Numerical Simulation of Acoustofluidic Manipulation by Radiation Forces and Acoustic Streaming ...

166 Pages·2015·12.85 MB·English

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Numerical Simulation Tools for
the Design and the Analysis of
Acoustofluidic Devices
Doctoral Thesis
Author(s):
Hahn, Philipp
Publication date:
2015
Permanent link:
https://doi.org/10.3929/ethz-a-010606727
Rights / license:
In Copyright - Non-Commercial Use Permitted
This page was generated automatically upon download from the ETH Zurich Research Collection.
For more information, please consult the Terms of use.
Diss. ETH No. 23041
Numerical Simulation Tools for the
Design and the Analysis of Acoustofluidic
Devices
A thesis submitted to attain the degree of
DOCTOR OF SCIENCE of ETH ZURICH
(Dr. sc. ETH Zurich)
presented by
PHILIPP HAHN
MSc., University of Wisconsin-Madison
born March 20, 1984
citizen of Germany
accepted on the recommendation of
Prof. Dr. Jürg Dual, examiner
Prof. Dr. Henrik Bruus, co-examiner
2015

Acknowledgements
The present work was carried out at the Institute of Mechanical Systems (IMES) at
ETH Zürich from 2010 to 2015. I would like to express my gratitude for valuable
contributions to this work and for the support I received:
• Prof. Dr. Jürg Dual, my supervisor, for his guidance and for the opportunity
to pursue this research project. I particularly appreciated the excellent work-
ing conditions at the institute and the academic freedom to explore the full
spectrum of theoretical, numerical, and experimental research.
• Prof. Dr. Henrik Bruus for kindly accepting to be my co-examiner, reviewing
my thesis, and supporting me with expert feedback.
• MyformeradvisorsProf. Dr. PeterEberhardfromtheUniversityofStuttgart,
Prof. Dan Negrut from the University of Wisconsin at Madison, and Dr.
Abhinandan Jain from JPL Caltech. I continue to benefit from everything I
learned from them.
• Ueli Marti and Jean Claude Tomasina for immediate solutions for all kinds of
electronic and mechanical problems.
• Allthestudentsthathavewrittenathesisundermysupervision. Inparticular,
I am happy that the numerical research in our group will be continued by
Thierry Baasch in his PhD project.
• Gabriela Squindo, Beate Fonfé, and Dr. Stephan Kaufmann for their excellent
administrative and IT support.
• Robert Ernst for the afternoon workout sessions.
• All my colleagues at the Center of Mechanics for the discussions over lunch
and the good time we had together.
Finally, I would like to thank my family and my friends for their support throughout
the whole time.
Philipp Hahn
Zurich, Juli 2015
iii

Contents
Abstract vii
Zusammenfassung ix
List of Symbols and Acronyms xiii
1. Introduction 1
1.1. Acoustofluidic particle manipulation . . . . . . . . . . . . . . . . . . . 1
1.1.1. A brief history of theoretical acoustofluidics . . . . . . . . . . 2
1.1.2. Alternative manipulation techniques . . . . . . . . . . . . . . 2
1.1.3. Applications of acoustofluidic particle manipulation . . . . . . 4
1.2. Overriding research question . . . . . . . . . . . . . . . . . . . . . . . 5
1.3. Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4. Numerical modeling of acoustofluidic processes . . . . . . . . . . . . . 9
1.4.1. Governing equations . . . . . . . . . . . . . . . . . . . . . . . 13
1.4.2. Device modeling . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4.3. Modeling of acoustic streaming . . . . . . . . . . . . . . . . . 21
1.4.4. Modeling of acoustic radiation forces . . . . . . . . . . . . . . 26
1.4.5. Numerical methods . . . . . . . . . . . . . . . . . . . . . . . . 33
2. A Numerically Efficient Damping Model for Acoustic Resonances in Mi-
crofluidic Cavities 35
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2. Damped device resonances . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.1. Basic device model . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.2. Quantification of losses in a device . . . . . . . . . . . . . . . 40
2.3. Damping mechanisms in the fluid cavity . . . . . . . . . . . . . . . . 44
2.3.1. Viscous damping in the bulk . . . . . . . . . . . . . . . . . . . 45
2.3.2. Thermal damping in the bulk . . . . . . . . . . . . . . . . . . 46
2.3.3. Viscous damping at the cavity walls . . . . . . . . . . . . . . . 46
2.3.4. Thermal damping at the cavity walls . . . . . . . . . . . . . . 48
