation by expressing the balance between Bjerknes forces and hydrodynamic forces on a bubble in a liquid medium. Results indicated that the influence of primary Bjerknes force, secondary Bjerknes force, and buoyancy force on the bubble translation depends on the position of the target bubble in the acoustic field. Moreover, it was found that increasing the size of a bubble or pressure amplitude can accelerate the bubble motion and enhance the bubble-bubble interaction. The secondary Bjerknes force between two bubbles can switch from an attractive one when they oscillate in phase to a repulsive one when the bubble oscillations are out of phase. These findings provide an insight into the multi-bubble translation near a surface and can be applied to future bubble motion control studies, especially in drug delivery, sonoporation, and ultrasonic cleaning.     

Suppressing shape instabilities to discover the Bjerknes force instability (L)

For sufficiently strong acoustic forcing in a standing wave field, subresonant size bubbles are predicted to be repelled from the pressure antinode. Single bubble sonoluminescence (SBSL) conditions in water do not allow the observation of this instability. This study investigates the possibility that increasing the viscosity of the host liquid can preferentially suppress shape instabilities of a bubble and allow SBSL experiments to be limited by the Bjerknes force instability.     

气泡在超声场中绕圈运动的高速摄影及其图像分析

借助高速摄影和图像分析技术对首次发现的附壁气泡的绕圈现象进行了实验研究,重点研究游移气泡的运动轨迹、附壁气泡的布阵过程、气泡的来源以及气泡的振动细节.研究发现游移绕圈气泡的运动轨迹呈现出不稳定、不规则、不光滑的特点.阵列气泡源于游移气泡,而游移气泡变成阵列气泡的方式主要是通过合并增大体积,从而减小所受的Bjerknes力,降低活性的方式实现的.游移气泡源于ALF(acoustic lichtenberg figure)空化云中大量空泡的合并,使以径向振动为主的空泡逐渐过渡到以表面波动为主的气泡.阵列气泡在Bjerknes力的作用下呈现出规则的表面波动,而体积更小受力更大的游移空泡的表面完全失稳,呈现极不规则的形貌,并对附近阵列气泡的表面波动产生影响.阵列气泡呈现出十分规则的排布,相邻阵列气泡之间的振动相位是相反的,表现为相互排斥.     

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.     

次Bjerknes力作用下气泡的体积振动和散射声场

利用Lagrange方程得到了次Bjerknes力作用下气泡的体积振动方程,并探讨了次Bjerknes力作用下不同参数对气泡体积振动振幅和振动初相位的影响,研究了振动初相位差为π和0的气泡对在液体中形成的散射声场特征.结果表明:次Bjerknes作用力下,相邻气泡半径、气泡间距、多方指数均能影响气泡的体积振动振幅,气泡对的均衡半径、气泡间距和驱动频率则对气泡振动初相位产生明显影响;相距很近、相位相差为π的两个气泡的散射声压与气泡体积振动振幅、气泡间距、驱动频率和振动初相位有关,随声场距离成反比减小,与声场位置有关,其平均散射声功率是单个孤立气泡的1/6(kd_(12))~2半径相同、相距很近、相位相同的两个6气泡的散射声压与气泡振动初相位、体积振动振幅、气泡间距、驱动频率有关,随声场距离成反比减小,其平均散射声功率是单个孤立气泡的4倍.     

Coupled dynamics of translation and collapse of acoustically driven microbubbles

Pressure gradients drive the motion of microbubbles relative to liquids in which they are suspended. Examples include the hydrostatic pressure due to a gravitational field, and the pressure gradients in a sound field, useful for acoustic levitation. In this paper, the equations describing the coupled dynamics of radial oscillation and translation of a microbubble are given. The formulation is based on a recently derived expression for the hydrodynamic force on a bubble of changing size in an incompressible liquid [J. Magnaudet and D. Legendre, Phys. Fluids 10, 550-556 (1998)]. The complex interaction between radial and translation dynamics is best understood by examination of the added momentum associated with the liquid motion caused by the moving bubble. Translation is maximized when the bubble collapses violently. The new theory for coupled collapse and translation dynamics is compared to past experiments and to previous theories for decoupled translation dynamics. Special attention is paid to bubbles of relevance in biomedical applications.     

