Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers

Starting from the exact acoustic scattering from a sphere immersed in an ideal fluid and centered along the propagation axis of a standing or quasi-standing zero-order Bessel beam, explicit partial-wave representations for the radiation force are derived. A standing or a quasi-standing acoustic field is the result of propagating two equal or unequal amplitude zero-order Bessel beams, respectively, along the same axis but in opposite sense. The Bessel beam is characterized by the half-cone angle β of its plane wave components, such that β = 0 represents a plane wave. It is assumed here that the half-cone angle β for each of the counter-propagating acoustic Bessel beams is equal. Fluid, elastic and viscoelastic spheres immersed in water are treated as examples. Results indicate the capability of manipulating spherical targets based on their mechanical and acoustical properties. This condition provides an impetus for further designing acoustic tweezers operating with standing or quasi-standing Bessel acoustic waves. Potential applications include particle manipulation in micro-fluidic lab-on-chips as well as in reduced gravity environments.     

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.     

Acoustic manipulation of active spherical carriers: Generation of negative radiation force

This paper examines theoretically a novel mechanism of generating negative (pulling) radiation force for acoustic manipulation of spherical carriers equipped with piezoelectric actuators in its inner surface. In this mechanism, the spherical particle is handled by common plane progressive monochromatic acoustic waves instead of zero-/higher- order Bessel beams or standing waves field. The handling strategy is based on applying a spatially uniform harmonic electrical voltage at the piezoelectric actuator with the same frequency of handling acoustic waves, in order to change the radiation force effect from repulsive (away from source) to attractive (toward source). This study may be considered as a start point for development of contact-free precise handling and entrapment technology of active carriers which are essential in many engineering and medicine applications.     

Acoustic radiation force on a rigid cylinder near rigid corner boundaries exerted by a Gaussian beam field

Acoustic manipulation is one of the well-known technologies of particle control and a top research in acoustic field. Calculation of acoustic radiation force on a particle nearby boundaries is one of the critical tasks, as it approximates realistic applications. Nevertheless, it is quite difficult to solve the problem by theoretical method when the boundary conditions are intricate. In this study, we present a finite element method numerical model for the acoustic radiation force exerting on a rigid cylindrical particle immersed in fluid near a rigid corner. The effects of the boundaries on acoustic radiation force of a rigid cylinder are analyzed with particular emphasis on the non-dimensional frequency and the distance from the center of cylinder to each boundary. The results reveal that these parameters play important roles in acoustic manipulation for particle-nearby complicated rigid boundaries. This study verifies the feasibility of numerical analysis on the issue of acoustic radiation force calculation close to complex boundaries, which may provide a new idea on analyzing the acoustic particle manipulation in confined space.     

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.     

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。      

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.     

Precise micro-particle and bubble manipulation by tunable ultrasonic bottle beams

This paper reports a method to generate tunable bottle beams using an ultrasonic lens, by which the bottle position can be precisely adjusted with the change of the acoustic frequency. Therefore, the position of a single particle or bubble in liquid can be manipulated without using phased array which is costly and huge with complex circuits. Furthermore, we introduced this method to multiple bubble manipulation using acoustic holography. The bottle properties against frequency are theoretically and experimentally analyzed. It is shown that the bottle position depends almost linearly on the operating frequency, which provides a basis for the precise manipulation of bubbles and particles. In addition, the relationship between the acoustic radiation force and the drag force under different incident acoustic pressures is considered, establishing a limit on the moving velocity of the trapped particles. The ultrasonic field observation is further demonstrated by Schlieren imaging system. The proposed method has potential biomedical applications, such as more flexible cell manipulation and targeted drug delivery in vivo, as well as potential applications in the study of chemical reactions between micro objects.     

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.     

非线性晶体产生的空心光束中大尺寸粒子囚禁与导引

提出了一种基于非线性ZnSe晶体产生的空心光束与光泳力的大尺寸粒子二维囚禁与一维导引、三维囚禁方案.理论上分析并计算了单个非线性ZnSe晶体产生的空心光束内粒子受到的横向与纵向光泳力,纵向光泳力的大小同粒子尺寸与光束尺寸比例的四次方成正比,与空心光束功率成正比,方向与光束传播方向一致.粒子尺寸与空心光束尺寸越接近时,横向光泳力的大小越大.结果表明该光泳力可以实现对大尺寸粒子的二维囚禁,同时可对粒子进行长距离(米量级)一维定向导引;理论上分析并计算了基于双非线性ZnSe晶体产生的局域空心光束内粒子所受横向与纵向光泳力情况,光泳力与系统参数的依赖关系与单个非线性晶体产生的空心光束中的粒子受力情况类似,不同的是该条件下纵向光泳力指向光束中心.结果表明该局域空心光束可以实现大尺寸粒子的三维有效囚禁.基于非线性ZnSe晶体产生的空心光束或者局域空心光束可以作为大尺寸粒子非接触式有效操控的工具,在现代光学以及生物医学中有潜在的应用.     

Axial and transverse acoustic radiation forces on a fluid sphere placed arbitrarily in Bessel beam standing wave tweezers

The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to an equilibrium position depending on the chosen size parameter ka   (where k$k$ is the wave-number and a$a$ the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study.     

