1.4. ACOUSTOFLUIDICS 5
Figure 1.3: (a) Sketch of an acoustophoresis microchip, adopted from the PhD-thesis by Rune Barnkob
Ref. 32. (b) Image of an acoustophoresis microchip, adopted from Augustsson et al. Ref. 25.
cal trapping 27. Figure 1.3 shows a sketch and an image of an acoustophoresis chip with
a long straight microchannel with a rectangular cross section. This is the channel we have
been modeling in the theoretical work presented in Refs. 28, 11, 29, 30 Appendixes A, B,
D, and E, and this chip was used for the experimental study in Ref. 11 Appendix B. In
Ref. 31 Appendix C a microchannel with a nearly-square cross section was used.
There are two approaches to numerical modeling of acoustic streaming in microchannels.
(i) The boundary layer approach, in which the acoustic boundary layers are resolved
and the acoustic elds and streaming ow are solved directly from the governing equations
and a set of physical boundary conditions. (ii) The eective slip velocity approach, in
which the acoustic boundary layers are not resolved, but instead the analytical eective
slip velocity expression is used for the boundary condition for the streaming ow. The
advantages of the boundary layer approach is that it correctly predicts the acoustic damping
and gives insight into the physics of the acoustic boundary layer and the generation
of the acoustic streaming ow. The eective slip velocity approach, on the other hand,
requires much less computational eort and thus allows for analysis of streaming ows in
more complicated three-dimensional systems.
The boundary layer approach was employed by Muller et al. to study the boundary
layers of the the acoustic elds and the cross-over between radiation force and streaminginduced
drag force dominated particle motion 28 Appendix A, the inuence of viscosity
perturbation on the acoustic streaming and transport of thermal energy in acoustophoresis
systems 29 Appendix D, as well as the time-dependent build-up of the acoustic resonance
and the streaming ow 30 Appendix E, all for bulk acoustic wave generation in a siliconglass
microuidic chip. A similar study was done by Nama et al. 33, in which the acoustic
resonance and particle motion was studied for a PDMS channel exited by surface acoustic
waves.
The eective slip velocity approach has successfully been employed by Lei et al. 34, 35
to study the acoustic streaming in three-dimensional problems and streaming ows in the