4 CHAPTER 1. INTRODUCTION
a gaslled tube, known as Kundt's tube, by Kundt in 1866 4. Lord Rayleigh derived
the framework for how a standing sound wave parallel to a wall can generate a steady
streaming ow. In 1932 Sclichting 5 revised Rayleigh's theory and described the presence
of ow rolls inside the boundary layer, which where responsible for driving the bulk ow.
Nyborg presented in 1958 6 a general treatment of the steady velocity generated along
an arbitrary smooth wall, thus not limited to a planar wall, in terms of the bulk acoustic
amplitude near the wall and the curvature of the wall. This theory was applicable to a
wide range of streaming phenomena, and was later extended by Lee and Wang in 1989
7 and by Rednikov and Sadhal in 2011 8, and was referred to as the limiting velocity
method.
The viscosity of the uid plays a key role in the generation of acoustic streaming.
Since the viscosity is dependent on the thermodynamic state of the uid it will be slightly
perturbed by the acoustic density and temperature oscillations, and in studies by Hamilton
et al. 9 and Rednikov and Sadhal 8, this was shown to have signicant inuence on the
magnitude of the acoustic streaming.
Lord Rayleigh's treatment of the boundary-driven acoustic streaming in a parallel plate
channel is only valid for channels where the height of the channel h is much larger than
the boundary layer thickness and much smaller than the acoustic wavelength , i.e.
h . These limitation of the theory was later solved when new applications of
standing acoustic waves presented a need for it. Hamilton et al. 10 derived the solution
for arbitrarily thin channels h , relevant for applications within thermoacoustic
engines, whereas Muller et al. 11 Appendix B derived the solution for arbitrarily tall
channels h , relevant for applications within microchannel acoustophoresis.
The acoustic radiation force had been observed in Kundt's tube in the nineteenth
century but was not explained theoretically until 1934 by King 12. The particle agglomeration
at pressure nodes was similar to the observed agglomeration of particle on
vibrating Cladni plates, at the points of least vibration. King's treatment was limited to
an incompressible spherical particle in an inviscid uid, and this was later extended to a
compressible particle in an inviscid uid by Yosioka and Kawasima 13 and Gorkov 14.
The eect of the viscous and thermal boundary layers around the particle was included in
the theory by Settnes and Bruus 15, respectively, Karlsen and Bruus 16.
1.4 Acoustouidics
The term acoustoudics refer to applications of acoustic pressure elds in microuidic
systems 17 and spans a wide range of applications involving manipulation of uids and
suspended particles, such as cell enrichment 18, separation of fat particles from blood 19,
raw milk quality control 20, particle trapping using seed particles 21, mixing of cells and
nutrients in multi-well plates 22, and acoustouidic pumping using sharp channel edges
23. A great eort has also been put into making experimental tools and measurements to
test the theoretical hypotheses, such as investigation of channel resonances and radiation
force dominated particle motion 24, 25, measurements of streaming dominated particle
motion 26, 11, and direct measurements of acoustophoretic forces on particles using opti