Appendix D
Paper published in Physical Review
E, October 2014
Numerical study of thermoviscous eects in ultrasound-induced
acoustic streaming in microchannels
Peter Barkholt Muller and Henrik Bruus
Abstract: We present a numerical study of thermoviscous eects on the acoustic streaming
ow generated by an ultrasound standing-wave resonance in a long straight microuidic
channel containing a Newtonian uid. These eects enter primarily through the temperature
and density dependence of the uid viscosity. The resulting magnitude of the streaming
ow is calculated and characterized numerically, and we nd that even for thin acoustic
boundary layers, the channel height aects the magnitude of the streaming ow. For the
special case of a suciently large channel height, we have successfully validated our numerics
with analytical results from 2011 by Rednikov and Sadhal for a single planar wall. We
analyzed the time-averaged energy transport in the system and the time-averaged secondorder
temperature perturbation of the uid. Finally, we have made three main changes in
our previously published numerical scheme to improve the numerical performance: (i) The
time-averaged products of rst-order variables in the time-averaged second-order equations
have been recast as ux densities instead of as body forces. (ii) The order of the
nite-element basis functions has been increased in an optimal manner. (iii) Based on the
International Association for the Properties of Water and Steam (IAPWS 1995, 2008, and
2011), we provide accurate polynomial ts in temperature for all relevant thermodynamic
and transport parameters of water in the temperature range from 10 to 50 C.
http://dx.doi.org/10.1103/PhysRevE.90.043016
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