Acoustic radiation force due to incident plane-progressive waves on coated spheres immersed in ideal fluids

In this study, the acoustic radiation force resulting from the interaction of a plane progressive wave with a coated sphere was examined. The linear acoustic scattering problem was obtained first by solving the classical boundary conditions to obtain the required coefficients. The radiation force was then determined by averaging the momentum flux tensor expressed in terms of the total scattering pressure or velocity potential in an ideal fluid. Numerical calculations of the radiation force function Yp , which is the radiation force per unit energy density and unit cross-section, were displayed versus the dimensionless size parameter x=k1 b (k1 is the wave number in the exterior fluid and b the radius of the uncoated sphere) over a large range of frequencies. Particular emphasis has been focused on the coating thickness and the absorption of sound inside the outer covering layer. The fluid-loading effect on the radiation force function curves was also analysed.     

柱面波对多层球的轴向声辐射力

在理论和数值上研究柱面波对多层球的声辐射力.基于声波的散射理论,得到声辐射力的解析解,并给出数值仿真.结果表明：在特定的ka和kr₀处,柱面行波的辐射力可以是负值（k是波数,a是多层球的半径,r₀是多层球到声源的距离）.随着kr₀增加到无穷大,仿真结果退化为平面波的情形.对双层球而言,每层的相对厚度影响曲线共振峰的大小和位置,但对三层球而言没有显著影响.当最内层的介质换成空气时,由于声阻抗差异较大,共振峰更加明显.该研究可以为研发新一代单行波声束声学镊子提供理论指导,该技术在生物医学超声和材料科学领域有广泛的应用.     

Acoustic streaming in a sound field near a free boundary

Stationary acoustic streaming that occurs near the free boundary of a compressible viscous liquid in the field of a standing sound wave excited along this boundary is theoretically investigated.     

Droplet combustion in standing sound waves

Interaction between droplet combustion and acoustic oscillation is clarified. As the simplest model, an isolated fuel droplet is combusted in a standing sound wave. Apart from the conventional idea that oscillatory component of flow influences heat and mass transfer and promotes combustion, a new model that a secondary flow dominates combustion promotion is examined. The secondary flow, found by the authors in the previous work, is driven by acoustic radiation force due to Reynolds normal stress, and named as thermo-acoustic streaming. Since the force is described by the same equation as buoyancy, i.e., F = ΔρVg, the nature of the streaming is thought to be the same as natural convection. The flow patterns of the streaming are analyzed and its influence on burning rate of a droplet is predicted. Experimental investigation was mainly done with burning droplets located in the middle of node and anti-node of standing sound waves. This location realizes the strongest streaming. By varying sound pressure level, ambient pressure, and acoustic frequency, the strength of the streaming was controlled. Flame configuration including soot and burning rate were examined. Microgravity conditions were employed to clarify the influence of acoustic field through the streaming, since it is similar to and must be distinguished from natural convection. Experiments using microgravity conditions confirmed the new combustion promotion model and the way to quantify it. By introducing a new non-dimensional number Gr_a, that is the ratio of acoustic radiation force to viscosity, burning rate constants for various ambient and sound conditions are rearranged. As a result, it was found that the excess burning rate (k/k₀ − 1) is proportional to or , for weak sound and for strong sound, respectively.     

Acoustic radiation pressure on a rigid cylinder: an analytical theory and experiments

Simple and general analytical expressions are derived for the acoustic radiation force on a long rigid cylinder with a small diameter, whose axis is perpendicular to the wave propagation. Results are expressed in terms of the time-averaged densities of kinetic and potential energies of the incident sound field. For the case of a standing-wave field, which was used in these experiments, the theoretical results agree well with the experimental observations.     