2.3.5. Viscous damping due to suspended particles . . . . . . . . . . 50
2.3.6. Radiation losses . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.3.7. Other losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.4. Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.4.1. Validation for viscous damping at cavity walls . . . . . . . . . 56
2.4.2. Validation for thermal damping at cavity walls . . . . . . . . . 61
2.4.3. Validation for viscous damping due to suspended particles . . 62
2.5. Implementation of an efficient numerical device model . . . . . . . . . 65
v
Contents
2.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3. Modeling and Optimization of Acoustofluidic Micro-Devices 73
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.2. Modeling of acoustofluidic Devices . . . . . . . . . . . . . . . . . . . . 76
3.2.1. The Basic Device Model . . . . . . . . . . . . . . . . . . . . . 76
3.2.2. Advanced Modeling and Acoustic Streaming . . . . . . . . . . 78
3.2.3. Material Properties and Loss Mechanisms . . . . . . . . . . . 79
3.2.4. Remarks on the Numerical Implementation . . . . . . . . . . . 81
3.3. Device Design by Genetic Algorithm Optimization . . . . . . . . . . . 82
3.3.1. Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3.2. Parametrization of the Device . . . . . . . . . . . . . . . . . . 83
3.3.3. Objective Function . . . . . . . . . . . . . . . . . . . . . . . . 84
3.3.4. Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 84
3.4. Optimization Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.4.1. Optimization of a Planar Resonator . . . . . . . . . . . . . . . 85
3.4.2. Optimization of a 3D Micro-Device . . . . . . . . . . . . . . . 89
3.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4. NumericalSimulationofAcoustofluidicManipulationbyRadiationForces
and Acoustic Streaming for Complex Particles 95
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.2. Numerical model for the simulation of acoustofluidic particle motion . 99
4.2.1. Time-harmonic device model . . . . . . . . . . . . . . . . . . . 99
4.2.2. Acoustic streaming in the fluid cavity . . . . . . . . . . . . . . 102
4.2.3. Acoustic radiation forces and torques on complex particles . . 103
4.2.4. Time-averaged particle dynamics model . . . . . . . . . . . . . 104
4.3. Simulation results and discussion . . . . . . . . . . . . . . . . . . . . 107
4.3.1. Rotation of a glass micro-fiber . . . . . . . . . . . . . . . . . . 108
4.3.2. Trajectory of an alumina micro-disk in a 1D field . . . . . . . 109
4.3.3. Trajectory of a red blood cell in a realistic micro-device . . . . 115
4.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5. Conclusions and Outlook 119
A. Material parameters 123
B. Numerical expressions 125
References 129
Curriculum vitae 143
List of Publications 145
Journal publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Conference proceedings: talks and posters . . . . . . . . . . . . . . . . . . 146
Book contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
vi
Abstract
The research domain of acoustofluidics is concerned with the effects of acoustic
fields inside fluidic devices. The arising time-averaged phenomena called acoustic
streaming and acoustic radiation forces can be used to manipulate fluid-suspended
micro-particlesinacontactlessfashion. Ihasbeenshownthatacoustofluidicparticle
handling has some clear advantages over competing technologies like hydrodynamic,
dielectrophoretic, magnetophoretic, or optical manipulation strategies. Acoustoflu-
idic particle manipulation does not require specific electric, magnetic, or optical
particle properties and it is known for excellent cell viability when processing living
biological samples like cells, bacteria, or larger organisms. Massively parallel parti-
cle manipulation can be achieved easily because the acoustic force fields spread over
the volume of the fluid cavity, enabling the simultaneous manipulation of hundreds
or thousands of particles at a time. During the past years, a number of promis-
ing applications in the miniaturization of process steps in the life sciences has been
demonstrated by experimental acoustofluidic setups. In this context, miniaturiza-
tion is key for the development of novel products such as medical diagnostic rapid
tests since it allows to drastically reduce the sample size and the processing time.
