Development of an automated and scalable lab-on-a … of impedance-based drop sensing techniques...
Transcript of Development of an automated and scalable lab-on-a … of impedance-based drop sensing techniques...
Development of an automated and scalable lab-on-a-chip
platform with on-chip characterization
by
Ryan Fobel
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy – Biomedical Engineering
Institute of Biomaterials and Biomedical Engineering
University of Toronto
© Copyright by Ryan Fobel (2016)
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Development of an automated and scalable lab-on-a-chip platform with on-chip characterization
Ryan Fobel
Doctor of Philosophy – Biomedical Engineering
Institute of Biomaterials and Biomedical Engineering
University of Toronto
2016
Abstract
Digital Microfluidics (DMF) is a fluid-handling technique that enables precise control of
drops on an array of electrodes using electrostatic forces. In contrast to most other lab-on-a-
chip technologies (e.g., channel-based microfluidics), DMF is highly reconfigurable (i.e.,
function is defined by software and not by the physical structure of the chips). Thus, DMF
offers the possibility for a truly general-purpose lab-on-a-chip platform, where a wide variety
of biological and chemical protocols may be implemented at the microscale, under
automated control, and on a generic chip. Widespread adoption of this technology has thus
far been limited by: (1) lack of access to control hardware/software, (2) the high-cost and
specialized equipment required for fabricating DMF chips, (3) an incomplete understanding
of DMF device physics, and (4) lack of methods for performing on-chip characterization.
This thesis aims to address these limitations. We describe the development of a control
instrument and software capable of applying a precise electrostatic force and measuring
device capacitance, drop position, and drop velocity on-chip. We also demonstrate a low-cost
method for fabricating DMF devices that does not require a cleanroom facility: inkjet
printing of silver electrodes on paper. We present new on-chip methods for characterizing the
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resistive forces that oppose drop movement on DMF and report the results from an initial
screen of conditions, establishing the effects of surface tension, conductivity, viscosity,
protein content, and driving frequency on resistive forces. Finally, we demonstrate an
extension of impedance-based drop sensing techniques (e.g., device capacitance, drop
position, and drop velocity) to facilitate measurement across multiple electrodes in parallel.
In combination, these advancements represent significant progress toward the goal of
establishing a general-purpose lab-on-a-chip platform that is accessible to the wider
biomedical and chemical research communities.
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In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.
– Richard Hamming
Measurement is the first step that leads to control and eventually to improvement.
If you can’t measure something, you can’t understand it.
If you can’t understand it, you can’t control it.
If you can’t control it, you can’t improve it.
– H. James Harrington
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Acknowledgments
This thesis was made possible by the support of many people. I would like to express my
sincere gratitude to Professor Aaron Wheeler for his supervision and guidance. He is an
excellent scientific role model and provided a stimulating research environment where I felt
free to explore; I looked forward to going to the lab every day. Aaron is an exceptional
communicator and he taught me a great deal about the art of scientific writing.
I would also like to thank my supervisory committee members, Professors Ramin
Farnood and Kevin Truong, for their thoughtful feedback and guidance over the years,
Professor Edgar Acosta for agreeing to act as my internal-external reviewer and Professor
Frieder Mugele for serving as my external examiner and offering his expertise.
I am grateful to have had the pleasure of working with so many bright and talented
lab members: Alphonsus Ng, ever generous with his time and expertise, and one of the most
competent and nicest people that I know; Sam Au, for his sharp mind and countless thought-
provoking debates (both scientific and otherwise) and for letting me beat him at squash once
in a while; Steve Shih, for showing me the ropes early on; Ian Swyer, for not being afraid of
equations and for helpful comments on Chapter 4; Edward Sykes, for supporting me with my
robot building addiction; Andrea Kirby, Christopher Dixon, and Stephen Ho, for continuing
to find new and interesting uses for inkjet printers; and to the rest of the Wheeler lab, thanks
for making it a great place to work: Sara Abdulwahab, Irena Barbulovic-Nad, Dario Bogevic,
Dean Chamberlain, Alex Chebotarev, Kihwan Choi, Michael Dryden, Irwin Eydelnant,
Lindsey Fiddes, Yan Gao, Lorenzo Gutierrez, Mais Jebrail, Jihye Kim, Nelson Lafreniere,
Charis Lam, Betty Li, Vivienne Luk, Jared Mudrik, Nauman Mufti, Darius Rackus, Mahesh
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Sarvothaman, Brendon Seale, Motashim Shamsi, Haozhong Situ, Suthan Srigunapalan,
Uvaraj Uddayasankar, Michael Watson, Jeremy Wong, Hao Yang, and Yue Yu.
I want to thank my brother Christian Fobel, who joined the lab as a research associate
partway through my studies, for being my partner in crime and for helping to build
something that we can both be proud of. He’s shaped the way that I think about
programming and design, and has almost certainly shortened my graduation time by at least a
year by removing distractions from my plate. I am also grateful to my parents, Richard and
Maribeth, for their boundless support, generosity, and encouragement. They have always
been my number one cheerleaders.
During the course of my studies, I became a father to two beautiful bundles of joy,
Zidra and James. To the two of you, thanks for always putting a smile on my face and for
teaching me what is most important in life.
Finally, I want to thank the love of my life and my best friend, Aislinn. Being married
to a Ph.D. student cannot be easy, especially when raising two young children, but she has
been incredibly supportive and has pulled lots of extra weight around the house, especially
during the writing of this thesis. She claims that she wouldn’t understand a word of this
thesis, but she certainly contributed a great deal to it. Graduate school may not be the road to
riches, but she has always encouraged me to follow my passion and hasn’t complained
(much). She inspires me every day to want to be a better person.
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Table of Contents
Acknowledgments .......................................................................................................................ii
Table of Contents ......................................................................................................................vii
List of Figures ............................................................................................................................. x
List of Tables ............................................................................................................................xii
List of Equations ..................................................................................................................... xiii
List of Abbreviations ............................................................................................................... xiv
Overview of Chapters ............................................................................................................... xv
Overview of Author Contributions .........................................................................................xvii
Chapter 1: Introduction ............................................................................................................... 1
Chapter 2: Automated Control and On-Chip Characterization ................................................... 5
2.1 Introduction ................................................................................................................... 5
2.2 Results and discussion .................................................................................................. 7
2.2.1 System overview ...................................................................................................... 7
2.2.2 Impedance and amplifier output .............................................................................. 8
2.2.3 Velocity measurement ........................................................................................... 13
2.2.4 Amplifier-gain compensation ................................................................................ 15
2.2.5 Force normalization ............................................................................................... 18
2.3 Conclusion .................................................................................................................. 19
2.4 Experimental ............................................................................................................... 20
2.4.1 Reagents and materials .......................................................................................... 20
2.4.2 DMF device fabrication ......................................................................................... 20
2.4.3 DropBot hardware and software ............................................................................ 21
2.4.4 Calibration for parasitic capacitance ..................................................................... 22
2.4.5 Velocity experiments ............................................................................................. 23
2.4.6 Amplifier-loading effects....................................................................................... 24
2.4.7 Force normalization experiments .......................................................................... 25
Chapter 3: Inkjet-printed DMF on Paper .................................................................................. 26
3.1 Introduction ................................................................................................................. 26
3.2 Results and discussion ................................................................................................ 28
3.2.1 Printing resolution and conductivity ...................................................................... 28
3.2.2 Surface topology .................................................................................................... 30
3.2.3 Cost and printing time ........................................................................................... 32
3.2.4 Homogeneous chemiluminescence assay .............................................................. 33
3.2.5 Rubella IgG sandwich ELISA ............................................................................... 35
3.3 Conclusion .................................................................................................................. 37
3.4 Experimental ............................................................................................................... 37
3.4.1 Reagents and materials .......................................................................................... 37
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3.4.2 DMF device fabrication, characterization, and operation ..................................... 38
3.4.3 Homogeneous chemiluminescence assay .............................................................. 41
3.4.4 Rubella IgG immunoassay ..................................................................................... 41
Chapter 4: Quantitative Characterization of Resistive Forces .................................................. 43
4.1 Introduction ................................................................................................................. 43
4.2 Background and theory ............................................................................................... 45
4.2.1 Dynamics of drop motion ...................................................................................... 45
4.2.2 Electrostatic force .................................................................................................. 48
4.2.3 Threshold force ...................................................................................................... 50
4.2.4 Dynamic friction .................................................................................................... 50
4.2.5 Saturation ............................................................................................................... 54
4.2.6 Frequency effects ................................................................................................... 56
4.2.7 Proteins .................................................................................................................. 58
4.3 Results and discussion ................................................................................................ 58
4.3.1 Simulations of drop dynamics ............................................................................... 58
4.3.2 Benchmarking and calibration of impedance and velocity measurements ............ 63
4.3.3 Characterization of non-protein-containing liquids ............................................... 67
4.3.4 Characterization of protein-containing liquids ...................................................... 77
4.4 Conclusion .................................................................................................................. 84
4.5 Experimental ............................................................................................................... 86
4.5.1 Reagents and Materials .......................................................................................... 86
4.5.2 Simulations of drop dynamics ............................................................................... 86
4.5.3 Benchmarking and calibration of impedance and velocity measurements ............ 87
4.5.4 Characterization of non-protein-containing liquids ............................................... 89
4.5.5 Characterization of protein-containing liquids ...................................................... 91
Chapter 5: Multi-electrode Impedance Sensing ........................................................................ 93
5.1 Introduction ................................................................................................................. 93
5.2 Background and theory ............................................................................................... 96
5.3 Results and discussion .............................................................................................. 100
5.3.1 Effect of window length and duty cycle .............................................................. 100
5.3.2 Scalability ............................................................................................................ 103
5.3.3 Experimental demonstration of parallel sensing for translating drops ................ 106
5.3.4 Three-channel splitting simulation ...................................................................... 109
5.4 Conclusion ................................................................................................................ 111
5.5 Experimental ............................................................................................................. 112
5.5.1 Reagents and materials ........................................................................................ 112
5.5.2 Hardware and firmware modifications ................................................................ 112
5.5.3 Benchmarking of impedance measurements ....................................................... 113
5.5.4 Velocity versus duty cycle measurements ........................................................... 114
5.5.5 Noise-scaling simulation ..................................................................................... 114
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5.5.6 Experimental demonstration of parallel sensing for translating drops ................ 115
5.5.7 Three-channel splitting simulation ...................................................................... 115
Chapter 6: Conclusion and Future Directions ......................................................................... 117
6.1 Conclusion ................................................................................................................ 117
6.2 Future directions ....................................................................................................... 120
6.2.1 Hardware.............................................................................................................. 120
6.2.2 Devices ................................................................................................................ 121
6.2.3 High-level programming ..................................................................................... 122
6.2.4 Applications ......................................................................................................... 123
References ............................................................................................................................... 125
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List of Figures
Figure 2.1. The DropBot DMF automation system .................................................................... 9
Figure 2.2. Impedance and amplifier output measurement ...................................................... 12
Figure 2.3. Drop velocity measurements .................................................................................. 15
Figure 2.4. Amplifier-gain compensation ................................................................................ 17
Figure 2.5. Normalizing actuation voltage by electrostatic force ............................................ 19
Figure 3.1. Characterization of printing resolution and conductivity ...................................... 29
Figure 3.2. Surface topology and drop velocity ....................................................................... 32
Figure 3.3. Homogeneous chemiluminescence assay generated on a paper DMF device
though on-chip serial dilution of HRP mixed with luminol/H2O2 ......................... 34
Figure 3.4. Rubella IgG immunoassay performed on a paper DMF device with a
luminol/H2O2 chemiluminescent readout............................................................... 36
Figure 3.4. Rubella IgG immunoassay performed on a paper DMF device with a
luminol/H2O2 chemiluminescent readout............................................................... 40
Figure 4.1. DMF drop actuation – driving and resistive forces................................................ 60
Figure 4.2. Simulated behavior of a drop of PBS as it moves onto an actuated electrode
and magnitude of driving and resistive forces ....................................................... 62
Figure 4.3. Test board and results for the impedance measurement circuit ............................. 64
Figure 4.4. Estimation of drop velocity from capacitance measurements ............................... 65
Figure 4.5. Comparison of filter-types for drop velocity data .................................................. 67
Figure 4.6. Velocity-force characterization for a non-protein containing solution .................. 68
Figure 4.7. Threshold forces, saturation forces, and dynamic friction coefficients for
various liquids experimentally determined from velocity-force curves ................ 71
Figure 4.8. Viscous and contact line friction contributions to experimentally measured
dynamic friction coefficients (assuming Poiseuille flow)...................................... 75
Figure 4.9. Net force at saturation and saturation velocity for various liquids ........................ 76
Figure 4.10. Velocity-force characterization for a “worst case” protein-containing solution:
whole blood ............................................................................................................ 79
Figure 4.11. Evolution of the velocity-force curve, threshold force, and dynamic friction
coefficient for a protein-rich solution .................................................................... 80
Figure 4.12. An empirical model of the effects of fouling on drop velocity .............................. 83
Figure 4.13. Comparison of versions 1 and 2 of the impedance measurement circuit used to
evaluate droplet movement in DMF devices ......................................................... 88
Figure 5.1. Schematic representation of a single step being applied to three different
channels (electrodes) .............................................................................................. 97
Figure 5.2. Capacitance measurement error and relative velocity ......................................... 103
Figure 5.3. Scalability of multi-drop movement and sensing ................................................ 106
Figure 5.4. Experimental realization of multi-drop moving and sensing ............................... 108
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Figure 5.5. Simulation of multi-channel sensing during drop splitting .................................. 111
Figure 5.6. High-voltage switching board used for multi-electrode impedance sensing ....... 113
Figure 6.1. Abstraction layer hierarchy .................................................................................. 123
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List of Tables
Table 4.1. Summary of findings from velocity-force characterization experiments ..................... 72
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List of Equations
Equation 2.1 ..................................................................................................................................... 7
Equation 2.2 ................................................................................................................................... 10
Equation 2.3 ................................................................................................................................... 23
Equation 2.4 ................................................................................................................................... 23
Equation 2.5 ................................................................................................................................... 24
Equation 2.6 ................................................................................................................................... 24
Equation 4.1 ................................................................................................................................... 46
Equation 4.2 ................................................................................................................................... 46
Equation 4.3 ................................................................................................................................... 47
Equation 4.4 ................................................................................................................................... 47
Equation 4.5 ................................................................................................................................... 48
Equation 4.6 ................................................................................................................................... 48
Equation 4.7 ................................................................................................................................... 49
Equation 4.8 ................................................................................................................................... 49
Equation 4.9 ................................................................................................................................... 49
Equation 4.10 ................................................................................................................................. 50
Equation 4.11 ................................................................................................................................. 51
Equation 4.12 ................................................................................................................................. 51
Equation 4.13 ................................................................................................................................. 52
Equation 4.14 ................................................................................................................................. 52
Equation 4.15 ................................................................................................................................. 52
Equation 4.16 ................................................................................................................................. 53
Equation 4.17 ................................................................................................................................. 54
Equation 4.18 ................................................................................................................................. 54
Equation 4.19 ................................................................................................................................. 80
Equation 4.20 ................................................................................................................................. 81
Equation 4.21 ................................................................................................................................. 81
Equation 4.22 ................................................................................................................................. 81
Equation 4.23 ................................................................................................................................. 88
Equation 4.24 ................................................................................................................................. 91
Equation 4.25 ................................................................................................................................. 91
Equation 5.1 ................................................................................................................................... 98
Equation 5.2 ................................................................................................................................... 98
Equation 5.3 ................................................................................................................................... 99
Equation 5.4 ................................................................................................................................... 99
Equation 5.5 ................................................................................................................................. 100
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List of Abbreviations
AC Alternating current
AFM Atomic force microscopy
BSA Bovine serum albumin
DC Direct current
DEP Dielectrophoresis
DI Deionized
DMF Digital microfluidic(s)
ELISA Enzyme-linked immunosorbent assay
EWOD Electrowetting on dielectric
HRP Horseradish peroxide
ITO Indium tin oxide
PBS Phosphate buffered saline
PCB Printed circuit board
RMS Root-mean squared
SEM Scanning electron micrography
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Overview of Chapters
Chapter 2 describes the development of DropBot, an instrument (and associated software
interface) that enables automated drop control and characterization of DMF chips. This
system features two key functionalities: (1) application of constant electrostatic driving
forces though compensation for amplifier-loading and device capacitance, and (2) real-time
monitoring of instantaneous drop velocity (a proxy for resistive forces). The later
functionality (characterization of resistive forces using drop velocity) is further developed in
Chapter 4. This work resulted in the following publication: Fobel, R., Fobel, C. & Wheeler,
A. R. DropBot: An open-source digital microfluidic control system with precise control of
electrostatic driving force and instantaneous drop velocity measurement. Appl. Phys. Lett.