Controlling acoustic streaming in an ultrasonic heptagonal tweezers with application to cell manipulation

Acoustic radiation force has been demonstrated as a method for manipulating micron-scale particles, but is frequently affected by unwanted streaming. In this paper the streaming in a multi-transducer quasi-standing wave acoustic particle manipulation device is assessed, and found to be dominated by a form of Eckart streaming. The experimentally observed streaming takes the form of two main vortices that have their highest velocity in the region where the standing wave is established. A finite element model is developed that agrees well with experimental results, and shows that the Reynolds stresses that give rise to the fluid motion are strongest in the high velocity region. A technical solution to reduce the streaming is explored that entails the introduction of a biocompatible agar gel layer at the bottom of the chamber so as to reduce the fluid depth and volume. By this means, we reduce the region of fluid that experiences the Reynolds stresses; the viscous drag per unit volume of fluid is also increased. Particle Image Velocimetry data is used to observe the streaming as a function of agar-modified cavity depth. It was found that, in an optimised structure, Eckart streaming could be reduced to negligible levels so that we could make a sonotweezers device with a large working area of up to 13 mm × 13 mm.     

Acoustic radiation force on a multilayered sphere in a Gaussian standing field

We develop a model for calculating the radiation force on spherically symmetric multilayered particles based on the acoustic scattering approach. An expression is derived for the radiation force on a multilayered sphere centered on the axis of a Gaussian standing wave propagating in an ideal fluid. The effects of the sound absorption of the materials and sound wave on acoustic radiation force of a multilayered sphere immersed in water are analyzed, with particular emphasis on the shell thickness of every layer, and the width of the Gaussian beam. The results reveal that the existence of particle trapping behavior depends on the choice of the non-dimensional frequency ka, as well as the shell thickness of each layer. This study provides a theoretical basis for the development of acoustical tweezers in a Gaussian standing wave, which may benefit the improvement and development of acoustic control technology, such as trapping, sorting, and assembling a cell, and drug delivery applications.     

Acoustic streaming in a rotating fluid

Acoustic streaming theory is derived that is applicable to a fluid that is slow moving in a reference frame that rotates with a constant angular velocity omega. A simplified streaming equation is obtained for the special case in which the acoustic angular frequency omega is large relative to omega, and the change in fluid density due to rotation alone is negligible. For this special case it is shown that the "driving force" for the acoustic streaming is independent of omega. Thus, if no acoustic streaming is present in a fluid system that is stationary, then no steady-state acoustic streaming is predicted for a similar system that rotates with constant angular velocity. For a system in which acoustic streaming is present, the flow behavior depends on the relative magnitudes of the Coriolis forces and the viscous forces. If the Ekman number is large (that is, the viscous force dominates) then the predicted flow is identical to that which would exist in a stationary system. If, on the other hand, the Ekman number is small then the Coriolis force dominates and the component of flow in the direction of the axis of rotation can be much smaller in the rotating system than in a similar system at rest.     

声波作用下球形颗粒外声流分布的数值模拟

综合考虑声学边界层内的热损失和黏性损失,建立处于平面驻波声压波节位置二维球形颗粒外声流计算模型,利用分离时间尺度的数值方法对颗粒外声流流场特征进行模拟。将模拟结果与相应的解析解和实验结果对比,验证了数值模拟的可靠性。在此基础上,研究了雷诺数Re和斯特劳哈尔数Sr对球形颗粒声学边界层内二阶声流流场结构、涡流强度及范围的影响规律。结果表明,随Sr和Re增大,声学边界层内的涡流结构尺度呈指数形式减小,其涡流尺度与颗粒直径D和激励频率f成反比,与流体介质运动黏度v成正比;且满足低Sr和高Re的声振系统可形成范围较大、更强烈的声流运动。该数值方法可用于对任意物理模型外声流特性的评估。      

驻波声场中圆柱形管道周围颗粒的运动特性

针对圆柱形管道外部的流体与颗粒介质运动问题,提出了结合圆柱周围声辐射力和声流Stokes力的研究方法。从柱体外部声流方程出发,得到影响涡流结构的无量纲参数Rem≥325.27时,外涡最大流速大于内涡最大流速。在此基础上,采用Nyborg的边界滑移速度理论,获得管道外部声流的极限滑移速度,推导得出圆柱附近的声辐射力公式。基于此公式,在理论上推导出颗粒速度为0、声辐射力和声流Stokes力平衡时,颗粒临界直径的表达式。通过对圆柱位于不同位置时,圆柱外部的颗粒运动进行仿真模拟,得到与理论公式相一致的结论:颗粒的临界直径的大小与声波频率有关,当颗粒直径小于临界直径时,声流Stokes力为主导,颗粒随声流运动,颗粒直径大于等于临界直径时,声辐射力为主导,颗粒在声辐射力作用下逐渐向声辐射力的节点聚集。理论与仿真结果表明该方法可用于分析管道外颗粒的分布状态,其研究结果有助于解决电站中换热器的管道结垢、热交换率降低等问题。     

