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.     

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 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.     

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 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.     

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.     

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.     

Radiation force of acoustical tweezers on a sphere: The case of a high-order Bessel beam of quasi-standing waves of variable half-cone angles

Using the partial-wave series for the acoustic scattering of a high-order Bessel beam (HOBB) of counterpropagating quasi-standing waves of variable half-cone angles, a generalized radiation force expression is obtained. The radiation force function, which is the radiation force per unit cross-sectional surface and unit characteristic energy density, is expressed in terms of the order m of the HOBB, the quasi-standing waves’ amplitudes Φ₀ and Φ₁, as well as the variable half-cone angles β₁ and β₂. The features of the theory include the ability to suppress two resonances as well as exploring a broad range of parameters related to the beam shape and mechanical properties of the spherical target.     

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.     

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.     

Simple and high efficient optical trapping using a cylindrical lens and a single plane wave of incidence

We suggest a simple and high efficient method for trapping particles in the evanescent field. In this method, a single plane wave is normally incident on the cylindrical surface of a cylindrical lens and then incident on the plane surface of the lens at an angle larger than the critical angle. Multiple reflections of light within the cylindrical lens create two evanescent waves with different directions in the transmitted field. Interference of two evanescent waves comes into being a standing wave which can stably trap particles close to the top of the cylindrical lens. Based on the Rayleigh approximation, we obtain analytical expressions of optical force acting on a Rayleigh particle placed in the vicinity of the lens. We find that the trap stiffness and trap depth is dependent on the radius of the cylindrical lens, wavelength and polarization of light, and incident angle at the lens–liquid interface.     

Theoretical and numerical calculations for the time-averaged acoustic force and torque acting on a rigid cylinder of arbitrary size in a low viscosity fluid

In this paper, theoretical calculations as well as numerical simulations are performed for the time-averaged acoustic force and torque on a rigid cylinder of arbitrary size in a fluid with low viscosity, i.e., the acoustic boundary layer is thin compared to the cylinder radius. An exact analytical solution and its approximation are proposed in the form of an infinite series including Bessel functions. These solutions can be evaluated easily by a mathematical software package such as mathematica and matlab. Three types of incident waves, plane traveling wave, plane standing wave, and dual orthogonal standing waves, are investigated in detail. It is found that for a small particle, the viscous effects for an incident standing wave may be neglected but those for an incident traveling wave are notable. A nonzero viscous torque is experienced by the rigid cylinder when subjected to dual orthogonal standing waves with a phase shift even when the cylinder is located at equilibrium positions without imposed acoustic forces. Furthermore, numerical simulations are carried out based on the FVM algorithm to verify the proposed theoretical formulas. The theoretical results and the numerical ones agree with each other very well in all the cases considered.     

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.     

基于蜷曲空间结构的近零折射率声聚焦透镜

研究基于蜷曲空间结构的近零折射率声聚焦透镜.根据近零折射率材料的声波方向选择机理,采用蜷曲空间结构为基本单元进行排列,设计具有特定入射与出射界面的几何结构,对透射声波的出射方向进行调控,实现了平面声波与柱面声波的聚焦效应,并深入讨论了透镜内部刚性散射体对声聚焦性能的影响.在此基础上,改变近零折射率透镜的出射界面,可以精确调控声波阵面的形状与方向.该类型透镜具有单一的单元结构、高聚焦性能及高鲁棒性等优点.研究结果为设计新型近零折射率声聚焦透镜提供了理论指导与实验参考,同时也为研究声波阵面的调控提供了新思路.     

