Acoustic Radiation Torque Research Articles

Analytical solution for acoustic radiation force and torque on a spheroid near a rigid or free planar boundary.

An analytical solution is developed for the acoustic radiation force and torque caused by an arbitrary sound field that is incident on a compressible spheroid of any size near a planar boundary that is either rigid or pressure release. The analysis is an extension of a recent solution for a compressible sphere near a planar boundary [Simon and Hamilton, J. Acoust. Soc. Am. 153, 627-642 (2023)]. Approximations that account for a boundary formed by a two-fluid interface may be incorporated as in the previous analysis for a sphere. The present solution is based on expansions of the total acoustic pressure field in spheroidal wave functions and the use of addition theorems. Verification of the solution is accomplished by comparison with a finite element model. Examples are presented for incident fields that are either plane or spherical waves. Effects resulting from the presence of the boundary are studied by comparing the full theory with a simplified model in which multiple scattering is neglected. Numerical implementation of the proposed solution is also discussed.

Programmable spin and transport of a living shrimp egg through photoacoustic pressure.

In the fields of biomedicine and microfluidics, the non-contact capture, manipulation, and spin of micro-particles hold great importance. In this study, we propose a programmable non-contact manipulation technique that utilizes photoacoustic effect to spin and transport living shrimp eggs. By directing a modulated pulsed laser toward a liquid-covered stainless-steel membrane, we can excite patterned Lamb waves within the membrane. These Lamb waves occur at the interface between the membrane and the liquid, enabling the manipulation of nearby particles. Experimental results demonstrate the successful capture, spin, and transport of shrimp eggs in diameter of 220 µm over a distance of about 5 mm. Calculations indicate that the acoustic radiation force and torque generated by our photoacoustic manipulation system are more than 299.5 nN and 41.0 nN·mm, respectively. The system surpasses traditional optical tweezers in terms of force and traditional acoustic tweezers in terms of flexibility. Consequently, this non-contact manipulation system significantly expands the possibilities for applications in various fields, including embryo screening, cell manipulation, and microfluidics.

Reflective vortex focusing for acoustic contact-free object rotation

The use of acoustic vortex waves with angular momentum is a promising means of transferring mechanical torque to an object without making any physical contact. However, the existing passive-conversion vortex lenses are unable to produce strong acoustic radiation torque. To address this issue, we propose a flat reflector sculpted by spiral grooves. It reflects and converts incident waves into vortex-focusing waves that generate radiation torque. Compared with a transmission-type lens, a reflection-type vortex focusing plate exhibits superior functionality in converging sound waves and creating a stronger circular intensity flow. In this work, we analyze the vortex-focusing sound by Rayleigh-Sommerfeld integral theory and boundary element simulation, confirmed by experiments. The number, depth and direction of spiral grooves determine the topological charge, focusing intensity and torque direction, respectively. We evaluate the local and total acoustic radiation forces and torques, acting on small and large fixed spherical targets in the vortex-focusing beam. As a result, spinning a centimeter-size origami pinwheel several times larger than the wavelength at 40 kHz is realized without direct contact, by utilizing the enhanced acoustic radiation torque converged by the reflector. This technology enables efficient convergence of acoustic waves and simultaneous contactless transfer of mechanical torque to an object, thereby presenting potential applications in sound energy harvesting and wireless power supplies.

Acoustofluidic separation of prolate and spherical micro-objects

Most microfluidic separation techniques rely largely on object size as a separation marker. The ability to separate micro-objects based on their shape is crucial in various biomedical and chemical assays. Here, we develop an on-demand, label-free acoustofluidic method to separate prolate ellipsoids from spherical microparticles based on traveling surface acoustic wave-induced acoustic radiation force and torque. The freely rotating non-spherical micro-objects were aligned under the progressive acoustic field by the counterrotating radiation torque, and the major axis of the prolate ellipsoids was parallel to the progressive wave propagation. The specific alignment of the ellipsoidal particles resulted in a reduction in the cross-sectional area perpendicular to the wave propagation. As a consequence, the acoustic backscattering decreased, resulting in a decreased magnitude of the radiation force. Through the variation in radiation force, which depended on the micro-object morphology enabled the acoustofluidic shape-based separation. We conducted numerical simulations for the wave scattering of spherical and prolate objects to elucidate the working mechanism underlying the proposed method. A series of experiments with polystyrene microspheres, prolate ellipsoids, and peanut-shaped microparticles were performed for validation. Through quantitative analysis of the separation efficiency, we confirmed the high purity and high recovery rate of the proposed acoustofluidic shape-based separation of micro-objects. As a bioparticle, we utilize Thalassiosira eccentrica to perform shape-based separation, as the species has a variety of potential applications in drug delivery, biosensing, nanofabrication, bioencapsulation and immunoisolation.

