On the forces acting on a small particle in an acoustical field in a viscous fluid

TL;DR

This paper derives an analytical expression for the acoustic radiation force on a small, compressible spherical particle in a viscous fluid, accounting for viscosity effects and applicable across various particle sizes and boundary-layer conditions.

Contribution

It introduces a new analytical model incorporating viscous boundary-layer effects into the calculation of acoustic radiation forces on particles.

Findings

The model accurately predicts the acoustophoretic response of microparticles.

Viscosity significantly influences the radiation force and particle behavior.

The results are applicable to microchannel acoustophoresis experiments.

Abstract

We calculate the acoustic radiation force from an ultrasound wave on a compressible, spherical particle suspended in a viscous fluid. Using Prandtl--Schlichting boundary-layer theory, we include the kinematic viscosity of the solvent and derive an analytical expression for the resulting radiation force, which is valid for any particle radius and boundary-layer thickness provided that both of these length scales are much smaller than the wavelength of the ultrasound wave (mm in water at MHz frequencies). The acoustophoretic response of suspended microparticles is predicted and analyzed using parameter values typically employed in microchannel acoustophoresis.