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Register a new userAcoustic radiation force and radiation torque beyond particles: Effects of non-spherical shape and Willis coupling
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Added by
Shahrokh Sepehrirahnama
Publication date
2021
fields
Physics
and research's language is
English
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Acoustophoresis deals with the manipulation of sub-wavelength 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 Gorkovs 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 in detail the cases of standing and travelling plane waves, showing 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 in general it is essential to account for shape of objects undergoing acoustophoretic manipulation, and this may have important implications for applications such as the manipulation of biological cells.
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The nonlinear interaction of a time-harmonic acoustic wave with an anisotropic particle gives rise to the radiation force and torque effects. These phenomena are at the heart of the acoustofluidics technology, where microparticles such as cells and microorganisms are acoustically manipulated. We present a theoretical model considering a generic acoustic beam interacting with a subwavelength spheroidal particle in a nonviscous fluid. Concise analytical expressions of the radiation force and torque are obtained in the scattering dipole approximation. The radiation force is given in terms of a gradient and scattering force; while the radiation torque has two fundamental contributions, namely, the momentum arm and acoustic spin (spin-torque effect). As a practical example, we use the theory to describe the interaction of two crossed plane waves and a prolate spheroidal particle. The results reveal the particle is transversely trapped in a pressure node and is axially pushed by the radiation force. Also, the momentum arm aligns the particle in the axial direction. At certain specific positions, only the spin-torque occurs. Our findings are remarkably consistent with finite-element simulations. The success of our model enables its use as an investigation tool for the manipulation of anisotropic microparticles in acoustofluidics.
We examine acoustic radiation force and torque on a small (subwavelength) absorbing isotropic particle immersed in a monochromatic (but generally inhomogeneous) sound-wave field. We show that by introducing the monopole and dipole polarizabilities of the particle, the problem can be treated in a way similar to the well-studied optical forces and torques on dipole Rayleigh particles. We derive simple analytical expressions for the acoustic force (including both the gradient and scattering forces) and torque. Importantly, these expressions reveal intimate relations to the fundamental field properties introduced recently for acoustic fields: the canonical momentum and spin angular momentum densities. We compare our analytical results with previous calculations and exact numerical simulations. We also consider an important example of a particle in an evanescent acoustic wave, which exhibits the mutually-orthogonal scattering (radiation-pressure) force, gradient force, and torque from the transverse spin of the field.
Willis coupling in acoustic materials defines the cross-coupling between strain and velocity, analogous to bianisotropic phenomena in electromagnetics. While these effects have been garnering significant attention in recent years, to date their effects have been considered mostly perturbative. Here, we derive general bounds on the Willis response of acoustic scatterers, show that they can become dominant in suitably designed scatterers, and outline a systematic venue for the realistic implementation of maximally bianisotropic inclusions. We then employ these inclusions to realize acoustic metasurfaces for sound bending with unitary efficiency.
Acoustic bianisotropy, also known as the Willis parameter, expands the field of acoustics by providing nonconventional couplings between momentum and strain in constitutive relations. Sharing the common ground with electromagnetics, the realization of acoustic bianisotropy enables the exotic manipulation of acoustic waves in cooperation with a properly designed inverse bulk modulus and mass density. While the control of entire constitutive parameters substantiates intriguing theoretical and practical applications, a Willis metamaterial that enables independently and precisely designed polarizabilities has yet to be developed to overcome the present restrictions of the maximum Willis bound and the nonreciprocity inherent to the passivity of metamaterials. Here, by extending the recently developed concept of virtualized metamaterials, we propose acoustic Willis metamaterials that break the passivity and reciprocity limit while also achieving decoupled control of all constitutive parameters with designed frequency responses. By instituting basis convolution kernels based on parity symmetry for each polarization response, we experimentally demonstrate bianisotropy beyond the limit of passive media. Furthermore, based on the notion of inverse design of the frequency dispersion by means of digital convolution, purely nonreciprocal media and media with a broadband, flat-response Willis coupling are also demonstrated. Our approach offers all possible independently programmable extreme constitutive parameters and frequency dispersion tunability accessible within the causality condition and provides a flexible platform for realizing the full capabilities of acoustic metamaterials.
We provide a detailed analysis on the acoustic radiation force and torque exerted on a homogeneous viscoelastic particle in the long-wave limit (the particle radius is much smaller than the incident wavelength) by an arbitrary wave. We assume that the particle behaves as a linear viscoelastic solid, which obeys the fractional Kelvin-Voigt model. Simple analytical expressions for the radiation force and torque are obtained considering the low- and high-frequency approximation in the viscoelastic model. The developed theory is used to describe the interaction of acoustic waves (traveling and standing plane waves, and zero- and first-order Bessel beams) with a low- and high-density polyethylene particle chosen as examples. Negative axial radiation force and torque are predicted when the ratio of the longitudinal to shear relaxation times is smaller than a constant that depends on the speed of sound in the particle. In addition, a full 3D tractor Bessel vortex beam acting on the high-density polyethylene is depicted. These predictions may enable new possibilities of particle handling in acoustophoretic techniques.
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