102, 193513 (2013).
Chapter 3 demonstrates an economical and scalable means of fabricating DMF devices
using inkjet printing of silver nanoparticles onto paper substrates. These paper-based DMF
devices have comparable performance to traditional photolithographically patterned DMF
devices (the current standard fabrication method) at a fraction of the cost. We implement a
sandwich ELISA as an example of a complex, multi-step diagnostic test that can be
performed using these low-cost disposable devices. This work resulted in the following
publication: Fobel, R., Kirby, A. E., Ng, A. H. C., Farnood, R. R. & Wheeler, A. R. Paper
Microfluidics Goes Digital. Adv. Mater. 26, 2838–2843 (2014).
Chapter 4 presents a set of fully-automated techniques for characterizing resistive forces on
DMF. While the applied (electrostatic) forces used to manipulate drops on DMF are well
understood, resistive forces that oppose drop movement are a relatively unexplored area with
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many open research questions. The presented framework builds on the velocity measurement
techniques developed in Chapter 2, and explores a matrix of experimental conditions
(surface tension, viscosity, conductivity, driving frequency and protein content). Several new
and interesting trends are presented, as is the first known demonstration of manipulating
whole blood on DMF under ambient conditions. A manuscript describing this work is currently
in preparation.
Chapter 5 describes a method for extending the impedance-based position and velocity
measurement techniques developed in Chapters 2 and 4 to enable the tracking of multiple
drops in parallel. This functionality enables hardware-level validation of all unit operation
(move, mix, merge, split), which should facilitate development of fully-automated, and fault-
tolerant control of digital microfluidics. A manuscript describing this work is currently in
preparation.
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Overview of Author Contributions
Professor Aaron Wheeler provided guidance and support to all of the work presented in this
thesis and made significant editorial contributions.
Chapter 2 describes the development of the DropBot instrument and software. I initiated this
project and designed and built all hardware. Software was written by me with substantial
contributions from Dr. Christian Fobel (CF, a research-associate in the lab). I designed and
performed all experiments and analyzed the results.
Chapter 3 presents a method for fabricating paper-based DMF devices using inkjet printing.
I conceived of and lead the project. Dr. Andrea Kirby (then a graduate student) assisted with
device printing and testing. Dr. Alphonsus Ng (then a graduate student) assisted with the
homogeneous chemiluminescence assay and the rubella IgG immunoassay. Professor Ramin
Farnood contributed helpful discussions and access to the Dimatix printer. I designed and
performed all of the DMF experiments.
Chapter 4 demonstrates the design, implementation and results of applying a suite of
velocity-based characterization methods to estimate the resistive forces experienced by drops
moving on a DMF device. I designed and performed all experiments and wrote all of the
associated control, simulation, and analysis software.
Chapter 5 describes a multi-channel impedance sensing technique. CF and I conceived of
the project together and jointly developed the theoretical framework. I designed the
necessary hardware modifications to the high-voltage switching boards. CF and I co-
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developed the software and firmware. CF performed the duty cycle/velocity characterization
and multi-channel velocity experiments. I performed the software simulations.
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Chapter 1: Introduction
In the past 60 years, computers have progressed from massive machines taking up entire
rooms and hard-wired to perform specific tasks, to the present day, where they are
ubiquitous, many orders of magnitude more powerful, and in the case of smart phones, fit in
your pocket. Research in the field of microfluidics aims to do for biology and chemistry what
microelectronics has done for the field of information technology and computing: to
dramatically shrink today’s laboratories both in size and cost, a vision commonly referred to
as lab-on-a-chip.1,2
Within the general field of microfluidics, there are multiple paradigms, but they
typically share some common features: automation, integration, and miniaturization. The
advantages of automated systems are obvious: increased throughput, reduced labor costs,
reduced human error, and as a result, improved experimental reproducibility. Integration is
another key feature that is related to automation; it implies a contrast with the traditional
laboratory workflow which often involves manually transferring samples between a variety
of different instruments (e.g., centrifuge, hot plate, plate reader, etc.). Miniaturization can
refer to either reduced sample sizes – which often reduce costs or can lead to less invasive
procedures (e.g., requiring a drop instead of a vial of blood) – or to smaller and more
portable systems, enabling in-field analyses or point-of-care diagnostics.
The earliest microfluidic systems were based on continuous flow through channel
networks,3 and these types of systems still represent the dominant paradigm within the field.
Advances such as soft-lithography4 and the integration of active control elements (e.g., so-
2
called “Quake valves”5) have made channel-based microfluidics more convenient,
accessible, and capable. Another common microfluidic paradigm involves multiphase flow
of two immiscible fluids6 or a fluid and a gas
7 through microchannels. While channel-based
systems offer many advantages including the capability to achieve extremely high
throughputs, a significant disadvantage is that their functionality is defined by their structure.
Although active valves and pumps offer some degree of dynamic control, in most cases, each
application requires a new chip design (i.e., they are not reconfigurable). This particular
feature (chip reconfigurability) is the major differentiator of the microfluidic paradigm that is
the focus of this thesis: Digital Microfluidics (DMF). In DMF, nano- to microliter-sized
drops act as discrete, independently controllable reaction chambers; these drops (confined
between a top and bottom plate) can be moved, mixed, and split using electrostatic forces, all
on a generic, two-dimensional array of electrodes. There are no channels that restrict the
paths of these drops, and therefore, the functionality for this class of microfluidic systems is
decoupled from their physical structure; in this case, functionality can be controlled
dynamically by software.
This feature is incredibly powerful because it implies that any arbitrarily complex,
multi-step laboratory protocol can be decomposed into a combination of well-defined fluidic
operations. If these basic fluidic operations (e.g., drop splitting, translation, mixing) can be
well-characterized and validated by hardware/software (i.e., if the control system can
perform on-chip error-checking and implement dynamic rerouting in the case of faults), it
becomes possible to create a layer of abstraction such that these low-level details can be
guaranteed and safely automated (and hidden from the user). Abstracting away low-level
details is a common engineering strategy that often drives major productivity gains. Consider
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the example of software: programmers don’t need to worry about the low-level details of
transistor functionality nor do they have to write programs in assembly code; they can write
software in a high-level language (at the top of the abstraction hierarchy), confident that their
program will propagate down through the various layers of abstraction, until eventually it is
translated directly into modifications to the state of individual transistors on the processor
chip. This concept of an abstraction hierarchy suggests that if we can achieve reliable control
of the fundamental fluidic operations of DMF (i.e., the lowest level of the hierarchy), the
implementation of any arbitrary laboratory procedure can be translated into a problem
addressable within the software domain. This goal of achieving on-chip characterization and
robust control of low-level fluidic operations motivates the work in Chapters 2, 4 and 5.
The other major goal of this thesis to address challenges that restrict access to DMF
(e.g., the high cost of fabricating devices, lack of cleanroom access, lack of a commercially
available controller system, etc.). I describe these as issues of scalability because they relate
to scale, both in terms of the number of users able to use DMF, and to the amount of
experimental data any given user will choose to generate using DMF (e.g., if devices cost too
much or fabrication is too onerous, users will perform less experiments). This issue of
scalability motivates Chapters 2 and 3.
The specific aims for this thesis are as follows:
1.) Design a control instrument and software capable of applying a precisely
controlled electrostatic force and measuring device capacitance, drop position,
and velocity (Chapter 2).
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2.) Demonstrate a low-cost method for fabricating DMF devices that does not require
a cleanroom facility (Chapter 3).
3.) Develop methods for characterizing the resistive forces that oppose drop
movement on DMF and perform a screen across a range of physiochemical
properties (and driving frequency) to establish expected relationships
(Chapter 4).
4.) Extend impedance sensing functionality (e.g., capacitance, position, velocity) to
facilitate measurement across multiple electrodes in parallel (Chapter 5).
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Chapter 2: Automated Control and On-Chip
Characterization
2.1 Introduction
Digital Microfluidics (DMF) is an emerging fluid-handling technology that allows for
precise control of individually addressable drops on an array of electrodes using electrostatic
forces.8–10
Primary benefits of DMF over macro-scale techniques include reduced sample and
reagent volumes and amenability to automation. In the past decade, DMF has been applied to
a wide range of problems in biology, chemistry and medicine,11,12
but widespread adoption
of this technology requires improvements in device robustness and experimental
reproducibility. In response to this challenge, we present DropBot: an open-source
instrument for controlling drop actuation in digital microfluidics. DropBot features two
unique functionalities, both useful for improving device robustness and reproducibility: (1)
real-time monitoring of instantaneous drop velocity, and (2) application of a precise
electrostatic driving force regardless of device-specific properties.
The first functionality, measurement of instantaneous velocity, is intrinsically linked
to the sensitivity of drop movement to device surface variability. Small imperfections (e.g.,
scratches or dust) or the adsorption of proteins or other biomolecules can make it difficult to
move liquids over extended periods; this is especially true for devices operated in air (as
opposed to oil). While there has been significant progress in extending operation lifetimes
(e.g., using Pluronic additives13,14
and closed-loop control15,16
), the prospect for subsequent
improvements would be greatly enhanced by a tool for quantitatively measuring the impact
of various strategies. Under a given applied force, we assume that an increase in resistive
6
forces will result in a corresponding reduction in drop velocity; therefore, we propose that
instantaneous drop velocity should provide a useful proxy for the resistive forces experienced
by a drop on a DMF device. We contrast the instantaneous velocity, which can be measured
for an individual drop as it translates onto each individual electrode, from the average
velocity which can be measured for a drop after moving over many electrodes; both concepts
are useful, but only the former is useful for probing local surface heterogeneities, which is
critical for reliable DMF operation. Image-based methods9,17,18
are capable of measuring
instantaneous drop velocity, but obtaining sufficient time-resolution requires expensive high-
speed cameras and significant computational resources, making real-time measurements
impractical. Furthermore, optical systems impose strict constraints on visual contrast and
lighting. Thus, we propose that a more general solution is to use electrical impedance-based
sensing,15,16,19–27
which has been used previously to evaluate drop location15,16,26,27
and
average drop velocity.15
Unfortunately, measuring impedance during drop translation
(necessary for estimating instantaneous velocity) is more technically challenging because of
the required dynamic range and considerations for parasitic capacitance. DropBot is unique
in that it allows for instantaneous velocity measurements during drop movement.
The second functionality is the application of precise and reproducible actuation
forces. This has not been achievable in systems reported previously because of complications
arising from amplifier-loading and variability in device capacitance. Amplifier-loading refers
to the sensitivity of output voltage to the impedance of the load attached to an amplifier. This
problem is exacerbated by automated systems relying on solid-state switches because the
switches themselves contribute a significant capacitive load to the system. The second factor
limiting the reliable application of DMF driving forces is variability in device capacitance as
7
a function of differences in the thickness and dielectric constant of the insulating layer.
Dielectric thickness may vary batch-to-batch in fabrication or even across a given device if
the layer is applied unevenly. The force responsible for translating drops is related to
capacitance by the equation:28–30
2
2
1LcUFe (2.1)
where L is electrode width, c is capacitance per unit area, and U is actuation voltage;
therefore, variability in device capacitance requires adjustment of the actuation voltage to
maintain a consistent force. In all systems reported previously, operators have had to adjust
the voltage for each condition; however, this requires manual intervention and limits the
ability to make meaningful comparisons across devices and experiments. DropBot allows for
automated, real-time tuning of applied potentials to maintain constant driving forces for
devices that are radically different in composition.
2.2 Results and discussion
2.2.1 System overview
An overview of the DropBot system and a screenshot of the graphical user interface are
shown in Figure 2.1. Users can activate/deactivate electrodes on the DMF device by mouse-
clicking on the webcam video overlay, providing an intuitive interface with real-time visual
feedback. In addition, sequences of actuation steps can be pre-programmed, enabling fully
automated operation. The system is based on an Arduino Mega 2560 (SmartProjects, Italy)
microcontroller board and houses a custom circuit for measuring device impedance and
8
amplifier output (a simplified version of this circuit is shown in Figure 2.2a). Source code
and circuit schematics are available at http://microfluidics.utoronto.ca/dropbot.
2.2.2 Impedance and amplifier output
The DropBot system continuously monitors the amplifier output and device impedance to
maintain a stable actuation voltage and to track the position and velocity of drops. Accurate
measurements of these parameters are critical to automated DMF operation, but in each case,
we have observed that parasitic capacitance introduces a significant bias. The problem of
parasitic capacitance in automated DMF systems has never before been addressed, and we
believe that this has limited the precision and reproducibility obtainable with previously
reported systems.
9
Figure 2.1. The DropBot DMF automation system. (a) Block diagram. (b) Photograph of the DropBot system (which contains an Arduino-based control board and up to 8 40-channel high-voltage driver boards) connected to a high-voltage amplifier and a pogo-pin DMF device interface. (c) Screenshot from the custom Python software demonstrating live video overlay.
10
In the absence of parasitic capacitance, a voltage divider comprising a 10 MΩ resistor
in series with a reference resistor (either Rhv0 = 100 kΩ or Rhv1 = 1 MΩ) should provide
frequency-independent attenuation of 11- or 101-fold. The ability to switch between these
two attenuation levels facilitates an increased signal-to-noise ratio over a wide dynamic
range. The amplifier output is estimated from Uhv using the equation:
26
26
10210
1 hvi
hvi
hvtotal CR
UU
(2.2)
where Rhvi is the reference resistance and Chvi is the parasitic capacitance when resistor i is
selected, and is the frequency in Hz. The results using this approach are shown in the “no
compensation” data (square boxes) in Figure 2.2b, where Chvi is assumed to be equal to zero.
At high frequencies, the 10 V (measured with Rhv0) and 100 V (measured with Rhv1) signals
deviate from their expected values, consistent with a first-order low-pass filter (the capacitive
element arises from the parasitic capacitance of the resistor, copper traces, etc.). By
experimentally measuring and including this capacitive term in Equation 2.2, the expected
signals are recovered.
Parasitic capacitance also impacts the estimation of device capacitance, as
demonstrated in Figure 2.2c. Initially, there is little liquid on the active electrode; therefore,
the current passing through the device is low and the largest feedback resistor, Rfb3, is
required to obtain sufficient sensitivity. Ufb increases as the drop moves onto the electrode,
and before it surpasses 5 V, Rfb3 is swapped for the smaller Rfb1. This change in resistors at
t ≈ 100 ms produces a discontinuity in the “no compensation” data (blue markers); the same
data is plotted with compensation for parasitic capacitance (green squares). To explain the
11
origin of this discontinuity, Figure 2.2d shows a simulation of the feedback-to-actuation
voltage ratio (Ufb/Utotal). In the absence of parasitic capacitance, this ratio should be
proportional to frequency (dashed lines). In contrast, the solid lines include capacitive effects
(resembling first-order high-pass filters). It can be seen from Figure 2.2d that measurements
made with Rfb3 at 10 kHz will underestimate Ufb, leading to the discontinuity in Figure 2.2c.
