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Cite this: Lab Chip, 2012, 12, 4617–4627
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A numerical study of microparticle acoustophoresis driven by acoustic
radiation forces and streaming-induced drag forces
Peter Barkholt Muller,a Rune Barnkob,b Mads Jakob Herring Jensenc and Henrik Bruus*a
Received 28th May 2012, Accepted 18th July 2012
DOI: 10.1039/c2lc40612h
We present a numerical study of the transient acoustophoretic motion of microparticles suspended in
a liquid-filled 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 flow. These forces are calculated
numerically in two steps. First, the thermoacoustic equations are solved to first order in the imposed
ultrasound field taking into account the micrometer-thin but crucial thermoviscous boundary layer
near the rigid walls. Second, the products of the resulting first-order fields 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 quantified 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.
I Introduction
In the past decade there has been a markedly increasing interest
in applying ultrasound acoustofluidics as a tool for purely
mechanical and label-free manipulation of particle and cell
suspensions in MEMS and biologically oriented lab-on-a-chip
systems. Recent extended reviews of acoustofluidics can be
found in Review of Modern Physics1 and the tutorial series in Lab
on a Chip2 which, among other topics, treats the application of
ultrasound bulk3 and surface4 acoustic waves as well as acoustic
forces on particles from acoustic radiation5 and from streaminginduced
drag.6
When a standing ultrasound wave is established in a
microchannel containing a microparticle suspension, the particles
are subject to two acoustic forces: the acoustic radiation
force from the scattering of sound waves on the particles, and the
Stokes drag force from the induced acoustic streaming flow. The
resulting motion of a given particle is termed acoustophoresis,
migration by sound. Experimental work on acoustophoresis has
mainly dealt with the radiation force, primarily because this
force dominates over the streaming-induced drag force for the
studied aqueous suspensions of polymer particles or biological
cells with diameters larger than 2 mm. Detailed measurements of
the acoustophoretic motion of large 5 mm diameter polystyrene
particles in water7,8 have shown good agreement with the
theoretical predictions9,10 for the radiation force on compressible
particles with a radius a much smaller than the acoustic
wavelength l and neglecting the viscosity of the suspending fluid.
However, as the particle diameter 2a is reduced below 2 mm,
viscous effects are expected to become significant, because this
length corresponds to a few times the viscous penetration depth
or boundary-layer thickness d. Analytical expressions for the
viscous corrections to the radiation force valid in the experimentally
relevant limit of long wavelength l, characterized by a
%l and d %l, have been given recently,11 but have not yet been
tested experimentally. In addition to these modifications of the
radiation force, the acoustic streaming flow induced by viscous
stresses in the boundary layers near rigid walls, and depending
critically on the detailed geometry and boundary conditions, also
significantly influences the acoustophoretic particle motion as
the size of the particle or the confining microchannel is
reduced.12,13 The cross-over from radiation-dominated to
streaming-dominated motion has been observed in experiments,
14,15 and a scaling analysis of the critical particle diameter
for this cross-over has been provided in the literature16 and will
be restated in Section IV D.
Although acoustic streaming is a well-known phenomenon in
acoustics, it is pointed out in a recent review6 that streaming is
often misunderstood outside the relatively small circles of
acoustics experts due to the many forms in which it may arise
in, e.g., acoustofluidic microsystems. Not only is acoustic
streaming difficult to predict quantitatively due to its sensitivity
aDepartment of Physics, Technical University of Denmark, DTU Physics
Building 309, DK-2800 Kongens Lyngby, Denmark.
E-mail: bruus@fysik.dtu.dk
bDepartment of Micro- and Nanotechnology, Technical University of
Denmark, DTU Nanotech Building 345 East, DK-2800 Kongens Lyngby,
Denmark
cCOMSOL A/S, Diplomvej 373, DK-2800 Kongens Lyngby, Denmark
This journal is The Royal Society of Chemistry 2012 Lab Chip, 2012, 12, 4617–4627 | 4617
Downloaded by DTU Library on 27 February 2013
Published on 23 July 2012 on http://pubs.rsc.org | doi:10.1039/C2LC40612H
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