Acoustic interaction forces between small particles in an ideal fluid

TL;DR

This paper derives a theoretical expression for the acoustic interaction forces between small particles in an ideal fluid under acoustic waves, revealing aggregation and repulsion behaviors in different wave conditions.

Contribution

It introduces a new theoretical model for acoustic interaction forces applicable to small particles in ideal fluids, including a mean-field approximation for emulsions.

Findings

Particles aggregate along wave propagation direction.

Particles attract or repel transversely depending on conditions.

The model applies to both standing and traveling waves.

Abstract

We present a theoretical expression for the acoustic interaction force between small spherical particles suspended in an ideal fluid exposed to an external acoustic wave. The acoustic interaction force is the part of the acoustic radiation force on one given particle involving the scattered waves from the other particles. The particles, either compressible liquid droplets or elastic microspheres, are considered to be much smaller than the acoustic wavelength. In this so-called Rayleigh limit, the acoustic interaction forces between the particles are well approximated by gradients of pair-interaction potentials with no restriction on the inter-particle distance. The theory is applied to studies of the acoustic interaction force on a particle suspension in either standing or traveling plane waves. The results show aggregation regions along the wave propagation direction, while particles may attract or repel each other in the transverse direction. In addition, a mean-field approximation is developed to describe the acoustic interaction force in an emulsion of oil droplets in water.