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.     

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.     

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.     

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.     

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.     

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.     

On the choice of expansion functions in the Helmholtz equation least-squares method

This paper examines the performance of Helmholtz equation least-squares (HELS) method in reconstructing acoustic radiation from an arbitrary source by using three different expansions, namely, localized spherical waves (LSW), distributed spherical waves (DSW), and distributed point sources (DPS), under the same set of measurements. The reconstructed acoustic pressures are validated against the benchmark data measured at the same locations as reconstruction points for frequencies up to 3275 Hz. Reconstruction is obtained by using Tikhonov regularization or its modification with the regularization parameter selected by error-free parameter-choice methods. The impact of the number of measurement points on the resultant reconstruction accuracy under different expansion functions is investigated. Results demonstrate that DSW leads to a better-conditioned transfer matrix, yields more accurate reconstruction than both LSW and DPS, and is not affected as much by the change in measurement points. Also, it is possible to obtain optimal locations of the auxiliary sources for DSW, LSW, and DPS by taking an independent layer of measurements. Use of these auxiliary sources and an optimal combination of regularization and error-free parameter choice methods can yield a satisfactory reconstruction of acoustic quantities on the source surfaces as well as in the field in the most cost-effective manner.     

Optimal secondary source position in exterior spherical acoustical holophony

Exterior spherical acoustical holophony is a branch of spatial audio reproduction that deals with the rendering of a given free-field radiation pattern (the primary field) by using a compact spherical loudspeaker array (the secondary source). More precisely, the primary field is known on a spherical surface surrounding the primary and secondary sources and, since the acoustic fields are described in spherical coordinates, they are naturally subjected to spherical harmonic analysis. Besides, the inverse problem of deriving optimal driving signals from a known primary field is ill-posed because the secondary source cannot radiate high-order spherical harmonics efficiently, especially in the low-frequency range. As a consequence, a standard least-squares solution will overload the transducers if the primary field contains such harmonics. Here, this is avoided by discarding the strongly decaying spherical waves, which are identified through inspection of the radiation efficiency curves of the secondary source. However, such an unavoidable regularization procedure increases the least-squares error, which also depends on the position of the secondary source.This paper deals with the above-mentioned questions in the context of far-field directivity reproduction at low and medium frequencies. In particular, an optimal secondary source position is sought, which leads to the lowest reproduction error in the least-squares sense without overloading the transducers. In order to address this issue, a regularization quality factor is introduced to evaluate the amount of regularization required. It is shown that the optimal position improves significantly the holophonic reconstruction and maximizes the regularization quality factor (minimizes the amount of regularization), which is the main general contribution of this paper. Therefore, this factor can also be used as a cost function to obtain the optimal secondary source position.     

Excitation of the acoustic and leaky waves in the atmosphere by a sub-surface seismic source

We study excitation of acoustic, leaky, and surface waves by a time-harmonic force source located in a homogeneous isotropic elastic half-space contacting a homogeneous gas. The force acts in the normal direction to the interface between the media. We consider the case where the sound velocity in the gas is less than the velocity of the Rayleigh wave propagating along the surface of the solid. An expression is derived for the period-averaged radiation power of the surface Stoneley wave. The total radiation power is calculated for the acoustic wave in the gas and for the leaky pseudo-Rayleigh wave. Variations in the radiation powers of the surface and leaky waves are analyzed as functions of the source depth. If the velocities of compressional and shear waves in the elastic medium significantly exceed the sound velocity in the gas, then the radiation power of the Stoneley wave turns out to be a factor of 10⁶–10⁸ smaller than the radiation powers of other waves. The radiation power of the Stoneley wave decreases monotonically with increasing source depth, and the decrease becomes more pronounced with the increase in the difference between the acoustic impedances of the contacting media. If the shear-wave velocity in the solid is close to the sound velocity in the gas, then the radiation power of the Stoneley wave is comparable with the radiation powers of other waves and exhibits maximum at a certain source depth. For some parameters of the gas and the solid, and for certain source depths, the Stoneley wave carries away more than a half of the total radiation power. It is shown that, for certain relations between the parameters of the media, the radiation power of the Stoneley wave increases due to redistribution of the radiated power from the pseudo-Rayleigh leaky wave. The total power of these waves remains approximatly constant and, with accuracy of the order of 10⁻³, is equal to the radiation power of the Rayleigh wave at the vacuum-solid interface. It is shown that the acoustic-wave power which can be transmitted to the upper layers of the atmosphere during an earthquake does not exceed 0.01% of the total power radiated at a given frequency. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 7, pp. 577–592, July 2006.     

Laser generation of acoustic waves at a periodic domain structure in lithium niobate

Generation of coherent acoustic oscillations due to the interaction of laser pulses with the periodic domain structure formed in a lithium niobate single crystal is observed. It is found that the excitation of acoustic waves is most efficient when the generated wavelength is equal to the period of the domain structure. The proposed mechanism of the optical generation of acoustic oscillations consists of the photogeneration of free carriers, which compensate the polarization fields within the domains, and the occurrence of alternating elastic stresses caused by the piezoelectric effect.     

Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopies of ferroelectric materials

Nanoelectromechanics of piezoelectric indentation, including the structure of coupled electroelastic fields and stiffness relations, is analysed for flat, spherical, and conical indenter geometries. Exact solutions in elementary functions for electroelastic fields inside the material are obtained using the recently established correspondence principle between the elastic and the piezoelectric problems. The stiffness relations fully describe the indentation process and relate indentation depth, indentation force and bias to the relevant material properties and indenter parameters. This extends the results of Hertzian mechanics to piezoelectric materials. The stiffness relations are utilized for quantitative understanding of the electromechanical scanning probe microscopies (SPM) of ferroelectric and piezoelectric materials, including piezoresponse force microscopy, atomic force acoustic microscopy, scanning near-field acoustic microscopy, and heterodyne ultrasonic-electrostatic force microscopy. The structure of the electroelastic field yields a quantitative measure of signal generation volume in electromechanical SPMs and also provides a quantitative basis for the analysis of tip-induced polarisation switching and local hysteresis loop measurements.     