12
Figure 2.2. Impedance and amplifier output measurement. (a) Circuit schematic including parasitic capacitance (red). The gray dashed box contains the circuit model for a drop on a single actuation electrode. (b) Measurements of the amplifier output for 100 Vrms (blue) and 10 Vrms (red) signals, both with compensation for parasitic capacitance (dots) and without (squares). Solid lines represent the models used to apply the correction. (c) Device capacitance as a function of time as a drop is moving onto an actuated electrode with compensation (green squares) and without (blue markers). A solid blue line is used to guide the eye. (d) Simulation of the theoretical attenuation of the total voltage by each of the four feedback resistors (Rfb0 – dark blue, Rfb1 – green, Rfb2 – red, Rfb3 – light blue). Dashed lines represent attenuation in the absence of parasitic capacitance, while solid lines include capacitive effects. The vertical gray dashed line corresponds to the frequency applied in c, showing the effect of parasitic capacitance on measurements made with Rfb3.
13
2.2.3 Velocity measurement
We propose that instantaneous drop velocity is a useful feature to track because it provides a
unique proxy that is inversely related to the resistive forces opposing drop motion. Any local
modifications to the device surface or insulator (e.g., through biofouling or dielectric
damage) should manifest as changes in drop velocity. Figure 2.3 demonstrates the capability
of the DropBot system to extract instantaneous velocity from the derivative of the device
capacitance with respect to time (described in section 2.4.5). Figure 2.3b shows
representative velocity profiles for a drop of DI water being actuated at 100, 130 and
150 Vrms. Actuation force is proportional to voltage squared (Equation 2.1), so we expect
higher voltages to produce increased velocities. Figure 2.3c demonstrates this trend over a
range of voltages, showing an increasing peak velocity at driving voltages up to ~250 Vrms,
after which the velocity appears to saturate at 70–80 mm/s. While it is possible that the peak
velocity continued to increase beyond 80 mm/s for voltages greater than 250 Vrms, this could
not be confirmed because of limitations of the current system. In any case, we observed
successful drop movements for the full 50 repetitions for voltages up to and including
330 Vrms. Note that each data point represents the velocities of a fresh drop of DI water
translated across an unused set of electrodes, minimizing evaporation and other potential
cumulative effects between experiments.
At 350 Vrms, we observed an abrupt change in the voltage/velocity trend; Figure 2.3d
shows a gradual reduction in peak velocity on a single electrode over the course of 50
repetitions. We observed a similar effect on the other three electrodes and on multiple
devices operated at this voltage (data not shown). This suggests that for moving DI water on
a device of this composition, 350 Vrms represents an upper limit beyond which there is a
14
rapid and irreversible degradation of device performance. Interestingly, the drop was
successfully translated across all electrodes for the full 50 repetitions; however, by the end of
the experiment, the velocity was greatly reduced (<10 mm/s). There was no measurable
change in the capacitance of the dielectric, nor was there any evidence of electrolysis, which
suggests that this phenomenon was not driven by dielectric breakdown. The affected
electrodes were qualitatively observed to be hydrophilic by running a stream of DI water
over the device, consistent with suggestions in the electrowetting literature that excessive
voltage causes surface modifications through air ionization.31
Thus, we hypothesize that the
voltage-induced surface modifications increased the resistive force on the drops. We suspect
that this represents an additional mechanism beyond those commonly attributed to device
failure (i.e., biofouling13,14
and dielectric breakdown32
).
15
Figure 2.3. Drop velocity measurements. (a) Video frame from a sequence showing a drop of water moving across four electrodes. (b) Representative instantaneous velocity profiles for a drop of water actuated at 110 (blue), 130 (green), and 150 Vrms
(red) ( = 10 kHz) onto an electrode. (c) Average peak velocity of a drop of water
moving over four electrodes 50 times at different actuation voltages ( = 10 kHz, error bars represent ±1 standard deviation). (d) Peak velocities from c shown for each of the 50 repetitions for the 350 Vrms experiment.
2.2.4 Amplifier-gain compensation
High-voltage amplifiers are often used for DMF with the assumption that they have constant
gain – i.e., that they produce an output voltage that is a linear scaling of the input signal. But
we report here that this assumption is often invalid, and in fact, DMF automation systems are
16
frequently operated under conditions in which amplifier gain is unstable, causing unwanted
and unpredictable changes in output voltage. Figure 2.4a demonstrates that the Trek PZ700
amplifier used in our system has constant gain at frequencies below ~1 kHz; however, at
higher frequencies (up to ~20 kHz is common for DMF) and as additional switching modules
are added to the system, the behavior changes dramatically, with output variations of up to
±60%. This behavior is expected for driving large capacitive loads and is not unique to this
particular amplifier. In general, it is difficult to design amplifiers that can operate at (1) high
frequency, (2) high voltage, and (3) drive large capacitive loads, making it likely that any
amplifier used for DMF will be operated at or beyond its limits under certain experimental
conditions. Figure 2.4b shows that even the simple act of turning an electrode on/off can
significantly change the output voltage.
To compensate for non-ideal amplifier behavior, the DropBot system was designed to
monitor the amplifier output and adjust the input every 10 ms. Figure 2.4a–b demonstrates
the effectiveness of this approach for frequencies up to 20 kHz and with several reservoirs
actuated simultaneously.
17
Figure 2.4. Amplifier-gain compensation. (a) Amplifier output as a function of frequency for a target voltage of 100 Vrms with different numbers of solid-state switches (0 – dark blue, 40 – green, 80 – red, 120 – light blue) attached to the amplifier (all switches are in their off state). The magenta curve demonstrates the ability of the gain compensation feature to achieve a flat frequency response up to the maximum bandwidth of the amplifier (~20 kHz) with 120 switches attached. Error bars represent ±1 standard deviation from 10 replicate measurements. (b) Amplifier output voltage with gain compensation (green squares) and without (blue symbols) as a function of device capacitance for a frequency of 10 kHz. The ~0, 150 and 300 and 450 pF device loads are a result of actuating 0, 1, 2, or 3 reservoir electrodes each containing 10 μL. Error bars represent ±1 standard deviation from 100 replicate measurements.
Although this compensation scheme is effective under typical operating conditions,
there are other possible strategies for addressing amplifier-loading effects. One solution may
be to redesign the switching boards to present a lower capacitive load to the amplifier. This
could be achieved through a more optimal circuit board layout and/or by using relays with a
lower off-state capacitance. It may also be possible to find a high-voltage amplifier with
improved performance under high loads. For any given amplifier, the compensation scheme
described here should enable stable operation at higher frequencies and/or higher loads than
would be possible otherwise.
18
2.2.5 Force normalization
Small-batch, manual fabrication of DMF devices often results in loose tolerances over
insulator thickness. This requires ad hoc adjustments to actuation voltage to achieve
consistent drop movement across devices. Figure 2.5a shows the peak velocity for drops of
DI water driven with a range of actuation voltages on two DMF devices, each with a
different thickness of Parylene-C. Note that the device with the 2.2 μm dielectric layer
achieved equivalent peak velocities to the 6.2 μm layer device using much lower voltages.
This is expected because actuation force is proportional to dielectric capacitance (Equation
2.1), and the thinner dielectric exhibits a higher capacitance per unit area. Because the
DropBot system measures device capacitance and actuation voltage simultaneously, it can
estimate the actuation force for any arbitrary device connected to the system. Figure 2.5b
demonstrates that when peak drop velocity is normalized by the estimated actuation force,
the 2.2 and 6.2 μm devices are virtually indistinguishable. The capability to automatically
apply a consistent actuation force regardless of the particular device characteristics is
attractive from a user perspective, and is unique to the DropBot system. This feature also
allows for meaningful comparisons of drop velocity between devices with varying dielectric
properties.
19
Figure 2.5. Normalizing actuation voltage by electrostatic force. (a) Average peak velocity for a drop of water moving across the same electrode 50 times at different
actuation voltages ( = 10 kHz, error bars represent ±1 standard deviation from 50 measurements) for two thicknesses of Parylene-C (2.2 μm – blue and 6.2 μm – green). (b) Data from a plotted as a function of driving force as per Equation 2.1.
2.3 Conclusion
In conclusion, we have demonstrated DropBot’s ability to measure instantaneous drop
velocity and to precisely control the applied electrostatic force through compensation for
amplifier-loading and parasitic capacitance. We believe that these combined features will be
useful to end-users developing new assays or characterizing and optimizing device design
and control. We further suggest that the quantitative metrics provided by this system will be
useful for addressing some of the outstanding challenges in the field, including improved
device robustness and resistance to biofouling.
20
2.4 Experimental
2.4.1 Reagents and materials
Unless otherwise specified, general-use reagents were purchased from Sigma Chemical
(Oakville, ON, Canada) or Fisher Scientific Canada (Ottawa, ON, Canada). Deionized (DI)
water had a resistivity of ~18 MΩ·cm at 25°C.
2.4.2 DMF device fabrication
DMF devices were fabricated in the University of Toronto Emerging Communications
Technology Institute (ECTI) cleanroom facility using a transparent photomask printed at
20,000 DPI (Pacific Arts and Designs Inc., Markham, Ontario). Bottom-plates bearing
chromium electrodes were patterned by photolithography and etching of commercially
available chromium and positive photoresist-coated, 50×75 mm glass slides (Telic, Valencia,
CA). Substrates were exposed to UV through a mask (8 s, 29.8 mW/cm2), developed in MF-
321 (~2 min), and etched in CR-4 (5 min, OM Group, Cleveland, Ohio), followed by
washing with DI water and drying under a stream of nitrogen. Substrates were then
immersed in AZ 300T for 10 min to remove the photoresist, and again washed in DI water
and dried with nitrogen. Silanization solution was prepared by mixing 2 mL 3-
(Trimethoxysilyl)propyl methacrylate (Specialty Coating Systems, Indianapolis, IN), 200 mL
DI water, 200 mL isopropyl alcohol (IPA), and 1 mL acetic acid (BioShop, Burlington, ON,
Canada) for 2 hours at room temperature. Substrates were immersed in this silanization
solution for 10 min, rinsed with IPA and cured at 80°C for 10 min, followed by rinsing with
IPA and drying with nitrogen. Slides were then coated with Parylene-C by evaporating either
5 g (for most devices) or 15 g (for a few devices) of Parylene dimer in a vapor deposition
instrument (Specialty Coating Systems, Indianapolis, IN). Profilometry revealed these
21
thicknesses to be 2.2 and 6.2 m, respectively. Substrates were then coated with ~50 nm of
Teflon-AF 1600 (DuPont, Wilmington, DE) by spin-coating (1% wt/wt in Fluorinert FC-40,
1000 rpm, 30 s) and post-baking at 160°C for 10 min.
50×75 mm Indium tin oxide (ITO)-coated glass substrates (Delta Technologies Ltd.,
Stillwater, MN) were coated with Teflon-AF (50 nm, as above) for use as top-plate
substrates. All experiments were carried out on devices bearing a rectangular array of 15×4
square actuation electrodes (2.2×2.2 mm each), 8 reservoir electrodes (6.5×15 mm each), and
inter-electrode gaps of 25-75 μm. Each electrode is connected to a contact pad on the sides of
the device and contact pads are arranged in 6 columns of 15 rows (3 columns per side). The
contact pads are spaced every 2.54 mm, and are designed to interface with a custom pogo-pin
connector. Devices were assembled such that the ITO top plate was roughly aligned with the
outer edges of the reservoir electrodes on the bottom plate. The two plates were separated by
a spacer formed from two pieces of double-sided tape with a total thickness of ∼160 μm,
resulting in drops of ~0.8-1.0 μL covering a single actuation electrode.
2.4.3 DropBot hardware and software
The source code and circuit schematics are available at
http://microfluidics.utoronto.ca/dropbot. An overview of the system components is shown in
Figure 2.1. The graphical user interface is written in Python (http://www.python.org) using
the GTK toolkit (http://www.pygtk.org). The control board relies on an Arduino Mega 2560
(SmartProjects, Italy) and connects to a computer via USB. The control board houses a
custom circuit for measuring the amount of current passing though the device and through a
reference resistor to infer device impedance and amplifier output, respectively. A simplified
version of this circuit is shown in Figure 2.2a; the design builds on earlier versions,15,16,19
22
with the notable addition of a switchable bank of resistors (with resistances of 1 kΩ, 10 kΩ,
100 kΩ and 1 MΩ) to extend the dynamic range by several orders of magnitude and an extra
channel for measuring the amplifier output in addition to device impedance.
The control board generates a 0–1.4 Vrms variable-frequency sine wave using an
LTC6904 oscillator (Linear Technology, Milpitas, CA) and low-pass filter. This signal is
amplified by a PZ700 amplifier (Trek, Inc., Medina, New York) and is connected to the input
of three custom-built high-voltage driver boards, each housing 40 solid-state relay switches;
this gives the system a total of 120 channels. The amplifier output is also connected through
a 10 MΩ resistor back to the control board to facilitate amplifier-output monitoring. The
control board communicates with the driver boards over an i2c bus (NXP Semiconductors,
Eindhoven, Netherlands), and each relay switch connects to a single electrode on the DMF
device via a custom pogo-pin connector.
2.4.4 Calibration for parasitic capacitance
Figure 2.2a shows the circuit model for the impedance and amplifier monitoring circuit. The
capacitors (red) represent the combined parasitic capacitance of the coax cables, circuit board
traces, connectors, etc. Amplifier output, Utotal, was measured using a TDS2021 oscilloscope
(Tektronix, Beaverton, OR). The attenuated amplifier voltage, Uhv, was measured by the
Arduino for 30 frequencies evenly spaced between 0.1 and 30 kHz on a log10 scale. The input
signal was adjusted such that Uhv was within the measurable range for the Arduino (0–5 V).
The parameters Rhvi and Chvi (i = 0, 1) were estimated using the Levenberg–Marquardt
algorithm for nonlinear least-squares33
by fitting Equation 2.2. The Rfbj and Cfbj (j = 0, 1, 2, 3)
terms were estimated similarly by attaching load resistors of 1 or 10 MΩ in place of the
23
device. Using these calibration values, the device impedance was estimated using the
equation:
1
21)(
2fb
total
hvihvi
fbj
deviceU
U
CC
RZ
(2.3)
where Zdevice() is the device impedance in Ohms as a function of frequency, Ufb is the
voltage measured by the control board across resistor Rfbj, and Cfbj is the parasitic capacitance
when feedback-resistor j is selected.
2.4.5 Velocity experiments
Drops of DI water were translated across a set of four electrodes using a driving frequency of
10 kHz and voltages starting at 110 and increasing to 350 Vrms in steps of 20 V (a total of 12
conditions). For each condition, a fresh drop was dispensed and the cycle was repeated 50
times on a set of four unused electrodes. The complete set of conditions was tested using 12
columns on single device, eliminating any intra-device variability and cumulative effects
between conditions. Device impedance was estimated every 10 ms using Equations 2.2 and
2.3, and the impedance was attributed solely to the combined capacitance of the dielectric
and hydrophobic layers; therefore, the total capacitance of the device was calculated using
the equation:
)(2
1
ZC (2.4)
If each drop is assumed to take the square shape of an electrode, then at time t, its position
along the direction of travel, x(t), is related to the total device capacitance by the expression:
24
)(
)()(
2
fillerliquid
filler
ccL
cLtCtx
(2.5)
where C(t) is the capacitance at time t, L is the width of the square electrodes, and cliquid and
cfiller are the capacitance per unit area of an actuated electrode covered in liquid and filler
media (e.g., air or oil), respectively. Differentiation of Equation 2.5 yields the instantaneous
velocity:
)(
)()(2
fillerliquid
filler
ccL
cLtC
dt
d
dt
tdx
(2.6)
This derivative was approximated on the Arduino by the finite difference of the capacitance
time series.
2.4.6 Amplifier-loading effects
A 0.5 Vrms input signal (100 Vrms output, assuming a DC gain of 200) was swept between 0.1
and 30 kHz in 30 steps equally spaced on a log10 scale. Peak-to-peak voltage measurements
were collected using the Arduino for each frequency (10 measurements, 10 ms duration
each), and the amplifier output voltage, Utotal, was calculated according to Equation 2.2. The
experiment was repeated with 0, 1, 2 and 3 high-voltage switching boards connected to the
amplifier with all switches in their off state. The same experiment was repeated with
amplifier-gain compensation; in this case, the target voltage was set to 100 Vrms and the
Arduino modulated the amplitude of the input signal every 10 ms to maintain the target
output.