Universal Geometric Relations of Acoustic Spin, Energy Flux, and Reactive Power

An understanding of acoustic spin, energy flux, and reactive power is crucial for manipulating and directing near-field sound. However, despite their importance, the relationship between these physical quantities has not been fully explored. In this paper, we aim to address this gap in knowledge by presenting a proof of some universal geometric relations between the acoustic spin, the cross product of the time-averaged energy flux and reactive power, and the local vorticity of the energy flux. These relations are independent of the specific wave structure and are verified for various acoustic systems. Moreover, our study demonstrates the mechanical torques and forces on small lossy particles generated by three different types of acoustic near-field sources, namely Janus, Huygens, and spin sources. These findings reveal hidden locking relations beyond the simple spin-momentum locking of near-field waves and provide valuable insights into the fundamental principles underlying the relationship between acoustic spin, radiation torque, energy flux, and reactive power in the field of acoustics.

Acoustic rotation of non-spherical micro-objects: Characterization of acoustophoresis and quantification of rotational stability

Acoustic radiation force and torque arising from wave scattering have the potential to perform the biocompatible, contact-free, and precise translation and rotation of micro-objects. Controllable rotation of objects mainly relies on the use of sophisticated transducer arrays, while it is limited by the spatial Rayleigh limitation and would be costly to miniaturize the array for manipulated objects on the micron scale. Here, we make use of the shape asymmetry of an object and achieve micro-object trap and rotation using a simple standing wavefield. The conformal transformation approach is employed to map an axisymmetric, non-spherical object into a sphere, allowing fast analysis for design or real-time computer-controlled manipulation. A low-cost, simple rotational tweezing system is built, which confirms the theoretical prediction that micro-particles are trapped in the pressure nodes and remotely rotated by the action of the actuator boundaries. The rotational dynamics are guided by two stabilization modes, and Lyapunov stability analysis reveals that at least one mode leads to a stable equilibrium state. We demonstrate the significance of our approach in stably and controllably rotating micron-scale objects. The robustness and versatility of the new handy design hold promise for clinical applications and microscopic research such as drug delivery and microsurgery.

Acoustic radiation force and torque on an object near a penetrable interface or impedance boundary

An analytical approach for calculating radiation force and torque on a sphere or spheroid near a rigid or pressure release boundary due to an arbitrary incident acoustic field was developed recently by the authors [Proc. Meet. Acoust. 48, 045004 (2022)]. In that approach, the linear scattering problem is solved using the method of images along with expansions of the acoustic fields in spherical or spheroidal wave functions. The expansion coefficients can then be substituted into an existing expression to obtain the radiation force and torque on the object. In the present work, the aforementioned theory is extended to include penetrable interfaces and impedance boundaries using an approximation of the interfacial boundary conditions. For fluid-fluid interfaces, the object can be placed on either side of the interface with respect to the incident field. This approximate analytical approach is computationally efficient and compares well with the results from an independent finite element model. In addition, an experiment was conducted with a plastic sphere submerged in water and positioned near a boundary. Results from the experiment are discussed in relation to the analytical model. [BES is supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics.]

