Frequency dependence of the acoustic radiation force acting on absorbing cylindrical shells

The frequency dependence of the radiation force function Y(p) for absorbing cylindrical shells suspended in an inviscid fluid in a plane incident sound field is analysed, in relation to the thickness and the content of their interior hollow region. The theory is modified to include the effect of hysteresis type absorption of compressional and shear waves in the material. The results of numerical calculations are presented for two viscoelastic (lucite and phenolic polymer) materials, with the hollow region filled with water or air indicating how damping and change of the interior fluid inside the shell's hollow region affect the acoustic radiation force. The acoustic radiation force acting on cylindrical lucite shells immersed in a high density fluid (in this case mercury) and filled with water in their hollow region, is also studied.     

Amplitude-modulated acoustic radiation force experienced by elastic and viscoelastic spherical shells in progressive waves

The dynamic acoustic radiation force resulting from a dual-frequency beam incident on spherical shells immersed in an inviscid fluid is examined theoretically in relation to their thickness and the contents of their interior hollow regions. The theory is modified to include a hysteresis type of absorption inside the shells' material. The results of numerical calculations are presented for stainless steel and absorbing lucite (PolyMethyMethacrylAte) shells with the hollow region filled with water or air. Significant differences occur when the interior fluid inside the hollow region is changed from water to air. It is shown that the dynamic radiation force function Yd deviates from the static radiation force function Yp when the modulation size parameter deltax = mid R:x2 - x1mid R: (x1 = k1a, x2 = k2a, k1 and k2 are the wave vectors of the incident ultrasound waves, and a is the outer radius of the shell) starts to exceed the width of the resonance peaks in the Yp curves.     

Dynamic acoustic radiation force acting on cylindrical shells: theory and simulations

An object placed in an acoustic field is known to experience a force due to the transfer of momentum from the wave to the object itself. This force is known to be steady when the incident field is considered to be continuous with constant amplitude. One may define the dynamic (oscillatory) radiation force for a continuous wave-field whose intensity varies slowly with time. This paper extends the theory of the dynamic acoustic radiation force resulting from an amplitude-modulated progressive plane wave-field incident on solid cylinders to the case of solid cylindrical shells with particular emphasis on their thickness and contents of their hollow regions. A new factor corresponding to the dynamic radiation force is defined as Y(d) and stands for the dynamic radiation force per unit energy density and unit cross sectional surface. The results of numerical calculations are presented, indicating the ways in which the form of the dynamic radiation force function curves are affected by variations in the material mechanical parameters and by changes in the interior fluid inside the shell's hollow region. It was shown that the dynamic radiation force function Y(d) deviates from the static radiation force function for progressive waves Y(p) when the modulation frequency increases. These results indicate that the theory presented here is broader than the existing theory on cylinders.     

Calculation of the acoustic radiation force on coated spherical shells in progressive and standing plane waves

In this paper, analytical equations are derived for the time-averaged radiation force induced by progressive and standing acoustic waves incident on elastic spherical shells covered with a layer of viscoelastic and sound-absorbing material. The fluid surrounding the shells is considered compressible and nonviscous. The incident field is assumed to be moderate so that the scattered field from the shells is taken to linear approximation. The analytical results are illustrated by means of a numerical example in which the radiation force function curves are displayed, with particular emphasis on the coating thickness and the content of the hollow region of the shells. The fluid-loading on the radiation force function curves is analysed as well. This study attempts to generalize the various treatments of radiation force due to both progressive and standing waves on spherically-shaped structures immersed in ideal fluids. The results show that various ways can be effectively used for damping resonance peaks, such as by changing the fluid in the interior hollow region of the shells or by changing the coating thickness.     

球形粒子在Bessel波束照射下的轴向辐射力计算和分析

通过声散射理论,将水中粒子的Bessel波束声散射场的分波序列(PWS)表达公式加以推广,进而推导出声辐射力的表达公式,获得了液体球及弹性球在Bessel波束下声辐射力的变化规律。通过观察不同散射角形态函数,可发现声辐射力的产生与粒子背向散射抑制程度有关。对于液体球粒子,球壳厚度及材料介质对粒子声辐射力有着重要的影响,同时Bessel波束波锥角越大,产生负声辐射力的可能性越大。对于弹性球和弹性单层壳粒子,声辐射力的产生与其本身的共振特征存在很大的关系。同时,通过改变球壳内介质及壳层厚度的方法,可增加产生的负声辐射力的频率范围及幅值强度.      