To measure the effect of device loading, three high-voltage switching boards were
connected to the system and three reservoir electrodes of the DMF device were each loaded
25
with 10 μl of DI water. A 0.5 Vrms signal with a driving frequency of 10 kHz was applied to
the amplifier input and 0, 1, 2, or 3 electrodes were actuated simultaneously. In each case,
the amplifier output was measured 100 times over a period of one second. The same
conditions were applied with amplifier-gain compensation (i.e., modulation of the input
voltage every 10 ms to maintain a target output of 100 Vrms).
2.4.7 Force normalization experiments
Drops of DI water were translated across four electrodes as in the velocity experiments with
a driving frequency of 10 kHz and voltages of 60, 80 and 100 Vrms (devices with bottom-
plates coated with 2.2 μm Parylene-C) and 110, 130, 150, 170 and 190 Vrms (devices with
bottom-plates coated with 6.2 μm Parylene-C). Drop velocity was recorded every 10 ms and
the capacitance per unit area of liquid- and air-covered electrodes was measured by the
control board.
26
Chapter 3: Inkjet-printed DMF on Paper
3.1 Introduction
Paper microfluidics has recently emerged as simple and low-cost paradigm for fluid
manipulation and diagnostic testing.34–36
Compared to traditional “lab-on-a-chip”
technologies, it has several distinct advantages that make it especially suitable for point-of-
care testing in low-resource settings. The most obvious benefits are the low cost of paper and
the highly developed infrastructure of the printing industry, making production of paper-
based devices both economical and scalable.36
Other important benefits include the ease of
disposal, stability of dried reagents,37
and the reduced dependence on expensive external
instrumentation.38,39
While the paper microfluidics concept has transformative potential, this class of
devices is not without drawbacks. Many assays have limited sensitivity in the paper format
because of reduced sample volumes and limitations of colorimetric readouts.39
These devices
also exhibit large dead volumes as the entire channel must be filled to drive capillary flow.
But perhaps the most significant challenge for paper-based microfluidic devices is a product
of their passive nature itself, making it difficult to perform complex multiplexing and multi-
step assays (e.g., sandwich ELISA). There has been progress in expanding device complexity
through the development of three-dimensional channel networks40,41
and adapting channel
length, width and matrix properties can provide control of reagent sequencing and time of
arrival at specific points on the device.42
Active “valve” analogues have also been
demonstrated using cut-out fluidic switches,43
and manual folding44
; however, these
techniques require operator intervention which can introduce additional complications.
27
Some groups have implemented complicated, multi-step assays including sandwich
ELISA using paper “well plates” and manual pipetting.39,45–49
These assays are analogous to
those performed in standard 96-well polystyrene plates, but the “plates” are pieces of paper
patterned with hydrophobic/philic zones. The drawback to this class of devices is that they
are not truly “microfluidics” – unlike the methods described above, each reagent must be
pipetted into a given well to implement an assay, similar to conventional multi-well plate
techniques.
Here we report an alternative approach for implementing fully automated, complex,
multi-step reactions on paper-based substrates: the first example of so-called “digital
microfluidics” implemented on paper. Digital microfluidics (DMF) is a technology for
manipulating nano-to-microliter-sized liquid drops on an array of electrodes using electric
fields. Electrostatic forces can be used to merge, mix, split, and dispense drops from
reservoirs, all without pumps or moving parts. While DMF has been applied to a wide range
of applications,12
a significant challenge has been the lack of a scalable and economical
method of device fabrication – most academic labs use photolithography in cleanroom
facilities to form patterns of electrodes on glass and silicon. One scalable technique is the use
of printed circuit board (PCB) fabrication to form DMF devices,50–52
but we propose that the
new methods reported here, which rely on inkjet printing on paper, may offer superior
performance and be better suited for rapid prototyping. Moreover, we suggest that the new
device format described has the potential to combine the power and flexibility of DMF with
the many benefits of paper-based microfluidics.
28
3.2 Results and discussion
3.2.1 Printing resolution and conductivity
Paper DMF devices were formed by inkjet printing arrays of silver driving electrodes and
reservoirs connected to contact pads onto paper substrates optimized for inkjet printing. This
paper exhibits a smooth surface and a thin barrier to prevent ink from wicking into the fibers,
features typical of commercial inkjet photo paper.53
Figure 3.1a and b contain representative
photographs of such substrates; as shown, two different designs were used. In practice, each
paper substrate formed a device bottom plate, which was joined with a conductive top plate
to manipulate 400–800 nL drops sandwiched between them.
29
Figure 3.1. Characterization of printing resolution and conductivity. Photos of paper DMF devices patterned with (a) Design A and (b) Design B. (c) Photo of printed test pattern showing gradients of line/gap widths in horizontal and vertical directions. (d) Effect of sintering time on the resistance of 150 μm wide printed silver traces. (e) Average resistance of all traces for DMF device Design A fabricated by inkjet (silver on paper) and by standard photolithography (chromium on glass). Error bars are ±1 standard deviation.
A key feature for forming digital microfluidic devices is spatial resolution, as
adjacent electrodes separated by large gaps (>100 μm) are problematic for drop movement.54
A resolution test pattern in Figure 3.1c demonstrates horizontal and vertical feature
capabilities as small as 30 μm. In general, we observed that larger features had a lower
probability of failure caused by electrical shorts or breaks, so the driving electrodes in the
5 mm
b
a
contact pads
reservoirs
driving electrodes
5 mm
c
1 mm
90 μm 60 μm 30 μm
line width
30 μm 60 μm 90 μm
gap size
d
e
30
paper DMF devices used here were spaced between 60–90 μm from each other. In contrast,
typical PCB manufacturing processes cannot produce features smaller than 100 μm. Another
key feature is conductivity – thin electrodes with poor conductivity can result in Joule
heating and/or unplanned voltage drops. As shown in Figure 3.1d, inkjet-printed trace
resistance decreases as a function of sintering time. Sintering for ≥ 15 s caused a slight
browning of the paper (which did not seem to affect function), so in the work described
below, all devices were sintered for 10 s. Figure 3.1e shows that the printed traces were
found to have resistances that were 500 times lower than those for devices with identical
designs fabricated by standard photolithographic methods (i.e., chromium on glass).
3.2.2 Surface topology
A third key feature for DMF devices is surface topography: shape and roughness. We use
“shape“ to refer to the topographical pattern arising from differences in height between
electrodes and the gaps between them (i.e., “trenches“ with depth defined by the thickness of
the conductive/electrode layer), and “roughness“ to refer to random variations in surface
topography. The effects of surface topography for glass DMF devices bearing metal
electrodes patterned by photolithography (often used in academic labs) are negligible; in
contrast, the performance of DMF devices formed by PCB fabrication can be severely
compromised by topography.54
Scanning electron micrography (SEM) was used to evaluate the surface shape of the
paper devices used here (Figure 3.2a and b). As shown, the thickness of the silver layer on
inkjet printed paper devices is < 500 nm, which is much thinner than the 10–30 m thick
electrodes commonly found on devices formed from PCBs (note that deep “trenches“
31
between electrodes on PCB-based DMF devices have been reported be problematic for drop
movement51,52,54
). Atomic force microscopy (AFM) was used to evaluate surface roughness,
revealing a surface roughness (Ra) of Ra ≈ 250 nm for bare silver on paper substrates, and
Ra < 100 nm for silver-paper substrates after deposition of Parylene-C and Teflon. These
values are between one and two orders of magnitude smaller than those reported for PCB
DMF devices.50–52
The most straightforward measure of the effects of surface topography on
DMF performance is to evaluate the actuation of individual drops. Figure 3.2c and d
demonstrate the movability of water drops on paper devices. The instantaneous velocities of
drops of water were measured by impedance sensing (see Chapter 2) and the data suggests
that the performance of paper DMF devices is comparable to that of glass devices formed by
photolithography. In other words, paper DMF devices exhibit nearly identical performance to
glass devices, a remarkable observation given the differences in fabrication (inkjet printing
relative to lithography and etching in a cleanroom).
32
Figure 3.2. Surface topology and drop velocity. (a and b) SEM images showing cross-sectional views of a paper device with a printed silver electrode. (c) Series of video frames demonstrating translation of a drop of water on a paper device. (d) Peak velocities of water drops on a paper DMF device (orange circles) relative to those on a standard device fabricated by photolithography (blue squares). Error bars are ±1 standard deviation.
3.2.3 Cost and printing time
To date, we have fabricated more than one hundred working paper DMF devices. The
devices are inexpensive and fast to make; the cost of ink and paper is less than $0.05 per
device and designs A and B require approximately 1 and 2 minutes each to print. We expect
both cost and speed will improve dramatically as the printed electronics field matures and/or
if these methods are scaled to larger production runs for a couple of reasons: (1) commercial
1 μm
silver layer
10 μm
silver layer
b a
d c
t = 0 ms
50 ms
100 ms
1.65 mm
33
conductive inks are still relatively expensive when ordered in small quantities, e.g., ~$30/mL
and (2) typical office inkjet printers (which rely on the same piezoelectric principle) have
>100 nozzles compared to < 6 that were practical to use simultaneously in this study. Since
printing time is inversely proportional to the number of nozzles, we expect that in the future
it may be possible to reduce this time to just seconds per device. Most importantly, the new
paper substrates are imbued with the capacity to implement complex, multi-step assays,
representing an important new frontier for paper microfluidics.
3.2.4 Homogeneous chemiluminescence assay
Two tests were developed to probe the capacity of paper DMF devices for performing
complex, multi-step assays. As a first test, we explored the ability to generate an on-chip
serial dilution and calibration curve for a homogeneous chemiluminescence assay:
horseradish peroxide (HRP) mixed with luminol/H2O2. As depicted in Figure 3.3a, this
experiment requires 63 discrete steps: 27 dispense, 18 mix, 6 split, and 12 measure. From a
total of three initial pipette steps, a four-point calibration curve can be created in less than
1 h. Despite this complexity, the assay was straightforward to implement reproducibly on
paper DMF devices (Figure 3.3b, R2 = 0.993). The complexity of this assay is such that it
would likely be difficult or perhaps impossible to perform on a capillary-driven paper device.
34
Figure 3.3. Homogeneous chemiluminescence assay generated on a paper DMF device though on-chip serial dilution of HRP mixed with luminol/H2O2. (a) Cartoon showing individual steps in the assay. (b) Generated calibration curve (n = 3). Error bars are ±1 standard deviation. (c) Picture of a device after step 4 with top plate removed for visualization.
a b
c
35
3.2.5 Rubella IgG sandwich ELISA
As a second test to probe the feasibility of complex assay development using paper DMF and
to demonstrate the suitability of these devices for low-cost diagnostic testing, we chose to
implement a rubella IgG sandwich ELISA. Rubella, also known as German measles, is a
disease caused by the rubella virus. Although it poses few complications when acquired post-
natally, congenital rubella syndrome can cause serious developmental defects including
blindness, deafness and termination of pregnancy.55
As far as we are aware, this is the first
report of an assay for rubella using a microfluidic device of any format.
The ELISA for rubella required a larger electrode array, the use of magnetic-bead-
linked inactivated rubella virus, and a motorized magnet for separation and washing (Figure
3.4a).56
30 discrete steps were required for each concentration evaluated (11 dispense,
10 mix, 8 magnetic separation, and 1 measure), taking approximately 10 min. Most
importantly, as shown in Figure 3.4b, the method was reproducible (R2 = 0.988) and
sensitive (limit of detection = 0.15 IU/mL), demonstrating the ability to detect concentrations
well below the 10 IU/mL clinical threshold.57
The inset in Figure 3.4b shows the
immunocomplex for the assay. Note that unlike conventional ELISAs which use a capture
antibody specific to a target analyte, in this case, the beads are coated with an inactivated
virus and the primary antibody (rubella IgG) is the analyte. Conventional sandwich ELISAs
have also been performed on DMF using an analogous system,56,58
so this technique can be
applied to both cases. Furthermore, since magnetic beads are commercially available for a
wide variety of antibodies, we expect that this procedure can provide a general blueprint
toward quantifying a broad range of interesting biomarkers. In addition to the obvious benefit
36
of low device cost, this method retains high analytical performance with greatly reduced
sample volumes relative to conventional automated immunoassay analyzers.56,58
Figure 3.4. Rubella IgG immunoassay performed on a paper DMF device with a luminol/H2O2 chemiluminescent readout. (a) Still frames from a video sequence showing magnetic separation of beads from the supernatant and re-suspension in wash buffer. (b) Calibration curve for rubella IgG concentrations of 0, 1.56 and 3.125 IU/mL. Error bars are ±1 standard deviation. The inset shows the immunocomplex for the assay: a magnetic bead coated with inactivated virus, the primary antibody (rubella IgG) and the HRP-tagged secondary antibody.
Compared with traditional, capillary-driven paper microfluidics, the DMF format
presents obvious tradeoffs. In cases where capillary-driven flow is sufficient, the additional
complexity and cost of the required DMF instrumentation may be unwarranted. However, we
note that the added costs for DMF are modest (e.g., the open-source DMF control system
described in Chapter 2 can be reproduced for a few thousand dollars) and they represent a
one-time investment. Thus, we propose that for applications requiring flexibility and/or
precise control of multi-step reactions (e.g., a quantitative standard dilution curve for a
sandwich ELISA), these added costs are justified. Opportunities for reducing the
a b i
ii
iii
beads supernatant
magnet
engaged
beads re-
suspended
1 mm
magnetic bead
inactivated virus
primary antibody
secondary antibody
37
instrumentation costs (e.g., electrochemical readout59
) coupled with the low cost of the paper
DMF consumables means that over the instrument lifetime, the cost per test can be made
very low.
3.3 Conclusion
In conclusion, we have demonstrated the fabrication of DMF devices on paper using inkjet
printing. We propose that this advance significantly extends the range of applications that
can be easily implemented using paper-based microfluidics and is especially well-suited for
complex, automated, multi-step assays that would be difficult to perform with capillary-
driven techniques. In the future, DMF fluid manipulation may be combined with capillary
wetting features, thereby creating a form of paper “hybrid” devices that take advantage of the
unique capabilities of both formats. In addition, the fabrication technique described here may
be scaled to a roll-to-roll process53,60
for commercial production of low-cost DMF devices, or
alternatively, this method may appeal to researchers interested in rapid prototyping of new
DMF device designs.
3.4 Experimental
3.4.1 Reagents and materials
Unless otherwise specified, reagents were purchased from Sigma-Aldrich (Oakville, ON).
Deionized (DI) water had a resistivity of 18 MΩ·cm at 25°C. Pluronic L64 (BASF Corp.,
Germany) was generously donated by Brenntag Canada (Toronto, ON). Multilayer coated
paper substrates for device printing were graciously provided by Prof. M. Toivakka of Åbo
Akademi University, Finland.53
On-chip reagent solutions were either obtained from vendors
or were custom-made in-house. Reagents from vendors include rubella IgG standards and
38
rubella virus coated paramagnetic microparticles from Abbott Laboratories (Abbott Park,
IL), and SuperSignal ELISA Femto chemiluminescent substrate, comprising stable peroxide
(H2O2) and Luminol-Enhancer solution, from Thermo Fischer Scientific (Rockford, IL).
Custom DMF-compatible wash buffer and conjugate diluent were prepared as described
previously.56,58
Prior to use, rubella IgG standards diluted in Phosphate-Buffered Saline
(PBS) containing 4% Bovine Serum Albumin (BSA) and chemiluminescent substrate were
supplemented with Pluronic L64 at 0.05% and 0.025% v/v, respectively to reduce protein
adsorption and limit cross-contamination.14
Conjugate working solutions were formed by
diluting horse-radish peroxidase (HRP) conjugated goat polyclonal Anti-Human IgG (16
ng/mL) in conjugate diluent. The microparticle working suspension was formed by pelleting,
washing, and resuspending microparticles in Superblock Tris-buffered saline from Thermo
Fischer Scientific (Rockford, IL) at ~1.5×108 particles/mL.
