6.2. NUMERICAL MODELING OF ACOUSTIC STREAMING 53
6.2 Numerical modeling of acoustic streaming
The eld of acoustouidics was, and still is, very experimentally driven, and in many cases
it had become clear that a better understanding of the underlying physics was necessary
to progress even further. This need was addressed by the numerical model presented in
Ref. 28 Appendix A. The purposed of the model was to give a better insight into the
physical mechanisms of the acoustic resonance and the generation of the acoustic streaming
ow. The model solved the nonlinear acoustics using a perturbation expansion in the small
amplitude of the acoustic eld. The resonant acoustic eld was generated directly by an
oscillating velocity boundary condition, and the model resolved the thin acoustic boundary
layer at the walls. Consequently, the model was a very exible tool to investigate the physics
of acoustic streaming generation and it avoided the use of the analytical eective slip
velocity approximation. The resolution of the boundary layers enabled accurate estimations
of loss factors and detailed information about how the streaming ow was generated inside
these thin layers. However, the model was computationally heavy and further optimization
of the numerical scheme was needed.
This was addressed in Ref. 29 Appendix D, where the numerical scheme was optimized
for computational eciency. Furthermore, perturbations in the dynamic viscosity of
the uid, due to the oscillating perturbations of the temperature and the density, was included,
to provide even better comparison between the numerical model and experimental
studies. The model in Ref. 29 Appendix D also incorporated an automatic calculation
of the material parameters of water and their temperature and density derivatives. These
parameter values where based on the studies made by the International Association for
the Properties of Water and Steam (IAPWS). The IAPWS data is a collection of many
experimental studies, based on which the equation of state for water is tted using a function
with 56 parameters and covering the range T 1273:15 K and p 1000 MPa. The
formulation of this massive result is very complex, and we wanted to transform this into
something that was easy to implement in a numerical model. Ref. 29 Appendix D presented
polynomial ts, based on the IAPWS data, of all parameters and their derivatives
relevant for acoustouidic applications in the temperature range from 10 C to 50 C. This
was an important part of making the numerical model exible towards predicting outcomes
of acoustouidic experiments with various operating conditions. Furthermore, it ensured
high precision on all input parameters, which is necessary for quantitative comparison
between theory and experiment.
The main purpose of the numerical model was to enable comparison to experimental
measurements and to analytical calculations, however, it resulted in several other advantages.
Because the model gave direct access to the generating mechanism of the acoustic
streaming, it strengthened the understanding and intuition of the physics of acoustic
streaming. Furthermore, it was a tool to create a visual interpretation of the physics of
acoustic resonances and acoustic streaming, which was missing in many previous theoretical
studies, and which was necessary to reach out to an experimentally driven community.