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。      

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.     

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.     

Parametric amplification of the dynamic radiation force of acoustic waves in fluids

We report on parametric amplification in dynamic radiation force produced by a bichromatic acoustic beam in a fluid. To explain this effect we develop a theory taking into account the nonlinearity of the fluid. The theory is validated through an experiment to measure the dynamic radiation force on an acrylic sphere. Results exhibit an amplification of 66 dB in water and 80 dB in alcohol as the difference of the frequencies is increased from 10 Hz to 240 kHz.     

高斯波束对界面附近离轴球形粒子的轴向声辐射力

从声波的散射理论出发,利用级数展开法得到高斯波束的波束因子,推导其对阻抗边界下离轴球形粒子声辐射力.针对刚性球与液体球两种球形粒子进行数值模拟,与自由空间的情况进行比较.讨论边界反射系数、粒子与边界距离、束腰半径以及离轴角度与距离等对声辐射力的影响.仿真结果表明：边界反射系数的增大会引起声辐射力的增加,但不改变峰值的位置;在合适的频率处,可以产生负向声辐射力;声辐射力随粒子与边界距离呈周期性变化;束腰半径的影响主要体现在中高频;随着粒子偏离传播轴的距离和角度增大,声辐射力明显衰减.该研究为利用高斯波束实现对粒子的操纵提供理论基础.     

Acoustic radiation force of a quasi-Gaussian beam imparted to a solid spherical scatterer in a fluid

The radiation force generated upon the scattering of a quasi-Gaussian acoustic beam on a homo-geneous elastic sphere in a fluid is investigated. It is shown that the force depends nonmonotonically on the ratio between the sphere’s diameter and the beam’s waist. For a given beam power, the radiation force has its maximum value when the diameters are roughly egual to each other. This is due to the resonant excitation of shear waves on the sphere’s surface under the impact of acoustic wave in the surrounding fluid.     

Axial acoustic radiation force on an elastic spherical shell near an impedance boundary for zero-order quasi-Bessel–Gauss beam

Shell structures have increasingly widespread applications in biomedical ultrasound fields such as contrast agents and drug delivery,which requires the precise prediction of the acoustic radiation force under various circumstances to improve the system efficiency.The acoustic radiation force exerted by a zero-order quasi-Bessel-Gauss beam on an elastic spherical shell near an impedance boundary is theoretically and numerically studied in this study.By means of the finite series method and the image theory,a zero-order quasi-Bessel-Gauss beam is expanded in terms of spherical harmonic functions,and the exact solution of the acoustic radiation force is derived based on the acoustic scattering theory.The acoustic radiation force function,which represents the radiation force per unit energy density and per unit cross-sectional surface,is especially investigated.Some simulated results for a polymethyl methacrylate shell and an aluminum shell are provided to illustrate the behavior of acoustic radiation force in this case.The simulated results show the oscillatory property and the negative radiation force caused by the impedance boundary.An appropriate relative thickness of the shell can generate sharp peaks for a polymethyl methacrylate shell.Strong radiation force can be obtained at small half-cone angles and the beam waist only affects the results at high frequencies.Considering that the quasi-Bessel-Gauss beam possesses both the energy focusing property and the non-diffracting advantage,this study is expected to be useful in the development of acoustic tweezers,contrast agent micro-shells,and drug delivery applications.     

Flexural vibration of perforated plates and porous elastic materials under acoustic loading

This paper presents a method of theoretical treatment of acoustic coupling due to flexural vibration of perforated plates and plates of porous elastic materials. The analytical model is developed by introducing flow continuity at the plate surface in a spatially mean sense and air-solid interaction within the plate material. To demonstrate the method of application, some fundamental acoustic problems based on a classical thin-plate theory are analyzed and discussed in relation to the interactive effect of flexural vibration and plate permeability. For acoustic radiation from a vibrating plate excited by a harmonic point-force, the attenuation effect of power radiation appears at frequencies below the critical frequency of coincidence. In the problem of sound absorption of a perforated plate or a plate of porous elastic material backed by an air layer, as permeability decreases, the effect of plate vibration increases. For perforated absorber systems including plate vibration effects, the trend of variation from ordinary theory depends on plate thickness.     

