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.     

Measuring the radiation force of megahertz ultrasound acting on a solid spherical scatterer

The paper considers the problem of precise measurement of the acoustic radiation force of an ultrasonic beam on targets in the form of solid spherical scatterers. Using known analytic relations, a numerical model is developed to perform calculations for different sizes of spherical scatterers and arbitrary frequencies of the incident acoustic wave. A novel method is proposed for measuring the radiation force, which is based on the principle of acoustic echolocation. The radiation force is measured experimentally in a wide range of incident wave intensities using two chosen methods differing in the way the location of the target is controlled.     

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.     

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.     

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.     

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.     

Axial acoustic radiation force of progressive cylindrical diverging waves on a rigid and a soft cylinder immersed in an ideal compressible fluid

Background and motivation

Previous works investigating the radiation force of diverging spherical progressive waves incident upon spherical particles have demonstrated the direction of reversal of the force when the particle is subjected to a curved wave-front. In this communication, the analysis is extended to the case of diverging cylindrical progressive waves incident upon a rigid or a soft cylinder in a non-viscous fluid with explicit calculations for the radiation force function (which is the radiation force per unit energy density and unit cross-sectional surface) not shown in [F.G. Mitri, Ultrasonics 50 (2010) 620-627].

Method

A closed-form solution presented previously in [F.G. Mitri, Ultrasonics 50 (2010) 620-627] is used to plot the radiation force function with particular emphasis on the difference from the results of incident plane progressive waves versus the size parameter ka (k is the wave number and a is the cylinder’s radius) and the distance of the cylinder from the acoustic source r₀.

Results

Radiation force function calculations for the rigid cylinder unexpectedly reveal that under specific conditions determined by the frequency of the acoustic field, the radius of the cylinder, as well as the distance to the acoustic source, the force becomes attractive (negative force). In addition, the numerical results show that the radiation force on a rigid cylinder does not generally obey the inverse-distance law with respect to the distance from the source.

Conclusion and potential applications

These results suggest that it may be possible, under specific conditions, to pull a cylindrical structure back toward the acoustic source using progressive cylindrical diverging waves. They may also provide a means to predict the radiation force required to manipulate non-destructively a single cylindrical structure. Potential applications include the design of a new generation of acoustic tweezers operating using a single beam of progressive waves (in contrast to the traditional version of acoustical tweezers in which an acoustic standing wave field is produced using two counter-propagating acoustic fields) for investigations in the field of flow cytometry, particle manipulation and entrapment.     

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.     

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.     

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.      

Bessel驻波对椭球形液滴的声辐射转矩

在实际的声操控中,由于声辐射力、表面张力和重力的共同作用,液滴往往呈现出椭球的形状,在螺旋声场中会受到力矩的作用而发生转动。从声波的散射理论出发,根据部分波展开法求解得到了椭球形液滴在Bessel驻波场中的声散射系数,并给出了其受到的声辐射转矩的解析式。在此基础上,对椭球形不可压缩液滴和椭球形可压缩液滴分别进行数值计算。仿真结果表明,不可压缩液滴的声辐射转矩与声束半锥角的关系更密切,而可压缩液滴则更依赖于特定的频率;提升Bessel驻波场的阶数有利于增强声辐射转矩的峰值,但在中低频处较难对可压缩液滴产生明显的力矩。该研究结果预期对利用螺旋声场进行液滴的操控具有理论指导作用。      

Resonance compression of an acoustic beam in a crystal

The resonance excitation of an intense acoustic beam in a crystal is described for a special geometry of pump-wave reflection from the crystal surface. The resonance appears in the vicinity of the total internal reflection angle under the condition that the wave field in a compressed reflected beam propagating almost parallel to the surface is close to the volume eigenmode satisfying the free boundary condition. Criteria for the existence of such modes are considered in detail. Conversion conditions are analyzed under which a “parasitic” reflected wave of the same branch as the incident wave is absent and entire energy from the incident wave falls within a narrow intense acoustic beam of another branch. It is shown that, when the surface is chosen parallel to the crystal symmetry plane, the conversion criterion is reduced to the sole condition on the elastic moduli of the medium. Analysis is performed by analytic and numerical methods for skew cuts of monoclinic, rhombic, trigonal, and hexagonal crystals, when the boundary is the symmetry plane, while the sagittal plane has no symmetry. A number of crystals are found in which resonance excitation is very close to conversion.     

Theoretical calculation of the acoustic radiation force acting on elastic and viscoelastic cylinders placed in a plane standing or quasistanding wave field

In this work, a new expression of the acoustic radiation force function Yst for solid cylindrical targets, suspended in inviscid fluids in a plane standing wave field, is presented. The case of a plane quasistanding wave field is also considered. Numerical calculations of the radiation force function Yst are performed in a wide range of frequencies for elastic and viscoelastic cylinders and compared to those of rigid cylinders. The fluid-loading effect on the radiation force function curves is also analysed. The results show several features quite different from the rigid cylinder solution.     

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.     

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.     

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。      

Enhanced scattering of acoustic waves at interfaces

We propose a general method to realize a total scattering of an incident acoustic wave at interfaces between different media while allowing the flow of air, fluids and/or particles. This originates from the enlargement of the equivalent acoustic scattering cross section of an embedded object coated with acoustic metamaterials, which causes the coated object to behave as a scatterer bigger than its physical size. We theoretically design a model circular cylindrical object coated with such metamaterials whose properties are determined according to two different, but identical, methods. The desired function is confirmed for both far-field and near-field cases with full wave simulations based on the finite element method. This work reveals a promising way to achieve noise shielding and naval camouflage.     

Modeling the acoustic radiation force in microfluidic chambers

A procedure is demonstrated to quantitatively evaluate the acoustic radiation forces in microfluidic particle manipulation chambers. Typical estimates of the acoustic pressure and the acoustic radiation force are based on an analytical solution for a simple one-dimensional standing wave pattern. The complexities of a typical microfluidic channel limit the usefulness of this approach. By leveraging finite elements, and a generalized equation for the acoustic radiation force, channel designs can be investigated in two and three dimensions. Calculations and experimental observations in this report and the literature, confirm these claims.