Despite the significant economic potential of these applications, acoustofluidic de-
vices did not have their large-scale commercial break through yet. This is mainly
due to the fact that commercial process standards are challenging to meet in terms
of reliability, integrability, and efficiency.
Thecomplexityoftheunderlyingphysicsishighbecausetheinteractionsbetween
the piezo-electric transducer, the structural device design, the device support, and
the loading with different fluid-particle suspensions give rise to a large variety of
acoustofluidic effects. At first glance, most experimental setups look simple but
the interdependencies are too involved to be understood intuitively. This limits
the success of classical design approaches based on "design-experiment-redesign-
experiment-...". Due to the microscale of the device and the acoustofluidic effects,
experimental analysis techniques can also not provide sufficient insight to develop a
good sense of cause and effect. This is an important problem for both the analysis
of existing devices and the design of new devices. As the field of acoustofluidics is
moving toward commercial applications, the problem will become even more cru-
cial. An increased control over the device design and the acoustofluidic processes is
required to meet commercial standards. Numerical modeling can play a key role in
meeting theses goals.
In this thesis, the numerical modeling of acoustofluidic devices and processes is
reviewed and augmented to gain a more detailed understanding of acoustofluidic
devices, the underlying physical effects, and their interplay. A second goal is to
advance simulation models to a degree of accuracy that allows a quantitative pre-
vii
Abstract
diction of acoustofluidic manipulation processes and the use of automatic device
design strategies.
Damping limits the attainable acoustic amplitudes and acoustofluidic forces for
the particle manipulation but it is not easily included in a numerical device model.
In the acoustofluidic community, losses in the fluid are often approximated by an
empirically estimated loss factor. However in reality, the fluid cavity loss factor can
vary dramatically within a narrow frequency bandwidth because of its sensitivity on
the mode-specific boundary layer pattern at the cavity walls. To achieve a quantita-
tively accurate prediction of the acoustofluidic forces, a damping model including all
relevant acoustofluidic damping effects is developed. Semi-analytical expressions are
derived for the use in numerically efficient 3D simulations of realistic acoustofluidic
micro-devices.
In order to make a first step toward a more systematic and widely automatic
device design approach, the combination of numerical device simulation and opti-
mization routines is investigated. The discussion includes the mathematical formu-
lation of the optimization problem, the definition of a suitable objective function,
and the parameterization of the device design. Further, the implementation of the
optimization loop is addressed alongside with practical recommendations for the
chosen genetic algorithm optimization. The planar resonator with an established
set of optimal layer thicknesses serves as a validation example for the new device de-
sign strategy. The optimization of a typical 3D micro-device indicates that devices
can be designed to generate any physically feasible acoustic mode shape at maxi-
mum pressure amplitude. The presented automatic design approach can speed up
and facilitate the design-process of acoustofluidic micro-devices. It represents a step
toward the development of commercial level devices as optimal device performance
and integrability into other process steps can be achieved.
The numerical prediction of acoustofluidic particle motion is of great help for the
design, the analysis, and the physical understanding of acoustofluidic devices. It
also allows a simple and direct comparison with experimental observations. A 3D
trajectory simulation setup is presented to cover the full spectrum, comprising a
time-harmonic device model, an acoustic streaming model of the fluid cavity, a radi-
ation force simulation, and the calculation of the hydrodynamic drag. The acoustic
radiation forces and the hydrodynamic drag are calculated numerically to handle
particles of arbitrary shape, structure, and size. In this way, complex 3D particle
translation and rotation inside experimental micro-devices can be predicted. Differ-
ent applications of non-spherical particle manipulation are simulated and validated
against experimental observations. To demonstrate the full capability of the simula-
tion setup, the motion of a red blood cell inside a realistic micro-device is simulated
under the simultaneous effects of acoustic streaming and radiation forces.
