Dynamics of a spherical particle in an acoustic field: a multiscale approach

TL;DR

This paper presents a multiscale analysis of spherical particle dynamics in acoustic fields, identifying regimes of dominant effects and deriving governing equations to better understand particle-fluid interactions in microfluidic applications.

Contribution

It systematically assesses the relative importance of physical effects on particle motion, clarifies classical results, and introduces a new nonlinear regime in acoustic microfluidics.

Findings

Identified two regimes with different dominant effects on particle motion.

Derived governing equations for each regime, clarifying classical results.

Discovered a new nonlinear regime where particle motion is coupled to fluid flow.

Abstract

A rigid spherical particle in an acoustic wave field oscillates at the wave period but has also a mean motion on a longer time scale. The dynamics of this mean motion is crucial for numerous applications of acoustic microfluidics, including particle manipulation and flow visualisation. It is controlled by four physical effects: acoustic (radiation) pressure, streaming, inertia and viscous drag. In this paper, we carry out a systematic multiscale analysis of the problem in order to assess the relative importance of these effects depending on the parameters of the system that include wave amplitude, wavelength, sound speed, sphere radius, and viscosity. We identify two distinguished regimes characterised by a balance among three of the four effects, and we derive the equations that govern the mean particle motion in each regime. This recovers and organises classical results by King, Gor'kov and Doinikov, clarifies the range of validity of these results, and reveals a new nonlinear dynamical regime. In this regime, the mean motion of the particle remains intimately coupled to that of the surrounding fluid, and while viscosity affects the fluid motion, it plays no part in the acoustic pressure. Simplified equations, valid when only two physical effects control the particle motion, are also derived. They are used to obtain sufficient conditions for the particle to behave as a passive tracer of the Lagrangian-mean fluid motion.