4.1. CRITICAL PARTICLE SIZE 41
4.1 Critical particle size
The motion of the suspended particles are determined by the interplay between Frad and
Fdrag Eq. (4.2). Due to the dierence in the dependence on the particle size of the two
forces, the motion of suspended particles is largely determined by their size. The magnitude
of the acoustic streaming Eq. (3.27) can be expressed as
v2
= v2
a
cs
= 4 Eac
0cs
, where
is a factor of order unity, that depends primarily on the position of the particle in the
channel and also the thermodynamic state of the uid. Balancing the magnitude of the
two forces
Frad
=
Fdrag
for a xed particle,
u
= 0, yields
4a2c
= 24
0! )
2ac =
s
24
0!
=
r
12
s; (4.9)
where ac is the critical particle radius at which the magnitude of the two forces are equal.
In Eq. (4.9) the channel geometry enters through , particle and liquid material parameters
enters through , and liquid parameters and frequency through s. For polystyrene
particles in water at 2 MHz, the critical particle size ac is around 2 µm. Larger particles
are dominated by the acoustic radiation force and focused at the pressure nodes, whereas
smaller particles are dominated by the streaming-induced drag force and follow the rotational
motion of the uid. The transition in particle motion from radiation domination to
streaming domination is studied in Ref. 28 Appendix A.
This concludes the treatment of the forces acting on suspended particles in acoustouidic
systems. The acoustic streaming ow counteracts acoustophoretic focusing of particles
below the critical particle limit, such as bacteria or proteins. One of the main goals of this
thesis work has been to nd ways to overcome this limitation. This was achieved in Ref.
31 Appendix C by utilizing overlapping resonances of a nearly-square channel to create
a single roll streaming ow, that did not counteract the acoustophoretic focusing by the
weak radiation force.