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.      

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.     

Negative axial radiation forces on solid spheres and shells in a Bessel beam

Prior computations predict that fluid spheres illuminated by an acoustic Bessel beam can be subjected to a radiation force directed opposite the direction of beam propagation. The prediction of negative acoustic radiation force is extended to the cases of a solid poly(methylmethacrylate) PMMA sphere in water and an empty aluminum spherical shell in water. Compared with the angular scattering patterns for plane wave illumination, the scattering into the back hemisphere is suppressed when the radiation force is negative. This investigation may be helpful in the development of acoustic tweezers and in the development of methods for manipulating objects during space flight.     

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.     

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.     

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.     

Transition from progressive to quasi-standing waves behavior of the radiation force of acoustic waves—Example of a high-order Bessel beam on a rigid sphere

Prior computations have predicted the time-averaged acoustic radiation force on fluid spheres in water when illuminated by an acoustic high-order Bessel beam (HOBB) of quasi-standing waves. These computations are extended to the case of a rigid sphere in water which perfectly mimics a fluid sphere in air. Numerical results for the radiation force function of a HOBB quasi-standing wave tweezers are obtained for beams of zero, first and second order, and discussed with particular emphasis on the amplitude ratio describing the transition from progressive waves to quasi-standing waves behavior. This investigation may be helpful in the development of acoustic tweezers and methods for manipulating objects in reduced gravity environments and space related applications.     

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。      

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.     

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.     

Acoustic radiation force of high-order Bessel beam standing wave tweezers on a rigid sphere

Background and objective

Particle manipulation using the acoustic radiation force of Bessel beams is an active field of research. In a previous investigation, [F.G. Mitri, Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers, Annals of Physics 323 (2008) 1604–1620] an expression for the radiation force of a zero-order Bessel beam standing wave experienced by a sphere was derived. The present work extends the analysis of the radiation force to the case of a high-order Bessel beam (HOBB) of positive order m having an angular dependence on the phase ?.

Method

The derivation for the general expression of the force is based on the formulation for the total acoustic scattering field of a HOBB by a sphere [F.G. Mitri, Acoustic scattering of a high-order Bessel beam by an elastic sphere, Annals of Physics 323 (2008) 2840–2850; F.G. Mitri, Equivalence of expressions for the acoustic scattering of a progressive high order Bessel beam by an elastic sphere, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 56 (2009) 1100–1103] to derive the general expression for the radiation force function Y_Jm,st(ka,β,m), which is the radiation force per unit characteristic energy density and unit cross-sectional surface. The radiation force function is expressed as a generalized partial wave series involving the half-cone angle β of the wave-number components and the order m of the HOBB.

Results

Numerical results for the radiation force function of a first and a second-order Bessel beam standing wave incident upon a rigid sphere immersed in non-viscous water are computed. The rigid sphere calculations for Y_Jm,st(ka,β,m) show that the force is generally directed to a pressure node when m is a positive even integer number (i.e. Y_Jm,st(ka,β,m)>0), whereas the force is generally directed toward a pressure antinode when m is a positive odd integer number (i.e. Y_Jm,st(ka,β,m)<0).

Conclusion

An expression is derived for the radiation force on a rigid sphere placed along the axis of an ideal non-diffracting HOBB of acoustic standing (or stationary) waves propagating in an ideal fluid. The formulation includes results of a previous work done for a zero-order Bessel beam standing wave (m = 0). The proposed theory is of particular interest essentially due to its inherent value as a canonical problem in particle manipulation using the acoustic radiation force of a HOBB standing wave on a sphere. It may also serve as the benchmark for comparison to other solutions obtained by strictly numerical or asymptotic approaches.     