同振球型矢量水听器声波接收理论研究

对同振球型矢量水听器声压和质点振速的声波接收理论进行了研究。以同振球型振速水听器测量原理为基础,推导了自由运动刚性球体和弹性球体的声波接收响应数学表达式,分析了振速水听器几何尺寸、平均密度与其频响特性曲线之间的关系;另外,根据球面接收器的声波接收理论,推导了矢量水听器声压接收响应数学表达式,通过理论分析和数值计算,研究了振速水听器表面上的声压分布规律以及声压水听器的声波接收压力系数与其接收面的大小、质点振速水听器的半径、布放的位置和半径等参数之间的关系;从理论上建立了矢量水听器声波接收理论模型和分析方法,为矢量水听器的设计和研制提供了理论依据。      

Driving force of acoustic streaming caused by aperiodic sound beam in unbounded volumes

Instantaneous driving force of acoustic streaming in the thermoviscous medium is the subject of investigation. Dynamic equation of the Eulerian streaming velocity is a result of splitting the hydrodynamic equations into acoustic and non-acoustic parts. The acoustic force represents a sum of three parts, one is the classic one, which being averaged over the sound period coincides with the well-known expression. The second one is connected to the periodicity of the sound, it becomes exact zero after averaging for the strictly periodic sound but is not zero for other acoustic wave. The last term originates from the sound divergence. All terms are nonlinear and proportional to the overall attenuation. The consistent comparative analysis of both formula for quasi-periodic and modulated sound is proceeded.     

An expression for the radiation force exerted by an acoustic beam with arbitrary wavefront (L)

Most studies investigating the acoustic radiation force upon a target are based on symmetry considerations between the object and the incident beam. Even so, this symmetry condition is not always fulfilled in several cases. An expression for the radiation force is obtained as a function of the beam-shape and the scattering coefficients of an incident wave and the object, respectively. The expression for the radiation force caused by a plane wave on a rigid sphere is used to validate the formula. This method represents a theoretical advance permitting different interpretations and predictions concerned to the acoustic radiation force phenomenon.     

Near field acoustic holography with microphones on a rigid sphere (L)

Spherical near field acoustic holography (spherical NAH) is a technique that makes it possible to reconstruct the sound field inside and just outside a spherical surface on which the sound pressure is measured with an array of microphones. This is potentially very useful for source identification. The sphere can be acoustically transparent or it can be rigid. A rigid sphere is somewhat more practical than an open sphere. However, spherical NAH based on a rigid sphere is only valid if it can be assumed that the sphere has a negligible influence on the incident sound field, and this is not necessarily a good assumption when the sphere is very close to a radiating surface. This Letter examines the matter through simulations and experiments.     

Acoustic force model for the fluid flow under standing waves

An acoustic Strouhal number is introduced to demonstrate that the viscosity of fluid can be ignored in the process of sound propagation and acoustic streaming is independent on the frequency of the acoustic wave. Furthermore, acoustic force based on the periodic velocity fluctuation caused by standing acoustic wave is introduced into Navier–Stokes equation in order to describe the fluid flow in the acoustic boundary layer. The numerical results show that the predicted results are consistent with the analytic solution. And the effect of the nonlinear terms cannot be ignored so the analytic solution derived by boundary-velocity condition is only an approximation for acoustic streaming.     

Acoustic radiation from the elastic impact of a sphere with a slab

The transient sound radiation from the impact of a spherical object with a slab is analysed theoretically and compared with experimental results. It is shown that the major source of sound radiation when a sphere impinges on a massive plate is due to the sudden change of velocity of the sphere. By using the method of images, an analytical expression predicting the sound pressure waveform is obtained. Experimental results confirm the theoretical analysis and provide further explanation of this rigid body type of acoustic radiation.     

