Chapter 6
Streaming studies
This chapter presents an extended conclusion on this thesis work by summarizing the main
results of the ve journal papers and discussing their relations to each other and to the
eld of acoustouidics. The studies are not treated chronologically but rather in a way to
address relevant topics, for which some are addressed in more than one of the papers.
6.1 Analytical streaming calculations
As mentioned in Chapter 1 there have been many analytical studies of acoustic streaming
through out the last hundred years. However, there was a gap between the analytical
studies and the experimental systems that were used in the acoustouidic community. Most
theoretical studies treat very thin channel cross sections, i.e. low aspect ratio h=w 1,
because it is theoretically easier and it is relevant for applications within the eld of
thermoacoustic engines. In acoustouidic applications, the aspect ratio is typically in the
range from 0.2 to 1. This issue was addressed in ref. 11 Appendix B, in which an analytical
calculation of the acoustic streaming is presented, valid for arbitrarily large aspect ratios.
Furthermore, the eects of the sidewalls on the streaming ow was taking into account by
introducing a no-slip condition on the sides, that resulted in a retardation of the streaming
ow. This was in contrast to previous analytical studies, which treated the channel cross
section as innite parallel plates, thus not taken into account the eect of the sidewalls,
which is only a good approximation for low aspect ratio channels. These extensions brought
the analytical model closer to the experimental systems and enabled direct comparison
between theoretical predictions and experimental measurements of acoustouidic systems,
which was not possible before.
In acoustouidic experiments the most convenient way to measure the magnitude of
the acoustic streaming ow is to measure the velocity of small particles in the horizontal
center plane of the channel, z = 0 in Fig. 6.1. The streaming ow rolls are generated at
the top and bottom walls and have a nite extend in the vertical direction. Thus for a tall
channel the magnitude of the streaming ow decays towards the center of the channel, as
shown in Fig. 6.1(a). The streaming ow for higher-order resonance have a higher spatial
frequency in the horizontal direction and thus also a faster decay from the top and bottom
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