Appendix E
Paper submitted to Physical Review
E, September 2015
A theoretical study of time-dependent, ultrasound-induced acous-
tic streaming in microchannels
Peter Barkholt Muller and Henrik Bruus
Abstract: Based on rst- and second-order perturbation theory, we present a numerical
study of the temporal build-up and decay of unsteady acoustic elds and acoustic streaming
ows actuated by vibrating walls in the transverse cross-sectional plane of a long straight
microchannel under adiabatic conditions and assuming temperature-independent material
parameters. The unsteady streaming ow is obtained by averaging the time-dependent
velocity eld over one oscillation period, and as time increases, it is shown to converge
towards the well-known steady time-averaged solution calculated in the frequency domain.
Scaling analysis reveals that the acoustic resonance builds up much faster than the acoustic
streaming, implying that the radiation force may dominate over the drag force from streaming
even for small particles. However, our numerical time-dependent analysis indicates that
pulsed actuation does not reduce streaming signicantly due to its slow decay. Our analysis
also shows that for an acoustic resonance with a quality factor Q, the amplitude of the
oscillating second-order velocity component is Q times larger than the usual second-order
steady time-averaged velocity component. Consequently, the well-known criterion v1 cs
for the validity of the perturbation expansion is replaced by the more restrictive criterion
v1 cs=Q. Our numerical model is available in the supplemental material in the form of
Comsol model les and Matlab scripts.
http://arxiv.org/abs/1509.02554v1
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