Appendix A
Paper published in Lab on a Chip,
July 2012
A numerical study of microparticle acoustophoresis driven by
acoustic radiation forces and streaming-induced drag forces
Peter Barkholt Muller, Rune Barnkob, Mads Jakob Herring Jensen and
Henrik Bruus
Abstract: We present a numerical study of the transient acoustophoretic motion of microparticles
suspended in a liquid-lled microchannel and driven by the acoustic forces
arising from an imposed standing ultrasound wave: the acoustic radiation force from the
scattering of sound waves on the particles and the Stokes drag force from the induced
acoustic streaming ow. These forces are calculated numerically in two steps. First, the
thermoacoustic equations are solved to rst order in the imposed ultrasound eld taking
into account the micrometer-thin but crucial thermoviscous boundary layer near the rigid
walls. Second, the products of the resulting rst-order elds are used as source terms in
the time-averaged second-order equations, from which the net acoustic forces acting on the
particles are determined. The resulting acoustophoretic particle velocities are quantied
for experimentally relevant parameters using a numerical particle-tracking scheme. The
model shows the transition in the acoustophoretic particle motion from being dominated
by streaming-induced drag to being dominated by radiation forces as a function of particle
size, channel geometry, and material properties.
http://dx.doi.org/10.1039/c2lc40612h
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