Chapter 4
Acoustouidic forces on particles
In this chapter we describe the forces acting on a particle suspended in a water-lled
microchannel and in the presence of an acoustic eld. The treatment is partly based on
the analytical study of the acoustic radiation force presented by Karlsen and Bruus Ref.
16. The particle is dened by its volume
(t), its surface @
(t), the outward-pointing
surface normal vector n(r; t), and the velocity of its center of mass u(t), which all depend
on time due to the acoustic oscillations of the particle. The total force on the particle is
given by the stress on the particle surface, exerted by the surrounding uid, and the body
force densities f acting on the particle volume,
m
du
dt
=
I
@
(t)
n dA +
Z
(t)
f dV: (4.1)
In the following, we neglect the gravitational body force on the particle and the buoyancy
contribution to the surface stress from the hydrostatic pressure. This is reasonable for
most studies of microparticles in water, as the sedimentation time is much longer than
other relevant timescales, such as focusing time. It is customary to further separate the
surface force into two parts: the radiation force Frad originating from the stress exerted
directly by the acoustic wave, and the drag force Fdrag originating from the stress exerted
by an external ow,
m
du
dt
= Fdrag + Frad: (4.2)
Frad represents the force from scattering of an acoustic wave on a particle in an innite,
initially quiescent uid domain, thus also including the eects of streaming ow generated
at the particle surface. Fdrag represents the eects of a nite domain, and assuming an
initially quiescent state of the uid, Fdrag is given by the Stokes drag force induced by the
acoustic streaming ow generated at the boundaries of the nite water domain.
We dene the acoustic radiation force by
Frad =
I
@
(t)
��
�� ext
n dA; (4.3)
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