Dynamical motion of an oblate shaped particle exposed to an acoustic standing wave in a microchannel

We study the dynamics of an oblate shape micro-particle exposed to standing bulk acoustic waves in a microchannel. A parametric study examines the effects of initial orientation, aspect ratio, size, and initial location of the particle on the translational and rotational motion. We find that the particle undergoes rotation to minimize the acoustic radiation torque potential. The direction of rotation of the particle was found to change from anticlockwise to clockwise beyond a critical aspect ratio and larger particles are found to rotate faster and closer to the nodal plane. These results can be relevant to the dynamics of an elongated microorganism or biological cells in an acoustic field.

Soundiation: A software in evaluation of acoustophoresis driven by radiation force and torque on axisymmetric objects.

Acoustic radiation force and torque arising from wave scattering are commonly used to manipulate micro-objects without contact. We applied the partial wave expansion series and the conformal transformation approach to estimate the acoustic radiation force and torque exerted on the axisymmetric particles. Meanwhile, the translational and rotational transformations are employed to perform the prediction of the acoustophoresis. Although these theoretical derivations are well-developed [Tang and Huang, J. Sound Vibr. 532, 117012 (2022), Tang and Huang, Phys. Rev. E 105, 055110 (2022)], coding the required systems, including generation of the wave function, implementation of the transformations, calculations between modules, etc., is non-trivial and time-consuming. Here, we present a new open-source, matlab-based software, called Soundiation [GitHub Repository: https://github.com/Tountain/SoundiationAcoustophoresis, GPL-3.0 license], to address the acoustic radiation force and torque while supporting the dynamic prediction of non-spherical particles. The implementation is basically generic, and its applicability is demonstrated through the validation of numerical methods. A graphical user interface is provided so that it can be used and extended easily.

Acoustic levitation of axisymmetric Mie objects above a transducer array by engineering the acoustic radiation force and torque.

Transducer arrays are a versatile tool for the contactless manipulation of spherical Rayleigh objects. Here we propose an analytical model for stable levitation of axisymmetric Mie objects through directly engineering the desired radiation force and torque. Acoustic contributions from multiple transducers are superimposed through the translation addition theorem, and the nonspherical objects are mapped into a sphere using the conformal transformation technique so that the scattered field can be asymptotically obtained. Then we give the acoustic radiation force and torque applied to a rigid nonspherical Mie object, which can be reconstructed as a series of quasiexplicit functions of the transducer (amplitude and phase) parameters. Through specifying the desired radiation force and torque exerted on the objects, a system of nonlinear equationsis produced, which could be iteratively solved to retrieve appropriate transducer parameters that stabilize the object in an equilibrium position. Practically, we demonstrate several examples of stable levitation of a sphere, a spheroid, and a disk with an averaged radius of a=7mm (size parameter of ka≈5.18) above a transducer array. The absolute acoustic pressure field surrounding the objects simulated by the finite-element method is illustrated to verify the trapping results. The developed analytical model provides an alternative approach to retrieve the transducer parameters for levitating macroscopic nonspherical rigid objects, which may help design the systematic dynamical manipulation of Mie particles.

Willis Coupling-Induced Acoustic Radiation Force and Torque Reversal.

Acoustic meta-atoms serve as the building blocks of metamaterials, with linear properties designed to achieve functions such as beam steering, cloaking, and focusing. They have also been used to shape the characteristics of incident acoustic fields, which led to the manipulation of acoustic radiation force and torque for development of acoustic tweezers with improved spatial resolution. However, acoustic radiation force and torque also depend on the shape of the object, which strongly affects its scattering properties. We show that by designing linear properties of an object using metamaterial concepts, the nonlinear acoustic effects of radiation force and torque can be controlled. Trapped objects are typically small compared with the wavelength, and are described as particles, inducing monopole and dipole scattering. We extend such models to a polarizability tensor including Willis coupling terms, as a measure of asymmetry, capturing the significance of geometrical features. We apply our model to a three-dimensional, subwavelength meta-atom with maximal Willis coupling, demonstrating that the force and the torque can be reversed relative to an equivalent symmetrical particle. By considering shape asymmetry in the acoustic radiation force and torque, Gorkov's fundamental theory of acoustophoresis is thereby extended. Asymmetrical shapes influence the acoustic fields by shifting the stable trapping location, highlighting a potential for tunable, shape-dependent particle sorting.