准高斯声束对超声造影剂的声辐射力研究*

超声造影剂的定向输运在超声医学成像领域有着极为重要的意义,而声辐射力作用是实现该过程的关键,相比于高斯声束,准高斯声束是无源亥姆霍兹方程的精确解,可以使用标准波分解法简化计算。因此,本文研究了准高斯声束对超声造影剂的声辐射力作用。文章首先分析了准高斯声束与高斯声束之间的相关性;随后通过数值计算求得了准高斯声束对超声造影剂模型的声辐射力函数与无量纲频率之间的关系;最后,本文研究了不同造影剂气泡情况下的声辐射力。研究结果表明:声辐射力函数随无量纲频率变化将在不同位置出现共振峰,不同的波束宽度值将改变辐射力强度,但不改变共振峰的位置。相关结果可为利用声辐射力定向输运超声造影剂至靶向位置提供理论参考。     

Mean force on a small sphere in a sound field in a viscous fluid

A mean force exerted on a small rigid sphere by a sound wave in a viscous fluid is calculated. The force is expressed as a sum of drag force coming from the external steady flow existing in the absence of the sphere and contributions that are cross products of velocity and velocity derivatives of the incident field. Because of the drag force and an acoustic streaming generated near the sphere, the mean force does not coincide with the acoustic radiation pressure, i.e., the mean momentum flux carried by the sound field through any surface enclosing the sphere. If the sphere radius R is considerably smaller than the viscous wave penetration depth delta, the drag force can give the leading-order contribution (in powers of delta/R) to the mean force and the latter can then be directed against the radiation pressure. In another limit, delta< or =R, the drag force and acoustic streaming play a minor role, and the mean force reduces to the radiation pressure, which can be expressed through source strengths of the scattered sound field. The effect of viscosity can then be significant only if the incident wave is locally plane traveling.     

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.     

Multifrequency radiation force of acoustic waves in fluids

In this article we introduce the concept of multifrequency radiation force produced by a polychromatic acoustic beam propagating in a fluid. This force is a generalization of dynamic radiation force due to a bichromatic wave. We analyse the force exerted on a rigid sphere by a plane wave with N frequency components. Our approach is based on solving the related scattering problem, taking into account the nonlinearity of the fluid. The radiation force is calculated by integrating the excess of pressure in the quasilinear approximation over the surface of the sphere. Results reveal that the spectrum of the multifrequency radiation force is composed of up to N(N−1)/2 distinct frequency components. In addition, the radiation force generated by plane progressive waves is predominantly caused by parametric amplification. This is a phenomenon due to the nonlinear nature of wave propagation in fluids.     

Gauss声束对离轴椭圆柱的声辐射力矩

利用部分波展开法求解得到了Gauss声束入射下刚性和非刚性椭圆柱的声散射系数,推导了一般情况下的声辐射力矩表达式.在此基础上,通过一系列数值仿真详细分析了离轴距离、入射角度和束腰半径对声辐射力矩的影响.结果表明:正向与负向声辐射力矩均可以在一定条件下存在;低频情况下刚性椭圆柱比非刚性椭圆柱更容易产生较强的声辐射力矩;特定频率的入射声场可以激发出非刚性椭圆柱不同阶的共振散射模式,因而非刚性椭圆柱的声辐射力矩峰值与频率的关系更密切;增加束腰半径有利于扩大散射截面,进而增加椭圆柱的声辐射力矩.该研究结果预期可以为利用声辐射力矩实现粒子的可控旋转和流体黏度的反演提供一定的理论指导.     

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.     

Analyses of radiation force and torque on a spherical particle near a substrate illuminated by a focused Laguerre-Gaussian beam

We present the analyses of radiation force and torque on a spherical particle illuminated by Laguerre-Gaussian beam. Since Laguerre-Gaussian beam has angular momentum, the particle can be rotated by illumination of Laguerre-Gaussian beam. Radiation forces and torques for a silver sphere and a silicon sphere near the silver substrate are analyzed. We found that the maximum torque on silicon sphere is about five times higher than the maximum torque on silver sphere and fine control of the focused spot is required to push the particle to the substrate.     

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.     

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.