3.4.2 DMF device fabrication, characterization, and operation
DMF bottom plates were formed by printing electrode patterns onto paper substrates using a
Dimatix DMP-2800 inkjet printer (FUJIFILM Dimatix, Inc., Santa Clara, CA) and
SunTronic U6503 silver nanoparticle-based ink according to the manufacturer’s instructions.
After printing, the substrates were sintered using a 1500 W infrared lamp60
at a distance of
~1 cm for 10 s. Two different device design patterns were used: Design A includes 5
reservoir electrodes (4.17 x 4.17 mm) and 19 driving electrodes (1.65 x 1.65 mm) and
Design B includes 8 reservoir electrodes (5.6 x 5.6 mm) and 38 driving electrodes (2.16 x
2.16 mm). Design A was also fabricated with chromium on glass substrates as described in
Chapter 2. Design B was used for the rubella IgG immunoassay assay while Design A was
used for all other experiments. Paper substrates were affixed to glass slides to ease handling.
39
Teflon thread seal tape (McMaster-Carr, Cleveland, OH) was wrapped around the electrical
contact pads to prevent them from being covered by subsequent insulating layers. Both types
of substrates (glass and paper) were coated with 6.2 m Parylene-C in a vapor deposition
instrument (Specialty Coating Systems, Indianapolis, IN) and ~50 nm of Teflon-AF 1600
(DuPont, Wilmington, DE) by spin-coating (1% wt/wt in Fluorinert FC-40, 1000 rpm, 30 s)
and post-baking at 160°C for 10 min. Indium-tin-oxide (ITO) coated glass plates (Delta
Technologies Ltd., Stillwater, MN) were also coated with 50 nm of Teflon-AF (as above) for
use as device top plates. Top and bottom plates were joined by stacking two pieces of
double-sided tape (~80 m ea.), resulting in a unit drop volume (covering a single driving
electrode) of ~440 nL (Design A) and ~750 nL (Design B). A side schematic of an
assembled device is shown in Figure 3.5.
40
Figure 3.5. Side schematic of a paper DMF device (not to scale). The bottom three layers (orange, turquoise, and yellow) comprise the multilayer coated paper53 used to form the devices described here. Working devices can also be formed from commercially available inkjet photo papers (e.g., Epson Premium Photo Glossy or HP Premium Plus Photo Glossy).
Reagent reservoirs were filled by pipetting the reagent adjacent to the gap between
the bottom and top plates and applying a driving potential to a reservoir electrode. The
conductivity across 2 cm long/150 μm traces of inkjet printed silver on paper (after sintering
for 5, 10, or 15 s) was measured with a Fluke 179 True RMS Digital Multimeter; 9 traces
were evaluated for each condition (3 on 3 separate devices). The resistance between contact
pads and driving electrodes was measured for all electrodes of Design A for 3 paper and 3
chromium on glass devices. These traces varied between 1–3 cm long and 100–150 m wide,
and the trace designs were identical for both paper and glass device formats. SEM images
were acquired with an S-3400N Variable Pressure SEM (Hitachi High Technologies
America, Inc., Schaumburg, IL) in secondary electron mode with an accelerating voltage of
41
5 kV. Surface roughness estimates are based on the arithmetic average of absolute height
values across a 125 x 125 m window (512 x 512 samples) measured in air with a Digital
Instruments Nanoscope IIIA multimode AFM (Bruker Nano Surface, Santa Barbara, CA) in
tapping mode (1 Hz scan rate). All images were subjected to a zero-order flatten and 2nd-
order plane fit filters prior to analysis. Devices were interfaced through pogo-pin connectors
to one of two variations of the open-source DropBot drop controller presented in Chapter 2,
either with56
or without integrated magnetic control. Electrodes were switched using solid-
state relays and velocities were measured using an impedance-based feedback circuit as
described in Chapter 2.
3.4.3 Homogeneous chemiluminescence assay
Drops of HRP standard (100 μU/mL in PBS supplemented with 0.05% v/v L64) and drops of
wash buffer were dispensed from reservoirs, mixed, and merged to form a dilution series (1x,
2x, 4x). One drop of SuperSignal chemiluminescent substrate was then dispensed, mixed,
and merged with each diluted drop of HRP, and the pooled drop was mixed for 60 seconds,
driven to the detection area, and the emitted light was measured after 2 minutes with an
H10682-110 PMT (Hamamatsu Photonics K.K.., Hamamatsu, Japan). Each condition was
repeated 3 times.
3.4.4 Rubella IgG immunoassay
Using DMF magnetic separation for reagent exchange and particle washing as described
previously,56
immunoassays were implemented in seven steps: (1) A ~1.6 μL drop (2 unit
volumes) containing paramagnetic particles was dispensed from a reservoir and separated
from the diluent. (2) One drop of rubella IgG standard (0, 1.56 or 3.125 IU/mL) was
dispensed, delivered to the immobilized particles, and mixed for 3 min. (3) The particles
42
were washed three times in wash buffer and separated from the supernatant. (4) One drop of
HRP conjugate solution was dispensed, delivered to the immobilized particles, and mixed for
2 min. (5) The particles were washed three times in wash buffer. (6) The particles were
separated from the wash buffer and resuspended in one drop of H2O2, and this drop was
merged and mixed with one drop of luminol-enhancer solution. (7) The pooled drop was
incubated for 2 min and the chemiluminescent signal was recorded using the PMT. Each
condition was repeated 2 times.
43
Chapter 4: Quantitative Characterization of Resistive
Forces
4.1 Introduction
Digital microfluidics (DMF), a technique in which drops of fluid are driven through endless
combinations of moving, merging, mixing, and splitting operations on an open surface,61
has
come of age. Whether the technique is applied to automated cell culture and analysis,62,63
multiplexed chemical synthesis,64,65
or parallel-scale clinical sample testing,66,67
the
flexibility, reconfigurability, and generic format of DMF has made it a uniquely powerful
tool for lab-on-a-chip applications. The most common form of DMF relies on electrostatic
forces to control the positions and volumes of moving drops on an array of electrodes. The
moving drops of DMF are contrasted with a related technique (often termed “electrowetting-
on-dielectric” or EWOD) in which the shapes of stationary drops are controlled by electrical
means (usually characterized in terms of their contact angle). The latter technique has great
promise for optical68,69
and display70,71
applications, but it is subject to a different set of
conditions and limitations relative to DMF. For example, while the electrical driving forces
for DMF and electrowetting are similar, the resistive forces that oppose the movement of
drops (for DMF) are distinct from those that oppose the shape changes of drops (for
electrowetting).* Furthermore, the oppositional forces in DMF often increase as a function of
device use (especially when the fluids to be manipulated contain proteins13,14,72
); over time,
these forces cause device failure and limit device lifetime and reliability. Surprisingly,
resistive forces on DMF are poorly understood. While several models and characterization
* Of course, drops in DMF experience shape/contact angle changes and are subject to forces opposing these
changes, but these are of secondary importance compared to the forces that resist bulk drop translation.
44
frameworks have been developed by physics and engineering-oriented groups,73–76
application-oriented researches (who are often more interested in developing new biological
and chemical assays) do not have access to simple tools to characterize these forces under
different operating conditions. It is this problem – the lack of an on-chip, integrated
framework for understanding and quantifying the resistive forces that oppose drop movement
in DMF – that motivates the work reported here.
In tackling the problem of resistive forces experienced by moving drops in DMF, we
note that in previous work, DMF has evolved largely through empirical refinements to
operating parameters (e.g., driving frequency and voltage) and device fabrication (e.g.,
choice of dielectric/hydrophobic materials). For example, for the case of driving frequency,
existing theories predict a reduced force as frequency is increased,29,77,78
but most research
groups have empirically settled on frequencies on the order of ~7–10 kHz62,65,79
with no
apparent theoretical justification for this choice. This empirical/intuitive approach to
parameter selection does not distinguish between their effects on driving forces (well
understood) and resistive forces (poorly understood), which confuses the issue further. We
propose that it is past time to investigate these aspects of uncertainty. Establishing a solid
theoretical foundation for DMF may be the key to unlocking its true potential by giving
researchers the requisite tools to push the technology to its limits. If the ultimate goal is
widespread adoption of DMF by non-expert users, factors such as device reliability,
consistency, and predictability will become increasingly important.
A few models have been proposed to describe the resistive forces present in DMF73–76
and several have been proposed for related electrowetting systems (e.g., sessile drop,80,81
capillary-rise,82,83
and electrostatic assist84
). Unfortunately, all of these previous studies
45
suffer from one or more of the following limitations: (1) they are limited to a small number
of test liquids (usually water or water plus salt), (2) they are limited to a single frequency,
(3) they rely on indirect measurements (e.g., contact angle changes), and/or (4) they are
limited to stationary drops. To address these limitations, we have developed a simple, on-
chip method for characterizing resistive forces based on drop velocity. We use this method to
explore the effects of surface tension, viscosity, conductivity, and frequency on the resistive
forces that are specific to moving (not stationary) drops. In addition, we demonstrate the
capability of this approach for quantifying resistive force dynamics – i.e., changes in the
resistive forces over time.
The results of this study point to broad trends that allow the user to predict the influence
of various parameters on drop mobility in DMF. Perhaps more importantly, the
characterization routines described here are fast (requiring only a few seconds) and fully
automated, meaning that they can be easily integrated into routine DMF experiments,
enabling real-time, quantitative, force-based diagnostics, and rapid characterization of new
liquids on-chip prior to use. This will facilitate ongoing characterization, the results of which
will continue to improve our understanding of the relevant device physics and facilitate a
more systematic approach to existing challenges such as increasing throughput, reducing
device costs, and improving reliability.
4.2 Background and theory
4.2.1 Dynamics of drop motion
The translation of a drop in a DMF device is an inherently complex process involving
internal three-dimensional flows,85,86
drop deformation,87
and contact line dynamics that are
46
not yet fully understood.88,89
However, to a first-order approximation, drop motion (i.e.,
position, velocity, and acceleration) along a single dimension is well described by a second-
order differential equation with the drop modeled as a point mass:73–76
dragviscousclfthe fffff
dt
xdm
2
2
(4.1)
where m is the mass of the drop, x is the position of the drop along the axis of translation, t is
time, fe is the electrostatic driving force, fth is a threshold force which must be overcome
before a stationary drop will start to move, fclf is contact line friction, fviscous is viscous
dissipation within the drop, and fdrag is viscous drag experienced by the drop as it moves
through a filler fluid.
In the work described here, we assume that all contact angles remain fixed at 90° and
that each drop moves as a solid-body (i.e., a cylinder confined between the top and bottom
plates) without changing shape in the x-y plane, i.e., a quasi-static assumption. There is
experimental evidence that drop length elongates during translation by ~5%87
; however, this
relatively small effect should not impact our results significantly. In general, the quasi-static
assumption is reasonable when inertial forces are small relative to surface tension, a
relationship quantified by the non-dimensional Weber number:
2
dt
dxL
forcestensionsurface
forcesinertialWe
(4.2)
where ρ is liquid density, L is the characteristic length (i.e., the electrode pitch in a DMF
device), dx/dt is the drop velocity, and γ is surface tension. For example, the highest Weber
number we expect under standard operating conditions is for a drop of water moving at
47
70 mm/s on 2.25 mm-long square electrodes, which has We ≈ 0.15.† Even this “worst-case”
scenario is well below the critical Weber number at which drops become unstable and break
up, Wecritical ≈ 10.90,91
We also assume that inertia is insignificant relative to viscous forces, a
ratio described by Reynold’s number:
dt
dxL
forcesviscous
forcesinertial
Re (4.3)
where μ is the dynamic viscosity of the liquid. For our experimental system, the highest
Reynolds number we expect is Re ≈ 160 for a drop of water moving at 70 mm/s on 2.25 mm-
long square electrodes.‡ This is well below the critical Reynold’s number at which Poiseuille
flow between parallel plates becomes turbulent, Recritical ≈ 5000.92
While inertia certainly
affects the complex dynamics of the liquid interface near the contact line (especially during
acceleration and deceleration of the drop), its relative contribution is low compared to other
forces experienced by the drop (e.g., viscous and surface tension), so we assume that the
2
2
dt
xdm term in Equation 4.1 can be safely ignored in the context of our simple point mass
model.
Finally, the capillary number gives a ratio of viscous to surface tension forces:
dt
dx
forcestensionsurface
forcesviscousCa
(4.4)
For water moving at up to 70 mm/s, Ca < 10-3
, suggesting that surface tension is the
dominant force which determines the shape of the drop once the flow is fully developed.
† ρ = 1000 kg/m
3 and γ = 0.072 N/m for water.
‡ μ = 0.001 Pa·s for water.
48
4.2.2 Electrostatic force
The electrostatic driving force used to transport drops on a DMF device fe, can be predicted
by considering the system (including the dielectric and hydrophobic layers, liquid, and filler
fluid) as a circuit model made up of resistors and capacitors. In this framework, known as the
electromechanical model, we calculate the total energy stored in the capacitive elements as a
function of the root-mean-squared driving voltage and frequency, and the x-position of the
drop (U, , and x, respectively):29,78
i i d
UxL
d
Ux
LxUE
i
2
i,fillerr.i,filler
i
2
i,liquidr.i,liquid0)()(
2),,(
(4.5)
where εr,i,liquid, Ui,liquid, and εr,i,filler, Ui,filler are the relative permittivities and voltage drops for
the sub-region of the activated electrode covered by the liquid drop and the filler fluid
surrounding the drop, respectively, ε0 is the permittivity of free space, and di is the thickness
of layer i. In a standard “two-plate” DMF system in which the bottom plate comprises square
driving electrodes (with pitch L) coated with dielectric and hydrophobic layers, and the top
plate comprises a contiguous counter-electrode coated with a hydrophobic layer, each i
subscript represents one of the dielectric, hydrophobic, or liquid/filler layers. The change in
energy as x goes from 0 to L is equivalent to the work done on the system; therefore,
differentiating Equation 4.5 with respect to x and dividing by L yields the electrostatic
driving force per unit length:
i i
ed
U
d
U
x
xUE
LUf
i
2
i,fillerr.i,filler
i
2
i,liquidr.i,liquid0)()(
2
),,(1),(
(4.6)
49
Note that this derivation ignores edge effects (i.e., fringe capacitance).88,93
Dividing by L
normalizes the force, putting it into the same units as surface tension (i.e., N/m), and allows
for simple scaling for different sizes of electrodes. The absolute force, which we define with
a capital letter Fe, is equal to the normalized force fe, multiplied by the y-axis projection of
the contact line overlapping the activated electrode, yproj:74
projee yUfUF ),(),( (4.7)
Every DMF device/liquid combination driven by an applied AC potential U has a
“critical frequency”, c, below which the drop behaves as a perfect conductor.29,78,94
This set
of frequencies ( < c) is sometimes called the electrowetting or EWOD regime, because
under these conditions, the contact angle of a stationary drop (with respect to the surface)
changes in response to U. Here, the capacitive contributions of the drop and filler fluid are
negligible, and Equation 4.6 simplifies to:
22
0
2
1
2)()( Uc
t
UUfUf device
deviceEWODe
(4.8)
where εdevice and t are the relative permittivity and thickness of the combined dielectric and
hydrophobic layers, respectively. The permittivity and thickness can also be expressed as a
single term, the dielectric capacitance per unit area, cdevice. Equation 4.8 can also be derived
from a thermodynamic perspective based on the Young-Lippmann equation,61,68–70,73–76
which describes the change in contact angle of a stationary drop in terms of voltage,
dielectric capacitance, and surface tension:
2
02
1coscos)( UcUf deviceUEWOD (4.9)
50
where θU is the apparent contact angle at three-phase contact line (formed between the drop,
the fluid surrounding the drop, and the surface of the device) when U is applied, and θ0 is the
contact angle when U is not applied.