Acoustic centering of sources measured by surrounding spherical microphone arrays

The radiation patterns of acoustic sources have great significance in a wide range of applications, such as measuring the directivity of loudspeakers and investigating the radiation of musical instruments for auralization. Recently, surrounding spherical microphone arrays have been studied for sound field analysis, facilitating measurement of the pressure around a sphere and the computation of the spherical harmonics spectrum of the sound source. However, the sound radiation pattern may be affected by the location of the source inside the microphone array, which is an undesirable property when aiming to characterize source radiation in a unique manner. This paper presents a theoretical analysis of the spherical harmonics spectrum of spatially translated sources and defines four measures for the misalignment of the acoustic center of a radiating source. Optimization is used to promote optimal alignment based on the proposed measures and the errors caused by numerical and array-order limitations are investigated. This methodology is examined using both simulated and experimental data in order to investigate the performance and limitations of the different alignment methods.     

Excitation of shear waves due to the interband absorption of laser radiation in a piezoelectric semiconductor-dielectric layered structure

Optical piezoelectric generation of shear bulk acoustic waves by volume-distributed electric fields in the vicinity of a hard planar interface between a piezoelectric semiconductor and a dielectric is described theoretically. Nonstationary and nonuniform electric fields are formed as a result of the spatial separation of electrons and holes photoexcited in the piezoelectric semiconductor due to the interband absorption of laser radiation. Frequency regions where the efficiency of the optical piezoelectric excitation of shear waves increases when the surface of the piezoelectric semiconductor is loaded by another piezoelectric with a high acoustic impedance are found. Numerical estimates of the applicability of the immobile hole model are presented.     

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.     

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.     

气体物理性质对近场超声悬浮特性的影响研究

在利用近场超声悬浮技术搬运晶圆的过程中,为提高近场超声悬浮力,该文研究了气体物理性质与近场超声悬浮力之间的关系。利用声辐射压理论与流体力学理论对不同气体介质下的悬浮力进行建模与求解。搭建了可测量不同气体环境中悬浮力的实验平台。实验发现氩气环境下超声悬浮力平均值相对空气环境下提升24.8%。结合实验与理论计算分析了气体密度、比热容比、声速与动力黏度对悬浮力的影响,推断气体的比热容比为影响近场超声悬浮力的主要参数。该方法为晶圆搬运的环境适用性提供了参考价值。     

Characterization of cylindrical ultrasonic transducers using acoustic holography

We present the results of studying the vibrational velocity distribution over the surface of cylindrical ultrasound transducers by acoustic holography. We describe two approaches for acoustic holography: the spatial spectrum method and the Rayleigh integral method. In the case of cylindrical sources the spectral method has a specific feature in comparison to the case of quasi-plane sources: small-scale spectrum components having the form of evanescent (nonpropagating) waves near the source, turn into propagating waves at a certain distance from the source. The use of such a mixed type of waves makes it possible to increase the holographic resolution. To conduct holography of cylindrical sources by the Rayleigh integral method, a modification consisting in the superimposing of boundaries on the integration region is proposed. We present the results of numerical simulation and physical experiments on holography of small cylindrical piezoelectric transducers. We demonstrate that the proposed methods of holography make it possible to recover the vibration structure of source surfaces up to order of the wavelength scales.     

Transient radiation of acoustic waves at the atmosphere-earth interface

Using the contour integration method, we solved the problem on the transient radiation of acoustic waves by a mass-production source which moves uniformly in a gas in the direction normal to the interface of homogeneous gaseous and elastic half-spaces and vanishes at the moment of the solid surface contact. Asymptotic formulas are derived for the transient radiation field which are valid at the fronts of spherical and lateral waves. An exact analytical expression is obtained for the transient radiation field at observation points in the source trajectory. The total internal reflection effects in the transient radiation of sound are analyzed. Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 4, pp. 420–431, April, 1997.     

Analysis of unidirectional broadband piezoelectric spherical shell transducers for underwater acoustics

This paper presents an analytical investigation and experimental verification of the properties of unidirectional broadband piezoelectric acoustic transducers utilizing axisymmetric vibrations of both complete and incomplete spherical piezoelectric shells and is a continuation of a previous paper that presented the electromechanical modal analysis part of the problem [J. Acoust. Soc. Am. 130(2), 753-763 (2011)]. The analysis covers the treatment of the acoustic radiation and reception problem by including analysis of the acoustic impedances and diffraction coefficients as a function of geometry and modal excitation as well as providing specific design examples including multimode spherical acoustic transducers with conformal baffles, and transducers made of incomplete shells (e.g., hemispheres and caps) with free circumferential boundary conditions. The energy method is used to obtain equivalent parameters for a multi-contour electromechanical circuit representation of the transducer and to calculate the transducer performance characteristic as sound projectors and as receivers. Experimental results are obtained on representative piezoceramic transducer prototypes and are in good agreement with the analytical results.     

宽带铁磁流体电动式声源

本文阐明了铁磁流体电动式声源的换能机理．我们详细地研究了它的磁路结构，及在振动活塞上安置一个大的橡皮充气球泡，它能提高低频的辐射效率．这声源具有4个倍频程的低频宽带发射响应