Theoretical framework to predict the acoustophoresis of axisymmetric irregular objects above an ultrasound transducer array.

Acoustic radiation force and torque arising from wave scattering are able to translate and rotate matter without contact. However, the existing research mainly focused on manipulating simple symmetrical geometries, neglecting the significance of geometric features. For the nonspherical geometries, the shape of the object strongly affects its scattering properties, and thus the radiation force and torque as well as the acoustophoretic process. Here, we develop an analytical framework to calculate the radiation force and torque exerted on the sound-hard or the sound-soft, axisymmetric particles excited by a user-customized transducer array based on a conformal transformation approach, capturing the significance of the geometric features. The derivation framework is established under the computation coordinate system (CCS), whereas the particle is assumed to be static. For the dynamic processes, the rotation of particle is converted as the opposite rotation of transducer array, achieved by employing a rotation transformation to tune the incident driving field in the CCS. Later, the obtained radiation force and torque in the CCS should be transformed back to the observation coordinate system for force and torque analysis. The radiation force and torque exerted on particles with different orientations are validated by comparing the full three-dimensional numerical solution in different phase distributions. It is found that the proposed method presents superior computational accuracy, high geometric adaptivity, and good robustness to various geometric features, while the computational efficiency is more than 100 times higher than that of the full numerical method. Furthermore, it is found that the dynamic trajectories of particles with different geometric features are completely different, indicating that the geometric features can be a potential degree of freedom to tune acoustophoretic process. The ability to predict the acoustophoretic process of nonspherical particles above a user-customized transducer array has improved our understanding of the effect of shape asymmetry, which can also be used to verify the effectiveness of acoustic tweezers in manipulating nonspherical objects.

Acoustic radiation torque of a cylindrical quasi-Gauss beam on a viscoelastic cylindrical shell near an impedance boundary

This work presents a comprehensive analytical formalism to calculate the acoustic radiation torque acting on a viscoelastic cylindrical shell near an impedance boundary, which is exerted by a cylindrical quasi-Gauss beam with an arbitrary incident angle propagating in an ideal fluid. An analytical expression in finite series form for the acoustic radiation torque is derived by applying the partial-wave series expansion method, the image theory and the translational addition theorem. Numerical computations for a viscoelastic cylindrical polyethylene shell immersed in water are provided, with particular emphasis on the effects of the reflecting coefficient of the interface, the shell-boundary distance, the position of the shell, the incident angle and the beam waist. Changing the relative thickness and the interior fluid medium are also considered. It is shown that the cylindrical shell can be rotated counter-clockwise or clockwise, depending on the beam frequency, the shell size, the reflecting coefficient and the incident angle. The periodical oscillation of acoustic radiation torque is also observed as the shell moves away from the boundary. The results of this study can improve our understanding of the acoustic radiation torque behaviors for viscoelastic particles near the boundary, which is commonly encountered in biomedical ultrasound and fluid dynamics.

Acoustic Radiation Force and Torque Acting on Asymmetric Objects in Acoustic Bessel Beam of Zeroth Order Within Rayleigh Scattering Limit

Acoustic momentum exchange between objects and the surrounding fluid can be quantified in terms of acoustic radiation force and torque, and depends on several factors including the objects’ geometries. For a one-dimensional plane wave type, the induced torque on the objects with arbitrary shape becomes a function of both, direct polarization and Willis coupling, as a result of shape asymmetry, and has only in-plane components. Here, we investigate, in the Rayleigh scattering limit, the momentum transfer to objects in the non-planar pressure field of an acoustic Bessel beam with axisymmetric wave front. This type of beam is selected since it can be practically realized by an array of transducers that are cylindrically arranged and tilted at the cone angle β which is a proportionality index of the momentum distribution in the transverse and axial propagation directions. The analytical expressions of the radiation force and torque are derived for both symmetric and asymmetric objects. We show the dependence of radiation force and torque on the characteristic parameters β and radial distance from the beam axis. By comparing against the case of a plane travelling plane wave, zero β angle, we demonstrated that the non-planar wavefront of a zeroth order Bessel beam causes an additional radial force and axial torque. We also show that, due to Willis coupling, an asymmetric object experiences greater torques in the θ direction, by minimum of one order of magnitude compared to a plane travelling wave. Further, the components of the partial torques owing to direct polarization and Willis coupling act in the same direction, except for a certain range of cone angle β. Our findings show that a non-planar wavefront, which is quantified by β in the case of a zeroth-order Bessel beam, can be used to control the magnitude and direction of the acoustic radiation force and torque acting on arbitrarily shaped objects, implying that the wavefront should be adjusted according to the object’s shape to impart acoustic momentum in all directions and achieve a desired acoustophoretic response.