Sonoluminescence

Sonoluminescence (SL) is the name given to the light emitted when a liquid is cavitated in a particular (rather violent) manner. The appropriate cavitation conditions can be realized by using high intensity ultrasound, a spark discharge, a laser pulse, or by flowing the liquid through a Venturi tube. SL occurs in a wide variety of liquids, its intensity and spectrum depending on the nature of the solvent and the solute (including dissolved gas). The intensity, but apparently not the spectrum, also depends on the frequency of the sound and on the temperature and hydrostatic pressure of the liquid. In a standing wave sound field the SL originates from bubbles attracted to the pressure antinodes and has its maximum intensity when the bubble volume is a minimum. The phase of the sound cycle at which this occurs depends on the amplitude and frequency of the sound field. Spectral measurements show that SL originates mainly from the recombination of free radicals created within the high temperature and high pressure environment of a bubble undergoing an adiabatic compression, as may happen either during transient cavitation or during highly non-linear, but stable, cavitation. In discussing these, and other, attributes of SL this review emphasizes developments over the past 20 years. Because of the importance of the dynamical theory of bubbles to a full understanding of SL, it includes an account of bubble dynamics. In addition, it describes the various experimental techniques employed in the creation and analysis of SL. Although the review lays particular stress on the SL produced via acoustic cavitation, it also examines the characteristics of the SL produced using other methods of cavitation.     

Translational instability of a spherical bubble in a standing ultrasound wave

Translational bubble dynamics is much less studied than the dynamics of radial bubble oscillation, while in many scientific and engineering applications the control of space location of cavitation bubbles is of great practical importance. This paper aims at the theoretical study of various aspects of the translational motion of a spherical gas bubble in a high-frequency standing wave. In particular, it is shown that the translational instability that gives rise to the reciprocal translation of a spherical bubble between the pressure antinode and the pressure node is caused by the hysteresis in the main resonance of the bubble. Different types of translational trajectories that can occur in a standing wave are illustrated by numerical simulations. A general classification of the observed translational trajectories is proposed.     

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.     

A simple model of ultrasound propagation in a cavitating liquid. Part II: Primary Bjerknes force and bubble structures

In a companion paper, a reduced model for propagation of acoustic waves in a cloud of inertial cavitation bubbles was proposed. The wave attenuation was calculated directly from the energy dissipated by a single bubble, the latter being estimated directly from the fully nonlinear radial dynamics. The use of this model in a mono-dimensional configuration has shown that the attenuation near the vibrating emitter was much higher than predictions obtained from linear theory, and that this strong attenuation creates a large traveling wave contribution, even for closed domain where standing waves are normally expected. In this paper, we show that, owing to the appearance of traveling waves, the primary Bjerknes force near the emitter becomes very large and tends to expel the bubbles up to a stagnation point. Two-dimensional axi-symmetric computations of the acoustic field created by a large area immersed sonotrode are also performed, and the paths of the bubbles in the resulting Bjerknes force field are sketched. Cone bubble structures are recovered and compare reasonably well to reported experimental results. The underlying mechanisms yielding such structures is examined, and it is found that the conical structure is generic and results from the appearance a sound velocity gradient along the transducer area. Finally, a more complex system, similar to an ultrasonic bath, in which the sound field results from the flexural vibrations of a thin plate, is also simulated. The calculated bubble paths reveal the appearance of other commonly observed structures in such configurations, such as streamers and flare structures.     

Viscous effects on the interaction force between two small gas bubbles in a weak acoustic field

The relative motion of two gas bubbles in an acoustic field is investigated by calculating the time-averaged interaction force known as the secondary Bjerknes force. The surrounding medium is assumed to be an incompressible viscous liquid and the separation distance between the bubbles much larger than their radii. A refined formula for the interaction force is derived, which allows for translational oscillations of the bubbles, the vorticity of the linear scattered field, and acoustic streaming. The boundary condition of slippage on the gas-liquid interface is assumed. It is shown that viscous effects can cause small bubbles, driven well below resonance, to repel each other within a relatively wide parameter range. This result discloses a significant boundedness of the classical Bjerknes theory according to which bubbles of this sort are capable of mutual attraction alone.     

Emission from electronically excited metal atoms during single-bubble Sonoluminescence

Variations in sonoluminescence (SL) from an acoustically driven but rapidly translating bubble in solutions of sulfuric acid with alkali-metal salts coincide with variations in translational bubble dynamics. At low acoustic pressures, emission from Ar excited states is observed and the bubble motion is smooth and elliptical. At elevated acoustic pressures, SL intensity decreases, emission from excited alkali-metal atoms is observed, and the bubble motion becomes increasingly erratic with frequent and abrupt changes in direction. These results provide a direct experimental link between single and multibubble SL and point toward the origins of sonochemical reactivity of nonvolatile species.     