Axial radiation force of a bessel beam on a sphere and direction reversal of the force

An expression is derived for the radiation force on a sphere placed on the axis of an ideal acoustic Bessel beam propagating in an inviscid fluid. The expression uses the partial-wave coefficients found in the analysis of the scattering when the sphere is placed in a plane wave traveling in the same external fluid. The Bessel beam is characterized by the cone angle beta of its plane wave components where beta=0 gives the limiting case of an ordinary plane wave. Examples are found for fluid spheres where the radiation force reverses in direction so the force is opposite the direction of the beam propagation. Negative axial forces are found to be correlated with conditions giving reduced backscattering by the beam. This condition may also be helpful in the design of acoustic tweezers for biophysical applications. Other potential applications include the manipulation of objects in microgravity. Islands in the (ka, beta) parameter plane having a negative radiation force are calculated for the case of a hexane drop in water. Here k is the wave number and a is the drop radius. Low frequency approximations to the radiation force are noted for rigid, fluid, and elastic solid spheres in an inviscid fluid.     

Pulling force of acoustic-vortex beams on centered elastic spheres based on the annular transducer model

To solve the difficulty of generating an ideal Bessel beam, an simplified annular transducer model is proposed to study the axial acoustic radiation force(ARF) and the corresponding negative ARF(pulling force) exerted on centered elastic spheres for acoustic-vortex(AV) beams of arbitrary orders. Based on the theory of acoustic scattering, the axial distributions of the velocity potential and the ARF for AV beams of different orders generated by the annular transducers with different physical sizes are simulated. It is proved that the pulling force can be generated by AV beams of arbitrary orders with multiple axial regions. The pulling force is more likely to exert on the sphere with a smaller k_0a(product of the wave number and the radius) for the AV beam with a bigger topological charge due to the strengthened off-axis acoustic scattering. The pulling force decreases with the increase of the axial distance for the sphere with a bigger k_0a.More pulling force areas with wider axial regions can be formed by AV beams using a bigger-sized annular transducer.The theoretical results demonstrate the feasibility of generating the pulling force along the axes of AV beams using the experimentally applicable circular array of planar transducers, and suggest application potentials for multi-position stable object manipulations in biomedical engineering.     

Acoustic Absorption Characteristics of New Underwater Omnidirectional Absorber

We investigate a new underwater omnidirectional absorber with acoustic black hole effect to realize a broadband omnidirectional acoustic wave absorption. Based on multiple scattering theory, a two-dimensional axisymmetric model of underwater omnidirectional absorber comprised of an acoustic gradient refractive index structure and a hollow core is developed, and the mechanisms of omnidirectional absorption and dissipation of acoustic waves are studied. The numerical results indicate that the omnidirectional absorber developed here can achieve the omnidirectional absorption of incident acoustic waves in a broadband frequency and can effectively reduce the backscattering of acoustic waves. It potentially provides a new notion for underwater acoustic coating design.     

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。     

Characteristics of Biot waves produced by a vibration exciter in a fluid-saturated medium

Results of a theoretical calculation of the directional characteristics of elastic waves excited by an oscillating point force in a fluid-saturated porous medium are presented. Based on Boit’s theory and the theory of elementary acoustic sources, the wave amplitude and radiation power are calculated for two kinds of longitudinal waves and the transverse wave. An analysis of the spatial angular characteristics of elastic waves is performed for two types of rock, namely, water-and gas-saturated sandstones. The angular distributions of vibrations in the solid and liquid (gaseous) phases of the medium and the frequency dependences of the radiation power associated with each of the three types of acoustic waves are presented in graphical form.     

Axial acoustic radiation force on a fluid sphere between two impedance boundaries for Gaussian beam

The acoustic radiation force on a fluid sphere immersed in water between two boundaries given by a Gaussian beam is theoretically and numerically investigated in this work. Based on the finite series method, the Gaussian beam is expressed in terms of Bessel function and a weighting parameter. The effects of the two boundaries concerned in our study is worked out by the image theory. This work also provides a reference when considering the effects of certain factors such as the radius of the sphere and the distance between the sphere and two boundaries. The contrast with the acoustic radiation force on a fluid sphere near only one boundary is also made in this paper. Our study can offer a theoretical basis for acoustics manipulation, acoustic sensors in the field of biomedical ultrasound and material science.     

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.