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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, 212240 (1934)], Gor'kov ["On the forces acting on a small particle in an acoustical field in an ideal fluid," Sov. Phys. 6, 773775 (1962)], and Doinikov ["Acoustic radiation pressure on a rigid sphere in a viscous fluid," Proc. R. Soc. London A 447, 447466 (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 Lagrangianmean fluid motion. (C) 2014 AIP Publishing LLC.
Original language  English 

Article number  102001 
Number of pages  20 
Journal  Physics of Fluids 
Volume  26 
Issue number  10 
DOIs  
Publication status  Published  Oct 2014 
Keywords
 HEATCONDUCTING FLUID
 RADIATION FORCE
 RIGID SPHERE
 VISCOUSFLUID
 FLOW
 PRESSURE
 WAVES
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 1 Finished

Science and Innovation: Numerical Algorithms and Intelligent Software for the Evolving HPC Platform
1/08/09 → 31/07/14
Project: Research