Interaction of a bubble and a bubble cluster in an ultrasonic field

Using an appropriate approximation, we have formulated the interacting equation of multi-bubble motion for a system of a single bubble and a spherical bubble cluster. The behavior of the bubbles is observed in coupled and uncoupled states. The oscillation of bubbles inside the cluster is in a coupled state. The numerical simulation demonstrates that the secondary Bjerknes force can be influenced by the number density, initial radius, distance, driving frequency, and amplitude of ultrasound. However, if a bubble approaches a bubble cluster of the same initial radii, coupled oscillation would be induced and a repulsive force is evoked, which may be the reason why the bubble cluster can exist steadily. With the increment of the number density of the bubble cluster, a secondary Bjerknes force acting on the bubbles inside the cluster decreases due to the strong suppression of the coupled bubbles. It is shown that there may be an optimal number density for a bubble cluster which can generate an optimal cavitation effect in liquid for a stable driving ultrasound.     

Influence of dissolved-air concentration on spatial distribution of bubbles for sonochemistry

The pulsation of ultrasonic cavitation bubbles at various dissolved-air concentration in a sonochemical reaction field of standing-wave type is investigated experimentally by laser-light scattering. When a thin light sheet, finer than half the wavelength of sound, is introduced into the cavitation bubbles at an antinode of sound pressure, the scattered light intensity oscillates. The peak-to-trough light intensity is correlated with the number of bubbles that contribute to the sonochemical reaction. It is shown that as the dissolved air concentration becomes higher, the weighted center of the spatial distribution of the peak-to-trough intensity tends to shift towards the liquid surface. At higher concentration of the dissolved air, a great deal of bubbles with size distribution generated due to coalescence between bubbles disturbs sound propagation to change the sound phase easily. A standing wave to trap tiny oscillating bubbles is established only at the side which is nearer to the liquid surface. Also at higher concentration, liquid flow induced by drag motion of bubbles by the action of radiation force becomes apparent and position-unstable region of bubble is enlarged from the side of sound source towards the liquid surface. Therefore, the position of oscillating bubbles active for sonochemical reaction is limited at the side which is nearer to the liquid surface at higher concentration of the dissolved air.     

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.     

Numerical simulations of stable cavitation bubble generation and primary Bjerknes forces in a three-dimensional nonlinear phased array focused ultrasound field

We present a model developed for studying the generation of stable cavitation bubbles and their motion in a three-dimensional volume of liquid with axial symmetry under the effect of finite-amplitude phased array focused ultrasound. The density of bubbles per unit volume is determined by a nonlinear law which is a threshold-dependent function of the negative acoustic pressure reached in the liquid, in which nuclei are initially distributed. The nonlinear mutual interaction of ultrasound and bubble oscillations is modeled by a nonlinear coupled differential system formed by the wave and a Rayleigh-Plesset equations, for which both the pressure and the bubble oscillation variables are unknown. The system, which accounts for nonlinearity, dispersion, and attenuation due to the bubbles, is solved by numerical approximations. The nonlinear acoustic pressure field is then used to evaluate the primary Bjerknes force field and to predict the subsequent motion of bubbles. In order to illustrate the procedure, a medium-high and a low ultrasonic frequency configurations are assumed. Simulation results show where bubbles are generated, the nonlinear effects they have on ultrasound, and where they are relocated. Despite many physical restrictions and thanks to its particularities (two nonlinear coupled fields, bubble generation, bubble motion), the numerical model used in this work gives results that show qualitative coherence with data observed experimentally in the framework of stable cavitation and suggest their usefulness in some application contexts.     

匀强磁场对水中气泡运动的影响

基于Rayleigh-Plesset方程, 考虑极性水分子在均匀磁场运动受到磁场力作用, 根据能量守恒建立了外磁场作用下单气泡运动的控制方程, 并对附加压强的大小、性质及对气泡运动的影响进行了计算和分析. 结果表明: 随磁场强度的增强, 附加压强线性增大, 气泡膨胀率降低, 最大半径减小, 气泡坍缩速度下降; 外加磁场引起的气泡振动变化规律与增大静态压具有相似的效果.