An efficient semi-analytical procedure to calculate acoustic radiation force and torque for axisymmetric irregular bodies

With the attributes of being biocompatible, label-free, and contact-free, sound has been widely used to manipulate micro-objects, such as cells, soft matters, and living things, by the acoustic radiation force and torque arising from wave scattering. The analytical theory exists for the acoustic radiation force and torque on separable geometries, including sphere and ellipsoid. However, it is still a challenge to handle irregular surfaces subject to non-orthogonal and inseparable boundary conditions. Here, we present a calculation method for an axisymmetric geometry with irregular cross-section excited by a time-harmonic plane wave with arbitrary incidence in the inviscid fluid. The method is based on conformal mapping from the irregular surface to a sphere in the new coordinate system. In this way, the separation of variables can be used to solve the corresponding Helmholtz wave equation subjecting to the spherical boundary conditions in the new coordinate system. The radiation force and the torque are asymptotically obtained using the far-field, closed-form solutions. The method is validated by comparisons with full 3D numerical solutions over a wide range of frequencies and incident angles. With a typical discrepancy of less than 5%, the proposed method is much more efficient than the full numerical simulations (via finite element method). Furthermore, it is found that the radiation force acting on different geometries follows the same tendency. The difference is that the presence of the radiation torque ensures that the symmetry axis of the irregular bodies is coincident with or orthogonal to the wave propagating direction.

Born approximation of acoustic radiation force and torque

The Born approximation provides a simple method for calculating acoustic radiation force and torque on compressible objects of arbitrary shape, which may be inhomogeneous. The specific acoustic impedance throughout the object must not differ significantly from that of the background fluid. Also, the incident field must not be too similar to a progressive plane wave, because the approximation is associated with radiation forces due to time-averaged energy density gradients in the incident field. Comparisons with a complete theory for radiation force and torque exerted by standing plane waves on compressible spheroids, based on expansions of the incident and scattered fields in spheroidal wave functions, indicate that the Born approximation is accurate for impedance contrasts up to at least 30% and for spheroids with sizes on the order of a wavelength. This presentation will review the derivation, validation, and applications of the Born approximation. Closed-form solutions for spheres and finite cylinders are presented and for selected distributions of material inhomogeneity. Applications include acoustofluidic separation of biological targets, and acoustic forces on nonspherical objects near interfaces. The approximation also serves as a useful benchmark for other methods of calculation. [T.S.J. was supported by an ARL:UT McKinney Fellowship in Acoustics.]

Acoustic radiation force and torque on a spheroid near an interface

Acoustic radiation force and torque on a spheroid of arbitrary size near a rigid or pressure release interface are calculated using expansions of the pressure field in terms of both spherical and spheroidal wave functions. The spheroidal expansion coefficients are obtained by satisfying the boundary conditions at the interface and at the surface of the spheroid. Conditions at the interface are satisfied using a virtual (image) spheroid, while satisfying conditions at the spheroid surface require the use of addition theorems for spheroidal wave functions. The radiation force and torque are expressed as a summation of terms involving products of the coefficients in spherical wave expansions of the incident and scattered fields [Ilinskii et al., J. Acoust. Soc. Am. 144, 568–576 (2018)]. Far-field asymptotes are used to relate the spheroidal and spherical harmonic expansion coefficients analytically. Results from the present analytical model are compared with those from a finite-element model. The effect of the interface on the radiation force and torque relative to that on a spheroid in a free field is discussed. [B.E.S. is supported by the Applied Research Laboratories Chester M. McKinney Graduate Fellowship in Acoustics.]

