2 CHAPTER 1. INTRODUCTION
Bulk-driven acoustic streaming Boundary-driven acoustic streaming
(a) (b)
Figure 1.1: (a) Sketch of bulk-driven acoustic streaming in a rectangular uid chamber. The acoustic
traveling wave (magenta) is generated by the vibrating transducer (black lled rectangle to the left) and
absorbed in the uid (blue). The absorption of acoustic momentum leads to a force on the uid in
the direction of propagation of the acoustic wave, generating a steady ow (green arrows) in the uid
chamber. This type of streaming is also referred to as Eckart streaming. (b) Sketch of boundary-driven
acoustic streaming in the vertical cross section of a microchannel. The magenta lines represent a standing
acoustic wave, with a pressure node in the center of the channel and pressure anti-nodes at the sidewalls.
The non-linear interactions of the oscillating acoustic wave inside the boundary layers (dark blue) generate
a steady rotational ow (green arrows) in the bulk of the uid (light blue). This type of streaming is also
referred to as Rayleigh streaming.
1.2 Acoustophoresis
Particles in an acoustic wave experience a force due to scattering of the acoustic wave
on the particle, known as the acoustic radiation force Frad. In the case of a standing
acoustic wave, the radiation force pushes acoustically hard particles towards the nodal
points of the pressure oscillations, whereas acoustically soft particles are pushed towards
the antinodal points. The hardness of a particle is determined by the relative density
and compressibility of the particle and the suspending uid. By default we assume the
particles to be hard and focused at the pressure node, which is the case for most relevant
particles and biological cells. Furthermore, besides gravitation and buoyancy, which we
will disregard, the particles also experience a drag force Fdrag from the acoustic streaming
ow generated by the acoustic wave. The relative magnitude of the drag force and the
radiation force depends largely on the particle size. The motion of large particles are
dominated by the radiation force and focused at the pressure node, whereas small particles
are dominated by the streaming-induced drag force and follow the rotational motion of the
streaming ow. This is sketched in Fig. 1.2, where the directions and relative magnitudes
of the drag force and the radiation force are shown on a large and a small particle in a
standing acoustic wave.
1.3 Historic review
The theory of acoustic streaming was initially developed by Lord Rayleigh in 1884 3,
inspired by the observations of particle motion generated by a standing sound wave in