Appendix B
Paper published in Physical Review
E, August 2013
Ultrasound-induced acoustophoretic motion of microparticles
in three dimensions
P. B. Muller, M. Rossi, A. G. Marin, R. Barnkob, P. Augustsson, T.
Laurell, C. J. Kähler, and H. Bruus
Abstract: We derive analytical expressions for the three-dimensional (3D) acoustophoretic
motion of spherical microparticles in rectangular microchannels. The motion is generated
by the acoustic radiation force and the acoustic streaming-induced drag force. In contrast
to the classical theory of Rayleigh streaming in shallow, innite, parallel-plate channels,
our theory does include the eect of the microchannel sidewalls. The resulting predictions
agree well with numerics and experimental measurements of the acoustophoretic motion of
polystyrene spheres with nominal diameters of 0.537 and 5.33 m. The 3D particle motion
was recorded using astigmatism particle tracking velocimetry under controlled thermal
and acoustic conditions in a long, straight, rectangular microchannel actuated in one of its
transverse standing ultrasound-wave resonance modes with one or two half-wavelengths.
The acoustic energy density is calibrated in situ based on measurements of the radiation
dominated motion of large 5-m-diameter particles, allowing for quantitative comparison
between theoretical predictions and measurements of the streaming-induced motion of
small 0.5-m-diameter particles.
http://dx.doi.org/10.1103/PhysRevE.88.023006
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