Born approximation of acoustic radiation force and torque for an arbitrary particle in a zero-order standing Bessel beam

The calculation of acoustic radiation force and acoustic radiation torque is an important basis for the precise manipulation of particles. It is difficult to directly apply the partial-wave series expansion method based on the classical acoustic scattering theory to the study of complicated models, while pure numerical methods are not conducive to the parametric analyses of the system. Based on the basic principle of Born approximation, the expressions of acoustic radiation force and torque acting on an arbitrary particle located in the center of a zero-order Bessel standing wave field are derived at low frequencies. On this basis, the numerical simulations are systematically performed by taking spherical, spheroidal and cylindrical particles as examples. The effects of inhomogeneity on the acoustic radiation force and torque are also investigated. The simulation results show that the Born approximation method has a high accuracy in the low frequency range. As the frequency increases and the impedance matching between the particle and the fluid becomes worse, the accuracy of Born approximation will gradually decrease. An acoustic radiation torque caused by asymmetry will be exerted on spheroidal and cylindrical particles obliquely positioned in a zero-order Bessel standing wave field. When the particle size is much smaller than the wavelength, the acoustic radiation force is nearly independent of the particle shape, but this is not the case for acoustic radiation torque. Finally, viscous effect of the surrounding fluid is introduced and the expression of acoustic radiation force is corrected accordingly. The study is expected to provide a theoretical guide for the precise manipulation of small particles using standing wave acoustic tweezers in biomedicine and material sciences.

Acoustofluidics 24: theory and experimental measurements of acoustic interaction force.

The motion of small objects in acoustophoresis depends on the acoustic radiation force and torque. These are nonlinear phenomena originating from wave scattering, and consist of primary and secondary components. The primary radiation force is the force acting on an object due to the incident field, in the absence of other objects. The secondary component, known as acoustic interaction force, accounts for the interaction among objects, and contributes to the clustering patterns of objects, as commonly observed in experiments. In this tutorial, the theory of acoustic interaction forces is presented using the force potential and partial-wave expansion approaches, and the distinguishing features of these forces such as rotational coupling and non-reciprocity are described. Theoretical results are compared to experimental measurements of interaction forces using a glass micro-capillary setup to explain the practical challenges. Finally, the phenomenon of clustering patterns induced by the close-range interaction of objects is demonstrated to point out the considerations about multiple collision and the predicted clustering patterns entirely due to the interaction force. Understanding the principles of acoustic interaction enables us to develop novel acoustofluidic applications beyond the typical processing of large populations of particles and with focus on the controlled manipulation of small clusters.

Acoustic radiation force and radiation torque beyond particles: Effects of nonspherical shape and Willis coupling.

Acoustophoresis mainly deals with the manipulation of subwavelength scatterers in an incident acoustic field. The geometric details of manipulated particles are often neglected by replacing them with equivalent symmetric geometries such as spheres, spheroids, cylinders, or disks. It has been demonstrated that geometric asymmetry, represented by Willis coupling terms, can strongly affect the scattering of a small object; hence neglecting these terms may miss important force contributions. In this work, we present a generalized formalism of acoustic radiation force and radiation torque based on the polarizability tensor, where Willis coupling terms are included to account for geometric asymmetry. Following Gorkov's approach, the effects of geometric asymmetry are explicitly formulated as additional terms in the radiation force and torque expressions. By breaking the symmetry of a sphere along one axis using intrusion and protrusion, we characterize the changes in the force and torque in terms of partial components, associated with the direct and Willis coupling coefficients of the polarizability tensor. We investigate the cases of standing and traveling plane waves and show how the equilibrium positions and angles are shifted by these additional terms. We show that while the contributions of asymmetry to the force are often negligible for small particles, these terms greatly affect the radiation torque. Our presented theory, providing a way of calculating radiation force and torque directly from polarizability coefficients, shows that it is essential to account for shape of objects undergoing acoustophoretic manipulation, with important implications for applications such as the manipulation of biological cells.