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Register a new userAcoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities
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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.
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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.
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.
A uniformly-charged spherical shell of radius $R$, mass $m$, and total electrical charge $q$, having an oscillatory angular velocity $Omega(t)$ around a fixed axis, is a model for a magnetic dipole that radiates an electromagnetic field into its surrounding free space at a fixed oscillation frequency $omega$. An exact solution of the Maxwell-Lorentz equations of classical electrodynamics yields the self-torque of radiation resistance acting on the spherical shell as a function of $R$, $q$, and $omega$. Invoking the Newtonian equation of motion for the shell, we relate its angular velocity $Omega(t)$ to an externally applied torque, and proceed to examine the response of the magnetic dipole to an impulsive torque applied at a given instant of time, say, $t=0$. The impulse response of the dipole is found to be causal down to extremely small values of $R$ (i.e., as $R to 0$) so long as the exact expression of the self-torque is used in the dynamical equation of motion of the spherical shell.
Every university introductory physics course considers the problem of Atwoods machine taking into account the mass of the pulley. In the usual treatment the tensions at the two ends of the string are offhandedly taken to act on the pulley and be responsible for its rotation. However such a free-body diagram of the forces on the pulley is not {it a priori} justified, inducing students to construct wrong hypotheses such as that the string transfers its tension to the pulley or that some symmetry is in operation. We reexamine this problem by integrating the contact forces between each element of the string and the pulley and show that although the pulley does behave as if the tensions were acting on it, this comes only as the end result of a detailed analysis. We also address the question of how much friction is needed to prevent the string from slipping over the pulley. Finally, we deal with the case in which the string is on the verge of sliding and show that this will never happen unless certain conditions are met by the coefficient of friction and the masses involved.
We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a ${it scalar}$ potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement ${it vector}$ potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential representations, we put forward an acoustic ${it spinor}$ representation combining the scalar and vector representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.
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