Investigation of two-dimensional acoustic resonant modes in a particle separator

Within an acoustic standing wave particles experience acoustic radiation forces, a phenomenon which is exploited in particle or cell manipulation devices. When developing such devices, one-dimensional acoustic characteristics corresponding to the transducer(s) are typically of most importance and determine the primary radiation forces acting on the particles. However, radiation forces have also been observed to act in the lateral direction, perpendicular to the primary radiation force, forming striated patterns. These lateral forces are due to lateral variations in the acoustic field influenced by the geometry and materials used in the resonator. The ability to control them would present an advantage where their effect is either detrimental or beneficial to the particle manipulation process. The two-dimensional characteristics of an ultrasonic separator device have been modelled within a finite element analysis (FEA) package. The fluid chamber of the device, within which the standing wave is produced, has a width to height ratio of approximately 30:1 and it is across the height that a half-wavelength standing wave is produced to control particle movement. Two-dimensional modal analyses have calculated resonant frequencies which agree well with both the one-dimensional modelling of the device and experimentally measured frequencies. However, these two-dimensional analyses also reveal that these modes exhibit distinctive periodic variations in the acoustic pressure field across the width of the fluid chamber. Such variations lead to lateral radiation forces forming particle bands (striations) and are indicative of enclosure modes. The striation spacings predicted by the FEA simulations for several modes compare well with those measured experimentally for the ultrasonic particle separator device. It is also shown that device geometry and materials control enclosure modes and therefore the strength and characteristics of lateral radiation forces, suggesting the potential use of FEA in designing for the control of enclosure modes in similar particle manipulator devices.     

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.     

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.      

The selection of layer thicknesses to control acoustic radiation force profiles in layered resonators

Ultrasonic standing waves can be used to generate radiation forces on particles within a fluid. A number of authors have derived detailed representations of these forces but these are most commonly applied using an approximation to the energy distribution based upon an idealized standing wave within a mode based upon rigid boundaries. An electro-acoustic model of the acoustic energy distribution within a standing wave with arbitrary thickness boundaries has been expanded to model the radiation force on an example particle within the acoustic field. This is used to examine the force profile on a particle at resonances other than those predicted with rigid boundaries, and with pressure nodes at different positions. A simple analytical method for predicting modal conditions for combinations of frequencies and layer thickness characteristics is presented, which predicts that resonances can exist that will produce a pressure node at arbitrary positions in the fluid layer of such a system. This can be used to design resonators that will drive particles to positions other than the center of the fluid layer, including the fluid/solid boundary of the layer, with significant potential applications in sensing systems. Further, the model also predicts conditions for multiple subwavelength resonances within the fluid layer of a single resonator, each resonance having different nodal planes for particle concentration.     

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 on an air bubble and soft fluid spheres in ideal liquids: Example of a high-order Bessel beam of quasi-standing waves

The partial wave series for the scattering of a high-order Bessel beam (HOBB) of acoustic quasi-standing waves by an air bubble and fluid spheres immersed in water and centered on the axis of the beam is applied to the calculation of the acoustic radiation force. A HOBB refers to a type of beam having an axial amplitude null and an azimuthal phase gradient. Radiation force examples obtained through numerical evaluation of the radiation force function are computed for an air bubble, a hexane, a red blood and mercury fluid spheres in water. The examples were selected to illustrate conditions having progressive, standing and quasi-standing waves with appropriate selection of the waves’ amplitude ratio. An especially noteworthy result is the lack of a specific vibrational mode contribution to the radiation force determined by appropriate selection of the HOBB parameters.     

Second-harmonic pressure generation of a non-diffracting acoustical high-order Bessel vortex beam of fractional type α

Background and motivation

Generalized Bessel vortex beams are regaining interest from the standpoint of acoustic scattering and radiation force theories for applications in particle rotation, mixing and manipulation. Other possible applications may include medical and nondestructive imaging. To manipulate heavy particles in a host medium, a minimum threshold of the incident sound field intensity is required at relatively high wave amplitudes such that nonlinear wave propagation occurs and the generation of harmonics may be detected. Thus, predictions of the harmonics generation become crucial from the standpoint of experimental design, and the present analysis should assist in the development of more complete models related to the (nonlinear) scattering and radiation forces under such circumstances. The purpose of this research is to construct a theoretical model for the second-harmonic pressure generation associated with a category of non-diffracting Bessel vortex beams known as high-order Bessel vortex beams of fractional typeα (HOBVBs-Fα).

Method

The weakly nonlinear wave propagation of a HOBVB-Fα is investigated based on Lighthill’s formalism. Analytical solutions up to the second-order level of approximation are derived and discussed. Closed-form solutions are obtained, which are expressed as a function of first-order quantities available from the classical linear theory. Lateral profiles of the HOBVB-Fα are computed and compared.

Results and conclusion

The results show that the beam’s width reduces and becomes narrower, the side-lobes decrease in magnitude, and the hollow region diameter (or null in magnitude) increases as the order of nonlinearity increases. Furthermore, the nonlinearity of the medium preserves the non-diffracting feature of the beam’s second-harmonic generation within the pre-shock range.     

瑞利粒子在贝塞尔光束中的横向受力

 为寻找捕获瑞利粒子的最佳光场,利用电磁模型推导了贝塞尔光束捕获粒子的最小半径的表达式,并数值计算了瑞利粒子在贝塞尔光束和高斯光束中所受的横向力和势阱的深度。结果表明:当激光功率为4 W时,贝塞尔光束仅能在光轴处稳定地捕获瑞利粒子;当激光功率达到6 W时,贝塞尔光束能够在光轴和次极大位置捕获瑞利粒子。在相同的激光参数条件下,高斯光束无法克服布朗运动的影响稳定地捕获瑞利粒子,贝塞尔光束更有利于捕获瑞利粒子。     

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。