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Register a new userNonlinear interaction of acoustic waves with a spheroidal particle: radiation force and torque effects
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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.
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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.
We unveil the generation of universal morphologies of fluid interfaces by radiation pressure whatever is the nature of the wave, acoustic or optical. Experimental observations reveal interface deformations endowed with step-like features that are shown to result from the interplay between the wave propagation and the shape of the interface. The results are supported by numerical simulations and a quantitative interpretation based on the waveguiding properties of the field is provided.
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.
The nonlinear interaction of ultrasonic waves with a nonspherical particle may give rise to the acoustic radiation torque on the particle. This phenomenon is investigated here considering a rigid prolate spheroidal particle of subwavelength dimensions that is much smaller than the wavelength. Using the partial wave expansion in spheroidal coordinates, the radiation torque of a traveling and standing plane wave with arbitrary orientation is exactly derived in the dipole approximation. We obtain asymptotic expressions of the torque as the particle geometry approaches a sphere and a straight line. As the particle is trapped in a pressure node of a standing plane wave, its radiation torque equals that of a traveling plane wave. We also find how the torque changes with the particle aspect ratio. Our findings are in excellent agreement with previous numerical computations. Also, by analyzing the torque potential energy, we determine the stable and unstable spatial configuration available for a particle.
The purpose of this article is numerical verification of the thory of weak turbulence. We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves (swell) by two different methods: solution of primordial dynamical equations describing potential flow of the ideal fluid with a free surface and, solution of the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence. Comparison of the results demonstrates pretty good applicability of the weak turbulent approach.
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