Axial time-averaged acoustic radiation force on a cylinder in a nonviscous fluid revisited

Objective

The present research examines the acoustic radiation force of axisymmetric waves incident upon a cylinder of circular surface immersed in a nonviscous fluid. The attempt here is to unify the various treatments of radiation force on a cylinder with arbitrary radius and provide a formulation suitable for any axisymmetric incident wave.

Method and results

Analytical equations are derived for the acoustic scattering field and the axial acoustic radiation force. A general formulation for the radiation force function, which is the radiation force per unit energy density per unit cross-sectional surface, is derived. Specialized forms of the radiation force function are provided for several types of incident waves including plane progressive, plane standing, plane quasi-standing, cylindrical progressive diverging, cylindrical progressive converging and cylindrical standing and quasi-standing diverging waves (with an extension to the case of spherical standing and quasi-standing diverging waves incident upon a sphere).

Significance and some potential applications

This study may be helpful essentially due to its inherent value as a canonical problem in physical acoustics. Potential applications include particle manipulation of cylindrical shaped structures in biomedicine, micro-gravity environments, fluid dynamics properties of cylindrical capillary bridges, and the micro-fabrication of new cylindrical crystals to better control light beams.     

Analytic model of acoustic streaming in thermoacoustic waveguides with slowly varying cross-section

An analytic model of acoustic streaming generated in two-dimensional thermoa-coustic waveguides with slowly varying cross-section was developed for more general applications. The analytical solutions of acoustic streaming characteristics in the closed straight tube and the annular tube are given based on the model.The solution for the closed straight tube can be applied to the case with any transverse scale.The solution for the annular tube is obtained under the assumption that the width of the varying cross-section part is much larger than the viscous and thermal penetration depths.The effects of cross-section variation,time-averaged temperature distribution and components of sound field are reflected in the analytic solutions. The magnitude and distribution of acoustic streaming velocity vary with the characteristic scale of the waveguides.The analytic model of acoustic streaming can be applied in research under thermoacoustic and other physical backgrounds.     

Interaction of a spherical acoustic wave with an elastic spherical shell

The interaction of a spherical acoustic wave with an elastic spherical shell is treated analytically. The solution includes the coupling between the acoustic sound field and vibration of the shell with any degree of fluid loading. The formulation for the far-field acoustic pressure is derived in terms of natural spherical wave functions, the properties of the acoustic medium, and the material constants of the shell. The far acoustic field is computed for a thin aluminum shell and several sound source locations over a large range of ka, where k is the wavenumber, and a is the shell radius. It is shown that the acoustic pressure depends significantly on whether the shell is in air or is submerged in water, particularly when the sound source is very near the surface. In air, the sound field of the shell is nearly identical to that of a rigid sphere but, in water, the shell is more compliant, which results in a damped radiation field that is characterized by vibrational resonances throughout the range of frequencies considered. As the sound sources is moved further away from the surface, however, this resonance response decreases very rapidly, and the sound field corresponds more closely to that of the shell in air.     

Curle's equation and acoustic scattering by a sphere

Recent papers have initiated interesting comparisons between aeroacoustic theory and the results of acoustic scattering problems. In this paper, we consider some aspects of these comparisons for acoustic scattering by a sphere. We give a derivation of Curle's equation for a specific class of linear acoustic scattering problems, and, in response to previous claims to the contrary, give an explicit confirmation of Curle's equation for plane wave scattering by a stationary rigid sphere of arbitrary size in an inviscid fluid. We construct the complete solution for scattering by a rigid sphere in a viscous fluid, and show that the neglect of viscous terms in Curie's equation yields an incomplete prediction of the far field dipole pressure. We also consider the null field solution of the sphere scattering problem, and give its extension to the vorticity modes associated with viscosity. Finally, we construct a solution for an elastic sphere in a viscous fluid, and show that the rigid sphere/null field solution is recovered from the limit of infinite longitudinal and shear wave speeds in the elastic solid.