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

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 [“On the acoustic radiation pressure on spheres,” Proc. R. Soc. A 147, 212–240 (1934)], Gor'kov [“On the forces acting on a small particle in an acoustical field in an ideal fluid,” Sov. Phys. 6, 773–775 (1962)], and Doinikov [“Acoustic radiation pressure on a rigid sphere in a viscous fluid,” Proc. R. Soc. London A 447, 447–466 (1994)], clarifies the range of validitymore » 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.« less

Authors:
;  [1]
  1. School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, Edinburgh EH9 3JZ (United Kingdom)
Publication Date:
OSTI Identifier:
22310803
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids (1994); Journal Volume: 26; Journal Issue: 10; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; DRAG; EQUATIONS; FLOW VISUALIZATION; FLUIDS; IDEAL FLOW; LAGRANGIAN FUNCTION; MOMENT OF INERTIA; NONLINEAR PROBLEMS; PARTICLES; RADIATION PRESSURE; SOUND WAVES; SPHERES; SPHERICAL CONFIGURATION; VELOCITY; VISCOSITY; WAVELENGTHS

Citation Formats

Xie, Jin-Han, E-mail: J.H.Xie@ed.ac.uk, and Vanneste, Jacques. Dynamics of a spherical particle in an acoustic field: A multiscale approach. United States: N. p., 2014. Web. doi:10.1063/1.4896523.
Xie, Jin-Han, E-mail: J.H.Xie@ed.ac.uk, & Vanneste, Jacques. Dynamics of a spherical particle in an acoustic field: A multiscale approach. United States. doi:10.1063/1.4896523.
Xie, Jin-Han, E-mail: J.H.Xie@ed.ac.uk, and Vanneste, Jacques. 2014. "Dynamics of a spherical particle in an acoustic field: A multiscale approach". United States. doi:10.1063/1.4896523.
@article{osti_22310803,
title = {Dynamics of a spherical particle in an acoustic field: A multiscale approach},
author = {Xie, Jin-Han, E-mail: J.H.Xie@ed.ac.uk and Vanneste, Jacques},
abstractNote = {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 [“On the acoustic radiation pressure on spheres,” Proc. R. Soc. A 147, 212–240 (1934)], Gor'kov [“On the forces acting on a small particle in an acoustical field in an ideal fluid,” Sov. Phys. 6, 773–775 (1962)], and Doinikov [“Acoustic radiation pressure on a rigid sphere in a viscous fluid,” Proc. R. Soc. London A 447, 447–466 (1994)], 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.},
doi = {10.1063/1.4896523},
journal = {Physics of Fluids (1994)},
number = 10,
volume = 26,
place = {United States},
year = 2014,
month =
}
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