viii
Zusammenfassung
Das Forschungsgebiet der Akustofluidik beschäftigt sich mit den physikalischen Ef-
fekten in flüssigkeitsgefüllten Kavitäten, welche durch akustische Felder hervorge-
rufen werden. Akustische Strahlungskräfte (acoustic radiation force) und akustisch
induzierteStrömungen(acousticstreaming)könnenzurManipulationvonMikropar-
tikeln in Flüssigkeiten genutzt werden. Gegenüber alternativen Technologien wie
Dielektrophorese, Magnetophorese, sowiehydrodynamischeroderoptischerPartikel-
manipulation, hat die akustofluidische Partikelmanipulation klare Vorteile. Im Ge-
gensatz zu den genannten Technologien ist die Anwendung der akustofluidischen
Partikelmanipulation nicht durch spezielle elektrische, magnetische oder optische
AnforderungenandiePartikelbeschaffenheitbeschränkt. InExperimentenmitleben-
den Proben wie Zellen, Bakterien oder größeren Organismen hat sich zudem gezeigt,
dasshervorragendeÜberlebensquotenerreichtwerdenkönnen. Dasichdiegenutzten
akustofluidischen Krafteffekte über das gesamte Fluidvolumen erstrecken, können
hunderte oder tausende Partikel gleichzeitig manipuliert werden können, was für
viele Anwendungen vorteilhaft ist. Mithilfe akustofluidischer Ansätze ist es in
den letzten Jahren gelungen eine Vielzahl biowissenschaftlicher Prozessschritte zu
miniaturisieren. Dadurch kann eine enorme Reduktion der Testvolumina und der
Prozesszeitenerzieltwerden, wasfürdieEntwicklungneuartigerGerätewiediagnos-
tischer Schnelltests für Medizinanwendungen von essenzieller Bedeutung ist. Trotz
demhohemwirtschaftlichenPotentialistesbislangjedochnochnichtgelungenkom-
mertiellen Anwendungen im großen Maßstab zu erschließen. Ein Hauptgrund dafür
ist die Schwierigkeit die hohen Anforderungen bezüglich Verlässlichkeit, Integrier-
barkeit und Effizienz zu erreichen.
Die meisten akustofluidischen Geräte erscheinen einfach. Die Komplexität der
zugrunde liegenden physikalischen Effekte ist jedoch sehr hoch weil das Zusam-
menspiel zwischen der piezoelektrischen Anregung, den Strukturkomponenten, der
Auflage und der Befüllung mit unterschiedlichen Fluid-Partikel Suspensionen eine
große Bandbreite akustofluidischer Effekte hervorruft. Zieht man zudem noch die
Abhängigkeit der Effekte von verschiedenen Parametern in Betracht, ist es meist
nicht mehr möglich ein intuitives Verständnis der Zusammenhänge zu erlangen. Der
ErfolgklassischerEntwicklungsstrategien, basierendaufdemPrinzip"Konstruktion-
Experiment-Anpassung-Experiment-..." wird dadurch stark begrenzt. Aufgrund ex-
trem kleiner Gerätedimensionen können auch experimentelle Analyse- und Messver-
fahren derzeit keinen hinreichend detaillierten Einblick in die physikalischen Vor-
gänge im Innern der Mikrokavität bieten. Ursache-Wirkungs-Zusammenhänge blei-
ben so schwer zu erkennen. Dies ist ein großes Problem für die Analyse bestehender
und die Konstruktion neuer Experimente, besonder dann, wenn kommerzielle An-
wendungenangestrebtwerden. EineverbesserteKontrolleüberdieakustofluidischen
Effekte und die Gerätekonstruktion ist erforderlich, um die erforderlichen Prozess-
ix