Chapter 1
Introduction
This chapter presents a short description of the physical phenomena treated in this thesis
along with a historic review of the development of the theoretical framework. It is a
selection of studies that I nd important for the basis and context of my thesis work, and
by no means an exhaustive treatment. For a wider scope, the reader is referred to the
tutorial series on acoustouidics in Lab on a Chip 1 and the review article by Riley 2.
1.1 Acoustic streaming
Acoustic streaming is a steady uid ow generated by an oscillating acoustic eld. The
magnitude of the steady streaming ow is usually much smaller than the amplitude of
the oscillating velocity eld. Acoustic streaming can be categorized by its generating
mechanism into bulk-driven streaming and boundary-driven streaming, both illustrated in
Fig. 1.1. Bulk-driven streaming originates from the bulk absorption of acoustic momentum,
which result in a steady velocity in the direction of propagation of the acoustic wave. This
is observed for traveling acoustic waves in congurations where the spatial dimension of the
uid domain is comparable to or longer than the absorption length of the acoustic wave.
Boundary-driven streaming originates from the viscous stresses present in a thin region
close to boundaries, known as the acoustic boundary layer, where the amplitude of the
acoustic velocity oscillations has to transition from its bulk value to zero at the wall. Due
to nonlinearity, the viscous stresses inside the acoustic boundary layer generate a steady
velocity parallel to the wall, which drives a steady ow in the bulk of the uid. The spatial
periodicity of the steady velocity is twice that of the acoustic wave. For a rectangular
channel cross section with a standing wave parallel to the top and bottom walls, as sketched
in Fig. 1.1(b), we thus get four bulk ow rolls for each half acoustic wavelength. Bulk-driven
streaming is also referred to as Eckart streaming, whereas boundary-driven streaming is
also referred to as Rayleigh streaming in the bulk of the uid and Schlichting streaming
inside the boundary layers. In this thesis, only boundary-driven streaming is studied. Bulk
absorption is included in the theoretical models, but it has a negligible eect, because the
length scales of the uid domains are much shorter than the absorption length.
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