Frequencies above c are said to operate in the dielectrophorietic (DEP) regime, in
which the impedance of the drop and dielectric are of the same order of magnitude. In this
case, Equation 4.6 simplifies to:
htht
UUfUf
devicefiller
filler
deviceliquid
liquiddeviceDEPe
2)()(
2
0
(4.10)
where εfiller is the relative permittivity of the filler-fluid, and h is the spacer-height between
the top and bottom plates.
4.2.3 Threshold force
The “threshold” force fth, constitutes the minimum force required for a stationary drop to
begin moving. It is analogous to the static friction experienced when sliding a solid across a
surface. The origin of this force is random pinning of the drop’s contact line to surface
heterogeneities, and this force is also responsible for contact angle hysteresis (i.e., the
difference between the advancing and receding contact angle) that is commonly reported for
sessile drops.74,76,95,96
The threshold force is straightforward to determine experimentally.
4.2.4 Dynamic friction
We use the term dynamic friction to refer to resistive forces that arise from dissipative
mechanisms that occur while a drop is in motion. These forces scale with drop velocity, and
51
include components such as contact line friction fclf, viscous dissipation within the drop
fviscous, and viscous drag of the filler fluid fdrag.73,75,76
Within our simplified model, a first component in dynamic friction is contact line
friction, an oppositional force that manifests at the three-phase contact line of a moving drop.
Contact line friction is generally modeled according to the Molecular Kinetic Theory (MKT)
proposed by Blake and Haynes,97
which treats the macroscale contact line velocity based on
the statistics of molecular scale hopping events along its length. If these
adsorption/desorption events occur at sites that are distributed isotropically, the contact line
velocity vcl, can be expressed in terms of the average length of these molecular displacements
λ, and their equilibrium frequency κ0:
Tk
fv
B
clf
cl
2
0 sinh2
(4.11)
where fclf is the force per unit length required to bias the rate of molecular displacements in
the preferred direction (i.e., the contact line friction force), kB is Boltzmann’s constant, and T
is the absolute temperature. For small forces (where fclfλ2 << kBT), Equation 4.11 can be
approximated with a linear relationship:
clf
B
cl fTk
v302
(4.12)
In the linearized form, λ and κ0 cannot be uniquely determined, and they are often grouped
together with the temperature and Boltzmann constant into a single term, ξclf, commonly
referred to as the contact line friction coefficient:
52
clf
clf
cl fv
1 (4.13)
Applying the linearized MKT to the case of a two-plate DMF device (i.e., by replacing the
contact line velocity vcl, with the drop velocity dx/dt) results in the following equation for the
contact line friction force:
dt
dxf clfclf 4 (4.14)
where the factor of 4 accounts for the contact lines at the leading and trailing edges of the
drop on the top and bottom plates. This assumes that the contact line friction is equivalent in
all four locations, which may not necessarily be the case.
A second form of dynamic friction associated with DMF is viscous dissipation within
the drop. This force is the result of friction between adjacent layers of fluid moving at
different velocities (i.e., velocity gradients):22
dt
dx
h
LCf
drop
vviscous
2 (4.15)
where μdrop is the dynamic viscosity of the drop and Cv is an empirical constant. When a drop
moves between parallel plates, it is common to assume Poiseuille flow (characterized by a
parabolic velocity profile and a no-slip boundary condition) which translates to Cv = 6.76,82,98
We note that the validity of the no-slip boundary condition is questionable (e.g., a “slipping”
contact line is the basis of the MKT described above) and Cv values of up to 10–15 have
been reported for drops moving across an open surface when a strong contribution from the
contact line exists.99
Cv = 10–15 is equivalent to increasing the viscous dissipation force by
53
about 2–3 times relative to the Poiseuille flow condition, perhaps as a result of internal
circulatory flows within the drop.
The final component of dynamic friction is viscous drag caused by the filler fluid.
This force scales linearly with the dynamic viscosity of the filler μfiller, and the drop velocity:
dt
dxCf fillerddrag (4.16)
where Cd is an empirical constant. When the filler fluid is air (the configuration used for all
experiments described in this thesis), fdrag is insignificant compared to the other forces and
can be ignored; however, this drag force is known to be significant for oil-filled devices.73,76
Many previous studies across a variety of experimental setups assume a single
dominant dissipation mechanism for drops moving under electrostatic actuation,21,25–28,36–38
and a few studies have tried to combine several mechanisms simultaneously.73,76
Based on
the geometrical scaling of the relevant forces, contact line friction is believed to be the
dominant effect for drops manipulated in the “single-plate” DMF configuration (a format that
is not used in most serious applications of DMF, as it is not capable of drop splitting or
dispensing). In contrast, viscous dissipation within the drop should be increasingly
significant for the “two-plate” DMF configuration (the format used in most serious
applications of DMF62–67
and in all experiments in this thesis), since its contribution is
expected to increase as the gap between plates h is reduced (see Equation 4.15). Therefore,
for the two-plate DMF format, we assume that dynamic friction is composed of multiple
components.73
Because the magnitude of each of these components (fclf, fviscous, and fdrag) is
scaled by its own empirical constant (ξclf, Cv, and Cd, respectively), their relative
54
contributions cannot be determined from a single experiment. We note that all of the
dynamic friction forces described above (fclf, fviscous, and fdrag) are proportional to drop
velocity; therefore, it is possible to group them into a single resistive force equal to:
dt
dxkffff dfdragviscousclfdf )()( (4.17)
where we define kdf as the dynamic friction coefficient. This definition makes no assumptions
regarding the origin of the dissipative components; therefore, in contrast to the frameworks
proposed previously,21,25–28,36–38
our analysis is generally applicable even when the relative
contributions of fclf, fviscous, and fdrag are unknown.
Within any particular DMF system (i.e., comprising the same liquid and device), kdf
can be measured and applied to predict drop dynamics. Using this coefficient and ignoring
inertial effects (i.e., the 2
2
dt
xdm term), we can simplify Equation 4.1 to:
dt
dxkfUf dfthe )()(),( (4.18)
where we explicitly allow for the possibility that fth and kdf may depend on frequency. We
note that kdf is likely sensitive to factors such as fluid viscosity, surface tension and device
geometry. By measuring changes in kdf with respect to these parameters, it may be possible to
experimentally decouple the contributions from fclf, fviscous, and fdrag.
4.2.5 Saturation
In stationary drops (electrowetting), increasing the driving force fe causes a decrease in the
contact angle according to the Young-Lippmann equation (Equation 4.9); however, beyond a
55
certain limit fsat,, the contact angle fails to decrease further, a phenomenon commonly
known as contact angle saturation. This saturation limit is often expressed as a voltage,31
but
converting it to a force per unit length using Equation 4.9 facilitates comparisons between
devices with different dielectric properties. Contact angle saturation has been well
characterized,31,96
and has been attributed to numerous causes, including dielectric
breakdown,101
charge trapping in the dielectric,101,102
air ionization in the vicinity of the
contact line,31
ejection of satellite drops,31,103
ion adsorption to the surface,104
a zero solid-
liquid surface tension limit,105
and liquid conductivity effects.106,107
Based on evidence for
each of these mechanisms, it seems unlikely that there is a single cause of contact angle
saturation; rather, the causative mechanism is probably dependent on experimental
conditions.§
In DMF, increasing the driving force fe causes an increase in the drop velocity,
analogous to the contact angle change in electrowetting. There is a commonly held
assumption that the fsat, observed in electrowetting corresponds to an upper limit for the
force that can be applied to the moving droplets in DMF without causing irreversible damage
to the device.74,76
This implies a velocity saturation force fsat,velocity above which there should
be no further increase in velocity in moving drops; however, we are aware of only a single
report75
of an experimental measurement of velocity saturation. This previous study75
used
the (less common) “single-plate” DMF format, and the authors reported similar observed
values for contact angle saturation (fsat,and drop velocity saturation (fsat,velocity), suggesting
the possibility that the two observed effects are caused by the same underlying mechanism.
The authors noted that velocity saturation was reversible and did not lead to deterioration of
§ For example, with very thin dielectrics, contact angle saturation is likely to be driven by dielectric breakdown,
but if the dielectric thickness is increased, another mechanism may become the new limiting cause.
56
the dielectric or hydrophobic film, which is an interesting result given that contact angle
saturation is often associated with irreversible surface and/or dielectric
modifications.31,101,102,104
There are no previous reports of experimental measurements of
velocity saturation in the (much more common) two-plate format, which is the format used in
all work in this thesis, and there is (of course) no evidence that fsat,in sessile drops on an
open surface has any relationship to fsat,velocity in moving drops in two-plate DMF.
4.2.6 Frequency effects
In DMF, the AC driving frequency of the applied potential affects the magnitude of the
electrostatic driving force since it determines the regime of operation, i.e., EWOD or DEP
(see section 4.2.2). According to the electromechanical interpretation, the magnitude of the
driving force is sigmoidal in shape with respect to frequency, approaching a constant high
value at low frequencies (i.e., the EWOD regime, where << c) and a constant low value at
high frequencies (i.e., the DEP regime, where >> c). Because the force in the DEP regime
is always lower than force in the EWOD regime, one would conclude (in considering only
the driving forces) that DC voltage should provide the maximum drop velocity in all cases.
In practice, most research groups use AC driving voltages with frequencies in the range of 7–
10 kHz,62,65,79
but (as noted above) the theoretical justification for this preference is missing.
There have been few studies investigating the effects of AC driving frequency on
resistive forces. Mugele and coworkers81,108
used the sessile drop configuration
(electrowetting) to study contact angle hysteresis for drops moved by gravity on an inclined
plane. When AC driving potentials were applied, reduced contact angle hysteresis was
observed81
as well as a lower angle of inclination necessary to initiate gravity-driven drop
57
movement on the surface108
relative to DC. The authors hypothesized that this effect stems
from vibrational energy introduced by AC potential-driven oscillatory motion of the contact
line (analogous to mechanical shaking109
), which acts to “de-pin” the contact line. It is
unclear from these experiments how this effect might translate to a two-plate DMF system in
which drops are moved by electrostatic forces. Normally, reduced hysteresis implies a lower
threshold force; however, if fe < fth, the contact line will not move and therefore cannot
impart any vibrational energy. Alternatively, this frequency effect may manifest as a
reduction in dynamic friction for AC actuation.
Several experiments and numerical simulations in formats related to DMF (e.g.,
electrostatically assisted roll-coating,84
electrowetting of sessile drops,110,111
and height-of-
rise between parallel plates112
) have demonstrated a lower saturation contact angle (i.e., an
increased fsat,) by increasing the AC driving frequency. A particular challenge with
interpreting these results is that one must be careful to decouple the effects of AC driving
frequency on fsat, from those caused by transitioning from the EWOD to the DEP force
regime. In the DEP regime, electrostatic forces are distributed across the interface between
the drop and the filler fluid, and the lateral force acting on the drop interface is decoupled
from changes to the contact angle; therefore, saturation mechanisms related to the shape of
the drop (i.e., those attributed to the highly concentrated electric fields defined by the sharp
wedge at the contact line), may be suppressed. But in practical terms, even if moving drops
in the DEP regime suppresses some mechanisms of saturation, DEP is impractical for most
common lab reagents, especially those used in biological applications (e.g., aqueous buffers
containing salts) for which the critical frequencies are on the order of MHz. For this class of
58
reagents, the most important (and still unanswered) question is whether or not saturation is
dependent on frequency when operating in the EWOD regime.
4.2.7 Proteins
Protein-containing solutions are an important reagent-class for applications in DMF,
including cell-culture,62,63
diagnostic testing66,67
and proteomics.113–115
But in devices
operated with air as a filler fluid, proteins present a challenge because they tend to adsorb to
(or “foul”) the device surface over time and render it hydrophilic, such that drops can no
longer be moved. The specific mechanism by which adsorbed proteins act to resist drop
movement (e.g., through an increase in fth or dynamic friction or both) remains an open
question. Previous work demonstrated that a family of surfactants called Pluronics (when
dissolved in drops to be manipulated) can significantly reduce this effect and enable long-
term movement of protein-rich solutions (e.g., cell media).13,14
An alternative strategy is to
engineer surface coatings that combine low friction with the capacity to repel proteins in
solution.72
These and other strategies provide partial solutions to the problem, but all DMF
devices used to manipulate drops containing proteins (operated in air) eventually succumb to
fouling and stop working. There is great need for quantitative methods for characterizing the
rate of protein adsorption to the device surface, and the ability to link these measurements to
changes in the resistive forces experienced by moving drops.
4.3 Results and discussion
4.3.1 Simulations of drop dynamics
A representative DMF device is shown in Figure 4.1a–b. As indicated, key parameters that
govern drop mobility in our simplified model include the electrical driving force fe, viscous
59
dissipation in the drop fviscous, the contact line friction force fclf, and drag from the filler fluid
fdrag. A threshold force fth (attributed to contact line pinning), constitutes the minimum fe
required for a stationary drop to begin moving. All of these forces are defined as line forces
(i.e., they have units of force per unit length), and as such, they have the same units as
surface tension. To convert line forces to an absolute force, we multiply them by the
projection of the drop’s contact line onto the y-axis (in the plane of the electrode,
perpendicular to the axis of motion). This projection is usually well approximated by the
pitch of the square electrodes, L. Figure 4.1c demonstrates the dependence of the driving
force on the drop’s x-position, a result of changes to the length of the contact line
overlapping the active electrode. Two phenomena are apparent: (1) drops moving a distance
x onto an actuated electrode experience a small force (when x is small relative to L) that
increases to a maximum force (as x approaches 0.5L) and then decreases to a smaller force
again (when x is large relative to L), and (2) the larger the diameter D of the droplet, the
sooner the maximum force is experienced. Figure 4.1d shows theoretical electrostatic
driving force calculations based on the electromechanical model (Equation 4.6) as a function
of driving frequency for DI water, Phosphate-buffered saline (PBS), and 30% glycerol in
water. Each liquid has a sigmoidal trend with the highest fe generated at low frequency. The
mid-point of each sigmoid is the liquid’s unique critical frequency c above which point the
force is reduced as it transitions from the EWOD to the DEP regime. This relationship of fe
to is widely known and understood,78,94,116
and suggests to most DMF users that (other
parameters being equal) lower driving frequency is preferable.
60
Figure 4.1. DMF drop actuation – driving and resistive forces. (a) Top-view schematic (x-y axes) of a drop moving onto an activated DMF electrode. yproj is the projection of the contact line overlapping the activated electrode (yellow line) onto the y-axis, and is proportional to the absolute electrostatic driving force, Fe. (b) Side-view schematic (x-z axes) showing the force balance acting on the drop, including driving force fe (green) and resistive forces fth, fclf, fviscous, and fdrag (red). (c) Simulation of the relative electrostatic force as a function of x/L for drops with different diameters D relative to the electrode pitch (D/L = 1.0, 1.1, 1.2 and 1.3 in blue, orange, green, and pink, respectively). (d) Simulation of the electrostatic driving force as a function of driving frequency for DI water (brown), 30% glycerol in water (yellow), and PBS (purple) on a DMF device actuated at 100 Vrms with cdevice ≈ 5.5 pF/mm2.
Figure 4.2 shows the simulated position, velocity, acceleration, and a breakdown of
simulated driving and resistive forces acting on a circular drop of PBS translating onto an
activated electrode. The parameters of the model were designed to reflect a common
experimental condition in which the diameter of the drop is 120% of the electrode width.
Under these conditions, the entire process (with the drop starting as being stationary on the
61
origin-electrode and ending as being stationary on the destination-electrode) is completed
within ~80 ms. The maximum velocity plateaus once the leading edge of the contact line
covers the complete width of the destination-electrode and remains relatively constant until
the trailing edge of the drop starts to cross onto the corners of destination-electrode (which
causes deceleration). This implies that the maximum velocity (in contrast to the
instantaneous velocity during acceleration and deceleration) should be insensitive to the
shape of the contact line in the x-y plane (i.e., entrance effects), and that applied force during
the window of time when the drop is moving at maximum velocity should be directly related
to feL. This is important because it provides justification for the simultaneous estimation of
applied force and maximum velocity independent of drop shape (which cannot be easily
determined from capacitive measurements).
