# Acoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities

## TL;DR

This paper derives analytical expressions for acoustic radiation force and torque on small particles, linking them to fundamental acoustic field properties like canonical momentum and spin densities, with validation through simulations.

## Contribution

It introduces a novel analytical framework connecting acoustic forces and torques to canonical momentum and spin densities, extending optical analogies to acoustics.

## Key findings

- Derived simple analytical formulas for acoustic force and torque.
- Established relations between forces, torque, and field properties like momentum and spin.
- Validated results with numerical simulations and analyzed evanescent acoustic waves.

## Abstract

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.