Radiation force and torque on a two-dimensional circular cross-section of a non-viscous eccentric layered compressible cylinder in acoustical standing waves

The purpose of this study is to develop an analytical formalism and derive series expansions for the time-averaged force and torque exerted on a compound coated compressible liquid-like cylinder,insonified by acoustic standing waves having an arbitrary angle of incidence in the polar(transverse)plane.The host medium of wave propagation and the eccentric liquid-like cylinder are non-viscous.Numerical computations illustrate the theoretical analysis with particular emphases on the eccentricity of the cylinder,the angle of incidence and the dimensionless size parameters of the inner and coating cylindrical fluid materials.The method to derive the acoustical scattering,and radiation force and torque components conjointly uses modal matching with the addition theorem,which adequately account for the multiple wave interaction effects between the layer and core fluid materials.The results demonstrate that longitudinal and lateral radiation force components arise.Moreover,an axial radiation torque component is quantified and computed for the non-absorptive compound cylinder,arising from geometrical asymmetry considerations as the eccentricity increases.The computational results reveal the emergence of neutral,positive,and negative radiation force and torque depending on the size parameter of the cylinder,the eccentricity,and the angle of incidence of the insonifying field.Moreover,based on the law of energy conservation applied to scattering,numerical verification is accomplished by computing the extinction/scattering energy efficiency.The results may find some related applications in fluid dynamics,particle trapping,mixing and manipulation using acoustical standing waves.     

The mechanism of the attracting acoustic radiation force on a polymer-coated gold sphere in plane progressive waves

Acoustic plane progressive waves incident on a sphere immersed in a nonviscous fluid exert a steady force acting along the direction of wave motion. It is shown here that when an elastic gold sphere is coated with a polymer-type (polyethylene) viscoelastic layer, this force becomes a force of attraction in the long wavelength limit. Kinetic, potential and Reynolds stress energy densities are defined and evaluated with and in the absence of absorption in the layer. Without absorption, the mechanical energy density counteracts the Reynolds stress energy density, which causes a repulsive force. However, in the case of absorption, the attractive force is predicted to be a physical consequence of a mutual contribution of both the mechanical and the Reynolds stress energy densities. This condition provides an impetus for further designing acoustic tweezers operating with plane progressive waves as well as fabricating polymer-coated gold particles for specific biophysical and biomedical applications.     

Acoustic radiation force acting on elastic and viscoelastic spherical shells placed in a plane standing wave field

The theory of the acoustic radiation force acting on elastic spherical shells suspended in a plane standing wave field is developed in relation to their thickness and the content of their hollow regions. The theory is modified to include the effect of a hysteresis type of absorption of compressional and shear waves in the material. The fluid-loading effect on the acoustic radiation force function Y(st) is analyzed as well. Results of numerical calculations are presented for a number of elastic and viscoelastic materials, with the hollow region filled with water or air. These results show how the damping due to absorption, the change of the interior fluid inside the shells' hollow regions, and the exterior fluid surrounding their structures, affect the acoustic radiation force.     

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.     

Acoustic resonance scattering from a multilayered cylindrical shell with imperfect bonding

The method of wave function expansion is adopted to study the three dimensional scattering of a time-harmonic plane progressive sound field obliquely incident upon a multi-layered hollow cylinder with interlaminar bonding imperfection. For the generality of solution, each layer is assumed to be cylindrically orthotropic. An approximate laminate model in the context of the modal state equations with variable coefficients along with the classical T-matrix solution technique is set up for each layer to solve for the unknown modal scattering and transmission coefficients. A linear spring model is used to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the non-resonance (backgrounds) and resonance components. The solution is first used to investigate the effect of interlayer imperfection of an air-filled and water submerged bilaminate aluminium cylindrical shell on the resonances associated with various modes of wave propagation (i.e., symmetric/asymmetric Lamb waves, fluid-borne A-type waves, Rayleigh and Whispering Gallery waves) appearing in the backscattered spectrum, according to their polarization and state of stress. An illustrative numerical example is also given for a multi-layered (five-layered) cylindrical shell for which the stiffness of the adhesive interlayers is artificially varied. The sensitivity of resonance frequencies associated with higher mode numbers to the stiffness coefficients is demonstrated to be a good measure of the bonding strength. Limiting cases are considered and fair agreements with solutions available in the literature are established.