As shown in Figure 4.2a–c, there is a nearly instantaneous acceleration in the first
few milliseconds to about 10% of the maximum velocity and a similarly rapid deceleration
once the drop has reached its equilibrium position on the destination electrode. This near-
instantaneous acceleration/deceleration and the relative insignificance of the mass times
acceleration term (brown) relative to the other forces plotted in Figure 4.2d supports the
hypothesis that the drop’s velocity at any given time has a very weak dependence on its mass
(i.e., there is very low inertia). For the majority of the translation time (including the window
used for analysis during which the velocity has achieved its maximum value), inertia makes
up less than 1% of the applied force. The more moderate acceleration and deceleration
plotted in the inset of Figure 4.2c are a product of the changing width of the contact line
projection yproj as the drop moves onto the destination electrode. Ensuring that the contact
line projection is equal to the full electrode width by using the maximum velocity seems to
62
be the more important criterion (as opposed to inertial considerations) for the establishment
of fully-developed flow in this simplified point mass model.
Figure 4.2. Simulated behavior of a drop of PBS as it moves onto an actuated electrode and magnitude of driving and resistive forces. (a) x-position (b) velocity (i.e., dx/dt), (c) acceleration (i.e., d2x/dt2), and (d) driving (fe – blue) and resistive (fth – green, fclf – orange, fviscous – pink, and m(d2x/dt2)/L – brown) forces acting on a drop estimated by numerically solving the ordinary differential equation of motion (Equation 4.1). The magnitude of fe and fth are estimated using Equation 4.6 (the
electromechanical model) based on a driving frequency of = 10 kHz and an applied voltage (for fe) of U = 100 Vrms and a threshold voltage (for fth, from exp. observation) of U = 70 Vrms. The dynamic friction forces fclf and fviscous are calculated from Equations 4.14 and 4.15, respectively (details in section 4.5.2). The inset in (c) shows a magnified view of the acceleration for an intermediate time range (i.e., immediately after the initiation of movement and before the rapid deceleration that occurs when the drop has covered the electrode).
63
4.3.2 Benchmarking and calibration of impedance and velocity measurements
Drops moving in DMF devices were evaluated using an impedance measurement scheme. A
test board (inserted into the circuit in place of a DMF device) was developed to characterize
and calibrate this technique (Figure 4.3a).**
Representative frequency responses of a 33 pF
NP0 capacitor on the test board as well as of drops of DI water and PBS on a DMF device
are shown in Figure 4.3b. At low frequencies, the capacitance of the electrode covered with
DI water is indistinguishable from the same electrode covered by PBS, but for frequencies
greater than ~5 kHz, the capacitance of the DI water drop is reduced relative to PBS. This
result is consistent with a critical frequency c for water in the range of 5–20 kHz.††
Importantly, this experiment demonstrates the ability of this technique to determine whether
or not a liquid is being operated near its critical frequency.
Figure 4.3c and d show the root-mean-squared error in measured capacitance relative
to the nominal values of the NP0 capacitors on the test board (all measurements were
performed at 100 Vrms). In the majority of cases, errors are less than ~5% (comparable to the
tolerance of these capacitors, +/- 5%), and the errors are relatively insensitive to frequency.
The highest errors are seen at low capacitance values < ~3.3 pF, and since drops/electrodes
on typical DMF devices have capacitances in the range of 20–30 pF, these results provide
confidence in the ability of the techniques described here to precisely determine the
capacitance (and therefore, the position) of drops to within about 5%.
**
NP0 capacitors were chosen for the test-board because they exhibit very low frequency and temperature
dependence. ††
This (measured) critical frequency is an order of magnitude higher than that (predicted) in Figure 4.1d,
which is not surprising since the conductivity of DI water is known to increase upon exposure to atmosphere.
64
Figure 4.3. Test board and results for the impedance measurement circuit. (a) Photograph of the test board (bearing 40 NP0 capacitors) used to calibrate and benchmark the impedance measurement circuit for application to drop measurements. (b) Capacitance measurements across a range of frequencies for a 33 pF NP0 capacitor (green triangles) on the test board, a drop of PBS on a device (blue circles), and a drop of DI water (orange squares) on a device; error bars are +/- 1 standard deviation but are obscured by the markers. (c) Heat map showing the root-mean-squared error (dark – low error, bright – high error) from repeated measurements of the capacitance of all capacitors on the test board as a function of nominal capacitance and AC frequency (n = 10 for each frequency/capacitor pair). (d) Histogram of the data in c.
Having validated the performance of the measurement circuit, we subsequently
turned to experimental observations of drops moving onto an activated electrode in DMF.
For these experiments, we chose to use an aqueous drop with surfactant (PBS + 0.02% F88)
typical of common biological buffers. Note that the velocity of such drops is lower than that
65
of pure water or PBS (simulated in Figure 4.2), which results in a greater number of
capacitance readings per drop translation, and therefore longer time scales. Figure 4.4
demonstrates the procedure for converting a dynamic capacitance measurement of a moving
drop into an estimate of x-position through multiplication of a scaling factor (cdeviceL)-1
. The
slope of the linear fit to the x-position vs. time data (Figure 4.4b) represents the mean drop
velocity (dx/dt)avg, which is plotted in Figure 4.4c along with the “raw” instantaneous
velocity data. Note that raw velocity data tends to be very noisy because it is calculated from
the first difference (i.e., a numerical estimate of the derivative) of the x-position with respect
to time. Derivatives tend to amplify noise, so it is important to filter this data to recover a
smoother signal.
Figure 4.4. Estimation of drop velocity from capacitance measurements. (a) Measured capacitance as a function of time as a drop moves onto an activated electrode. (b) x-position as a function of time (solid blue line) calculated by scaling capacitance in (a) by (cdeviceL)-1 and a linear fit (dashed orange line) to the data between x = 0 and x = 0.95L. The slope of this line represents the mean drop velocity – i.e., (dx/dt)avg. (c) First-order finite-difference of the x-position data (solid blue line) which represents the “raw” velocity, and the mean velocity (dashed orange line).
Figure 4.5 compares the results of two different filtering strategies for handling the
noisy x-position data for moving drops: a simple moving average and a 3rd
-order Savitzky-
Golay filter.117
Moving averages are performed by convolving a flat symmetric window
function with the noisy data. Although this procedure is effective at reducing noise, it tends
66
to distort the underlying signal by suppressing the peak-height and broadening the peak
shape, and the relative degree of these distortions increases with the filter window width.
Savitzky-Golay filtering, also performed by convolving a window function with noisy data,
is equivalent to fitting an nth
-order polynomial at each time point based on its neighboring
data points. This helps to preserves the overall shape of the signal (e.g., peak height and
width), and these filters are commonly used in applications where such features are important
(e.g., spectroscopy).117
Note that there are several trade-offs to consider when choosing a
Savitzky-Golay filter implementation. Higher polynomial orders enable the fitting of more
complex signals but provide less noise suppression. The width of the filtering window is also
important, as it also represents a trade-off between noise suppression and signal distortion. In
general, the filtering window should be of comparable width to the minimally resolvable
feature with the minimum order that can adequately describe the signal. We have found that
3rd
-order filters with windows that are half the width of the drop velocity curve – equivalent
to 1/5.0
avgdtdxL – represent a good compromise between signal fidelity and noise
suppression (e.g., see the filter with the 252 ms window in Figure 4.5b). Note that
approximately doubling the width of the filter window (e.g., to 511 ms in Figure 4.5b) has
little effect on the shape of the resulting filtered velocity curve. Thus all experiments
reported here used a 3rd
-order Savitzky-Golay filter with a window that is half the width of
each velocity curve.
67
Figure 4.5. Comparison of filter-types for drop velocity data. (a) Raw velocity data (grey) and moving average-filtered drop velocity for a window size of 252 ms (solid blue line) and 511 ms (orange dashed line). (b) Raw velocity data (grey) and 3rd-order Savitzky-Golay-filtered drop velocity for a window size of 252 ms (solid blue line) and 511 ms (orange dashed line).
4.3.3 Characterization of non-protein-containing liquids
The goal of the work described in this chapter was to understand the nature of resistive forces
that oppose drop-movement in DMF. Our primary tool in this work is the “velocity-force”
curve, in which the maximum velocity is recorded from velocity-time profiles (introduced in
section 4.3.2) for drops moved with different driving forces fe (modulated by applying
different driving voltages U). We began our study with the (simplest) case of liquids not
containing proteins, as typified by the data in Figure 4.6a. Two phenomena are apparent in
these data. First, at low fe, there is a reproducible, linear relationship between drop velocity
and force. Second, at high fe, there is apparently a velocity saturation force fsat,velocity, such that
for fe > fsat,velocity, the slope of the velocity-force curve is dramatically reduced. As described
in section 4.2.5, this “velocity saturation” phenomenon has been experimentally
demonstrated only once before (by Bavière et al.75
) for a DMF device in the so-called “one-
plate” orientation (a format that is not commonly used). As far as we are aware, the data
68
shown in Figure 4.6a is the first observation of this phenomenon in the (much more
common) two-plate DMF orientation.
Figure 4.6. Velocity-force characterization for a non-protein containing solution. (a) Experimentally observed maximum velocities for drops of PBS + 0.1% L64 as a function of driving force fe with identification of the threshold force, fth, the coefficient of dynamic resistance, kdf, and the velocity saturation force, fsat,velocity. Velocities determined to be above and below fsat,velocity are represented in blue circles and blue triangles, respectively (and fe > fsat,velocity is shaded grey). (b) Maximum velocity as a function of time for repeated drop movements between two electrodes driven by forces between 15–40 μN/mm (from lowest to highest: blue, orange, green, pink, brown, and purple).
Figure 4.6b shows the results of a related experiment using the same liquid and DMF
device. In this case, the maximum drop velocity is plotted as a function of time for repeated
drop movements at a range of applied forces from 15–40 μN/mm. There are several
interesting features apparent from these results. First, when fe < fsat,velocity, drop velocity is
stable, allowing for more than 50 translations over the same pair of electrodes without
appreciable changes; however, when fe > fsat,velocity, maximum velocity decays rapidly (within
seconds) and this decay appears to be exponential with time. Second, for forces exceeding
fsat,velocity, the decay rate increases with increased fe, as demonstrated by comparing the
velocity decay for drops driven by 35 and 40 μN/mm (the brown and purple data points in
69
Figure 4.6b, respectively). Finally, it appears that fsat,velocity can be estimated by two methods.
One can either sweep droplets through a range of forces to identify the inflection point at
which the slope in the velocity decreases (as in Figure 4.6a), or one can evaluate repeated
drop movements as a function of time (e.g., over a period of several seconds to minutes), and
repeat this process for a range of increasing forces to identify the force at which velocity
begins to decay (as in Figure 4.6b) – the results obtained using both methods are in close
agreement (fsat ≈ 35 μN/mm). Most importantly, as far as we are aware, the trend observed in
Figure 4.6b (and which we have confirmed for all other liquids tested) represents the first
conclusive evidence that drop velocity on DMF decreases as a function of repeated drop
movements when fe > fsat,velocity. Further, the effect appears to be permanent. After completing
this type of experiment, water tends to preferentially “stick” to the surface of a device on
electrodes that have been operated at fe > fsat,velocity (indicating a long-term change in surface
energy). In addition, after operation at fe > fsat,velocity, when fe is subsequently reduced to a
“safe” level, the drop velocity does not return to the predicted value. The most probable
cause of this effect is the trapping of ions (i.e., charges) on the device surface.102
Note that
this contrasts with the observations of Bavière et al.,75
who reported a similar but reversible
effect for single-plate devices.
As noted in the introduction, DMF users have often adopted an empirical approach to
choosing a driving potential U and frequency in DMF experiments with different fluids and
devices. The data in Figure 4.6 suggests that this approach carries great risks for device
longevity – one should (apparently) determine the fsat,velocity and be sure to work with driving
forces below that limit. In fact, we propose that “best practice” for a DMF user evaluating a
new condition is to perform a rapid velocity-force characterization, which will identify
70
fsat,velocity and also the threshold force fth (the x-intercept for fe < fsat,velocity) and the dynamic
friction coefficient kdf (the inverse of the slope for fe < fsat,velocity).
DMF users regularly work with fluids that span a wide range of physicochemical
parameters including conductivity, surface tension, and viscosity. To elucidate the effects of
these factors on fth, fsat,velocity, and kdf, we performed velocity-force characterization
experiments for several aqueous liquids including (1) DI water, (2) PBS, (3) water +
0.01% F88 (DI water + 0.1 M NaCl + 0.01% F88 Pluronic), and (4) 30% glycerol (70% DI
water + 30% glycerol + 0.1 M NaCl) across a range of frequencies from 100 Hz to
10 kHz. Specifically, the effect of conductivity was tested by comparing PBS to DI water
(σPBS ≈ 1.6 S/m versus σwater ≈ 5.5×10-6
S/m),118,119
surface tension was tested by comparing
water + 0.01% F88 to DI water alone (γwater+0.01%F88 ≈ 50 μN/mm versus γwater ≈ 72 μN/mm),
120 and viscosity was probed by comparing 30% glycerol to DI water alone
(30% glycerol ≈ 2.5 mNs/m2 versus water ≈ 1.0 mNs/m
2).
119,121 In these experiments, NaCl was
added to liquids 3 and 4 to increase their critical frequencies beyond 10 kHz, ensuring that
any perceived differences were not attributable to the EWOD-DEP transition (see section
4.2.6). The data from these experiments are recorded in Figure 4.7. A summary of our
conclusions from these experiments is described in Table 4.1; specific cases are highlighted
below.
Threshold forces for drop movement (Figure 4.7a) varied by a factor of ~2, ranging
from 12–19 μN/mm. The most interesting trends were those observed for surface tension
(small reduction of fth for liquid 3 relative to liquid 1) and viscosity (small reduction of fth for
liquid 4 relative to liquid 1). The trend of reduced fth for low surface tension drops is
reproducible, supported by additional experiments with other low-surface tension liquids –
71
e.g., methanol and ethanol (data not shown). The trend of reduced fth for high viscosity drops
is unexpected and contrary to previous reports in which viscosity was found to be either
insignificant73
or to result in increased29
fth. Further testing is required to confirm the
relationship between fth and viscosity.
Figure 4.7. Threshold forces, saturation forces, and dynamic friction coefficients for various liquids experimentally determined from velocity-force curves. (a) Threshold force fth, (b) velocity saturation force fsat,velocity, (c) and dynamic friction coefficient kdf estimates for (1) DI water (blue squares), (2) PBS (orange circles), (3) water + 0.01% F88 (green ), and (4) 30% glycerol (pink ) across a range of frequencies from 100 Hz to 10 kHz. Error bars are +/- 1 standard deviation (n = at least 3 measurements per condition) and trend lines are linear (a and b) and quadratic (c).
72
Parameter Driving frequency Surface tension Viscosity Conductivity
Threshold force
(fth)
Weak increase of
fth with increasing
frequency
Weak increase
of fth with
increasing
surface tension
Weak decrease
of fth with
increasing
viscosity
No
dependence
of fth on
conductivity
Saturation force
(fsat,velocity)
Weak increase of
fsat,velocity with
increasing
frequency (for
most liquids)
Strong
increase of
fsat,velocity with
increasing
surface tension
No dependence
of fsat,velocity on
viscosity
Strong
decrease of
fsat,velocity with
increasing
conductivity
Dynamic friction
coefficient (kdf) Strong decrease
of kdf with
increasing
frequency (up to
~1 kHz for most
liquids)
Strong
decrease of kdf with increasing
surface tension
Strong
increase of kdf
with increasing
viscosity
Weak
decrease of kdf
with
increasing
conductivity
Table 4.1. Summary of findings from velocity-force characterization experiments. Bright and light red represent strong and weak decreases; bright and light green represent strong and weak increases.
Velocity saturation forces for drop movement (Figure 4.7b) also varied by a factor of
~2, ranging from ~25–50 μN/mm. As noted in section 4.2.5, there are open questions about
the relationship of two (potentially related) “saturation” effects – that of the velocity of
moving drops in DMF (fsat,velocity, as measured here), and that of contact angles of sessile
drops in electrowetting (fsat,, characterized previously31,96
). The most interesting trends
observed here were those for surface tension (large reduction of fsat,velocity for liquid 3 relative
to liquid 1 and conductivity (large reduction of fsat,velocity for liquid 2 relative to liquid 1). The
trend of reduced fsat,velocity for reduced surface tension drops mirrors that of a previous report31
of reduced fsat, for reduced surface tension drops in electrowetting. In contrast, the trend of
73
reduced fsat,velocity for increased conductivity drops (also observed for DI water + 0.1 M NaCl,
data not shown) is opposite to that of a previous report31
of increased fsat, for increased
conductivity drops in electrowetting. Whether this difference is related to specifics of the
experimental setups (e.g., device geometries, dielectric materials, etc.) or to a more general
distinction between the phenomena of velocity saturation and contact angle saturation
remains to be determined.
Dynamic friction coefficients for drop movement (Figure 4.7c) varied by nearly an
order of magnitude (0.3–2.5 μNs/mm2), suggesting that kdf is the dominant cause of
differences in drop movement. The most interesting trends were those observed for driving
frequency (large reduction of kdf for all liquids tested as is increased from 100 Hz to
~2 kHz), surface tension (large increase of kdf for liquid 3 relative to liquid 1) and viscosity
(large increase of kdf for liquid 4 relative to liquid 1). The trend of reduced kdf for increased
driving frequencies has never before been observed and reported. We are not sure of the
reasons for this effect, but hypothesize that it is related to the frequency-dependent hysteresis
and contact line pinning results observed previously81,108
in sessile drops. Regardless, this
observation provides a possible rationale for the fact that users have empirically/intuitively
gravitated to the = 7–10 kHz range for most practical DMF experiments, despite
widespread understanding that low driving frequencies are best to maximize fe (to remain in
EWOD vs. DEP regime; see section 4.2.6). The other two strong trends observed for the
dynamic friction coefficient, increased kdf for low surface tension drops and increased kdf for
high viscosity drops, are the opposite of the weak trends observed for fth. That is, it seems
that initiating drop movement is more facile for low surface tension or high viscosity liquids
(lower fth), but once moving, such drops tend to move more slowly (higher kdf). These types
74
of interesting dynamics, which could certainly influence what constituents a user is tempted
to dissolve in fluid manipulated by DMF, are only available through a thorough
understanding of the nature of the various resistive forces in DMF.
The method described above provides convenient means to determine fth, fsat,velocity,
and kdf and to evaluate their various effects on drop movement by DMF. But kdf is composed
of multiple forces, including contact line friction, viscous dissipation within the drop, and
drag from the filler fluid (which we assume to be negligible for cases in which air is the filler
fluid). To facilitate comparison of this new parameter with previous results from the
literature, we can decompose kdf into its contact line friction and viscous dissipation
components using some simplifying assumptions. Assuming Poiseuille flow (i.e., Cv = 6), we
can estimate the viscous fraction of kdf using Equation 4.24 (see section 4.5.4) to be at least
10–50% of kdf across all conditions tested. Note that this value is frequency independent, and
represents a lower bound on the viscous fraction, as Cv = 6 is a conservative estimate. As
shown in Figure 4.8a, the relative viscous contribution becomes increasingly significant
with increasing frequency. By subtracting the (estimated) viscous fraction from the
(experimentally measured) kdf and assuming that the remainder is caused by contact line
friction, we extract an estimate for the contact line friction coefficient ξclf, using Equation
4.25. As shown in Figure 4.8b, ξclf decreases with increasing frequency for all liquids –
except for the low surface tension liquid 3 for which we have no low-frequency
measurements of kdf.
The values determined here for the contact line friction coefficient of water on
Teflon-AF (ξclf = 0.1–0.35 μNs/mm2) are comparable to (though slightly higher than) values
reported in the literature (ξclf = 0.04–0.08 μNs/mm2).
73,100,122 Our potential over-estimate of
75
ξclf is consistent with our conservative estimate of Cv (i.e., assuming Cv > 6 would bring our
ξclf values into closer agreement with previous reports). Future experiments will attempt to
decouple the contact line friction and viscous components of kdf experimentally, by varying
device geometry and liquid viscosities.
Figure 4.8. Viscous and contact line friction contributions to experimentally measured dynamic friction coefficients (assuming Poiseuille flow). (a) Estimated viscous fraction of kdf and (b) estimated contact line friction coefficient for (1) DI water (blue squares), (2) PBS (orange circles), (3) water + 0.01% F88 (green ), and (4) 30% glycerol (pink ) across a range of frequencies from 100 Hz to 10 kHz. Trend lines are linear for a and quadratic for b.
Finally, having recorded measurements of fth, kdf, and fsat,velocity for the various test
liquid/frequency conditions, it is possible to represent safe operating limits for DMF in terms
of the net force at saturation or the saturation velocity (i.e., the maximum force that can be
applied and the maximum velocity that can be achieved without causing irreversible damage
to the device). The net force at saturation plot in Figure 4.9a demonstrates that some liquids
(e.g., those with low surface tension) must be manipulated within a narrow range of applied
76
forces to prevent saturation-induced velocity decay (and device damage).‡‡
The saturation
velocity plot in Figure 4.9b suggests that the maximum safe drop velocity is achieved for DI
water relative to all other test liquids. Increasing the viscosity or conductivity or reducing the
surface tension all seem to reduce the maximum achievable velocity. For all liquids tested,
the highest (safe) drop velocities were realized at frequencies > 1 kHz. Technical limitations
of our system prevented the testing of frequencies beyond 20 kHz, so we are unable to
predict whether higher frequencies may produce further benefits; however, the velocity of
some liquids (e.g., PBS and 30% glycerol) appears to plateau for frequencies > ~2 kHz.
Figure 4.9. Net force at saturation and saturation velocity for various liquids. (a) Net force at saturation and (b) saturation velocity (i.e., the maximum drop velocity at fe = fsat) for (1) DI water (blue squares), (2) PBS (orange circles), (3) water + 0.01% F88 (green ), and (4) 30% glycerol (pink ) across a range of frequencies from 100 Hz to 10 kHz. Error bars are +/- 1 standard deviation (n = at least 3 measurements per condition) and trend lines are linear.
To summarize the results presented in section 4.3.3, we have demonstrated a simple
and automated method for measuring the resistive forces that oppose drop-movement in
‡‡
This is why low-frequency data were impossible to collect for the low-surface tension test-liquid (liquid 3) in
Figure 4.7–9.
77
DMF: fth, kdf, and fsat,velocity. When liquids are driven by sub-saturation applied forces (i.e.,
when fe < fsat,velocity), drop translation is a fully reversible process as demonstrated by a
consistent drop velocity over time when using the same set of electrodes. “Safe” drop
velocities (that do not damage the device) can be increased by reducing fth or increasing
fsat,velocity or by reducing the dynamic friction coefficient, kdf; however, these parameters are
often coupled and have opposite effects on the resulting drop velocity (e.g., reducing surface
tension lowers fth, but increases kdf and reduces fsat,velocity). One parameter that seems to
universally increase the maximum safe drop velocity is driving frequency. For all liquids
tested, the maximum velocity was achieved for frequencies > 2 kHz, and the dominant
cause seems to be related to a frequency dependent reduction of kdf. Thus, contrary to what
one might assume from concern about maintaining a higher “EWOD-regime” driving force,
consideration of the resistive forces suggests that it is nearly always best to use higher
driving frequencies, particularly when working with fluids with high conductivity§§
(i.e.,
those with high c).
4.3.4 Characterization of protein-containing liquids
After evaluating the resistive forces that oppose the (simple) case of drops not containing
proteins, we turned our attention to the more complex case of fluids containing proteins. We
chose whole (undiluted) blood as our text matrix, as this liquid (a complex mixture of
proteins, salts, cells, and other constituents) is simultaneously very important for clinical
applications of DMF,66,67
but is also the “worst case” fluid to work with, as it fouls device
surfaces (rendering them unusable) very rapidly. In fact, we are not aware of any previous
report of manipulating undiluted blood in DMF devices filled with air; presumably, previous
§§
Note that many fluids that are relevant to biochemical applications, including many protein-containing
solutions (such as whole blood), fall into this category.
78
users have found device-fouling from blood to be an insurmountable challenge. In addition to
reducing the rate of protein adsorption (and the corresponding rate of velocity decay), our
findings in section 4.3.3 suggest that the addition of surfactants also increases net force
through a reduction of fth; without surfactants, drops of blood may have such a high initial fth
that they are impossible to move under any operating conditions. Thus, in all data reported
below, a surfactant additive was dissolved in the blood (0.1% L64 Pluronic) to reduce fth to a
level compatible with drop manipulation for periods of up to several minutes.
In initial experiments, care was taken to complete velocity-force characterizations of
blood as rapidly as possible (within 30 s of depositing the drop onto the device) to limit the
effects of fouling (Figure 4.10a). As shown, under these conditions, the data appear similar
to those observed for non-protein containing liquids (Figure 4.6a), allowing for
determination of fth, kdf, and fsat,velocity. In the next set of tests, blood drops were constantly
actuated for up to two minutes per electrode (i.e., 8 minutes total) to evaluate the effects of
device contact-time. As shown in Figure 4.10b, the maximum velocity decreases as a
function of time in all conditions, presumably because proteins (or cells or other constituents)
are adsorbing to the surface, rendering it more hydrophilic (and thus increasing the resistive
forces). This stands in marked contrast to the protein-free scenario (Figure 4.6b), in which
velocity only decreases as a function of time when fe > fsat,velocity. Further, the rates of velocity
decay in blood (Figure 4.10b) for fe < fsat,velocity are apparently highest at the lowest driving
forces, a (potentially surprising) result made more obvious in Figure 4.10c. This suggests an
optimal applied force foptimal (just less than fsat,velocity) that minimizes the rate of velocity
decay. Finally, the velocity decay curves were extrapolated to determine the device lifetime
tL, defined as the total duration that a drop can be moved continuously before it drops below
79
a “minimum useable velocity” (Figure 4.10d). Perhaps not surprisingly, the optimal force
that minimizes velocity decay was found to be the same force that ensures the greatest device
lifetime (although this may not always be the case).
Figure 4.10. Velocity-force characterization for a “worst case” protein-containing solution: whole blood. (a) Experimentally observed maximum velocities for drops of defibrinated sheep blood + 0.1% L64 as a function of driving force fe. Velocities determined to be above and below fsat,velocity are represented in blue circles and blue triangles, respectively. (b) Maximum velocity as a function of time for repeated drop movements between two electrodes driven at 15 μN/mm (blue), 20 μN/mm (orange), 25 μN/mm (green), 30 μN/mm (pink), 35 μN/mm (brown), and 40 μN/mm (purple). Dashed lines are fitted exponential decay curves. (c) Velocity rate constants for the exponentials fit to the data in b (higher value means a slower decay). (d) Device lifetime tL, defined as the duration for which a drop can be moved continuously before dropping below a “minimum usable velocity” (arbitrarily chosen here to be 1 mm/s). Arrows in c and d indicate the optimal force for minimizing velocity decay and maximizing device lifetime. The grey-shaded regions of a, c and d indicate fe > fsat,velocity.
80
Figure 4.11. Evolution of the velocity-force curve, threshold force, and dynamic friction coefficient for a protein-rich solution. (a) Velocity-force curve, (b) threshold force, and (c) dynamic friction coefficient as a function of contact time tc with drops of defibrinated sheep blood + 0.1% L64 Pluronic for tc = 0 min (blue circles), 5 min (orange ▲), 10 min (green squares), and 15 min (pink ▼). Data in b and c were extracted from fitting the velocity-force curves in a. The dashed black lines in b and c show the proposed model (Equation 4.19), with estimates for fth(0), fth(∞), 1/a, k1, k2 and 1/b.
Whereas Figure 4.10a plots a velocity-force curve at a single time point, we are
interested in the evolution of this curve as a function of (cumulative) protein contact-time
with the destination electrode tc. Figure 4.11a shows the evolution of the velocity-force
curve for tc = 0, 5, 10, and 15 min, which allows the extraction of the threshold force fth
(Figure 4.11b) and dynamic friction coefficient kdf (Figure 4.11c). As shown, both
parameters increase with contact-time, but their shapes are distinct. In an attempt to explain
these results, we developed an empirical model that captures the time-dependent increase in
resistive forces:
c
c
bt
at
thththe
cdf
cthec
ekk
effff
tk
tfft
dt
dx
21
)()0()(
)(
)()(
(4.19)
where dx/dt is the drop velocity, fth(0) and fth(∞) are the threshold forces on an electrode at
tc = 0 and tc = ∞, respectively, k1 and k2 are different components of the dynamic friction
coefficient at tc = 0, and a and b are time constants. This model is represented by dashed
81
black lines in Figure 4.11b and c. Note that k1 represents the fraction of kdf that is insensitive
to protein contact-time. A hypothesis that is consistent with this observation is that k1
corresponds to viscous drag within the drop and that cbtek2 describes the contact line friction
(which we would expect to increase with protein accumulation).
The full empirical model of time-dependent resistive force increase for protein-
containing solutions (Equation 4.19) is useful, but greater insight can be obtained by
assuming that cbtekk 21 (which is reasonable as the latter term rapidly increases with tc),
allowing us to separate Equation 4.19 into two separate, exponentially decaying components,
A and B:
ctbaththc e
k
fftA
)(
2
)0()()(
(4.20)
cbtthec e
k
fftB
2
)()( (4.21)
where the sum of the two components represents an approximation of the full model:
)()()( ccc tBtAtdt
dx (4.22)
One key finding from the simplified model is that the decay rate of component A (i.e., a + b)
is by definition greater than or equal to the decay rate of component B (i.e., b) meaning that
A represents a fast decay process relative to B. The other important insight from the
simplified model is that the driving force fe does not appear in component A – i.e., the fast
decay process is independent of the applied force. Therefore, the driving force acts to
82
modulate the relative weighting of the two components – that is, higher driving force makes
the slow decay the dominant effect. This is highlighted in Figure 4.12, which shows
simulation results (based on the parameters extracted from Figure 4.11) of maximum drop
velocity as a function of time for two applied forces, 20 and 30 μN/mm. Component A
represents a larger relative contribution in the 20 μN/mm condition (Figure 4.12a) than in
the 30 μN/mm condition (Figure 4.12b). Note that the simplified model (Equation 4.22,
dashed black line) closely approximates the full model (Equation 4.19, blue line) in both
conditions.
The fact that the velocity of protein-containing drops decays exponentially with tc is
not surprising given that plasma proteins are known to accumulate exponentially on Teflon
surfaces as a function of time.123
The multiple decay components observed here suggests that
there is more than one process occurring (e.g., protein adsorption/desorption and Pluronic
adsorption/desorption) or that as molecules adsorb to the surface, the resulting changes in
fth(tc) and kdf(tc) scale with different proportionality constants. The fast decaying component
A approaching zero as a function of time is equivalent to fth reaching its equilibrium value
fth(∞). A hypothesis that might explain the timing of this event (i.e., the time at which A ≈ 0)
is that at this time, the device surface has become saturated with one (or multiple) molecular
species. Beyond this time point, further reduction in drop velocity is a result of increases to
kdf(tc).
83
Figure 4.12. An empirical model of the effects of fouling on drop velocity. Simulated velocities as a function of contact time for a drop of defibrinated sheep blood + 0.1% L64 Pluronic driven repeatedly between two electrodes by a force of (a) 20 μN/mm and (b) 30 μN/mm. Both plots show the full model (Equation 4.19, solid blue line), the simplified model (Equation 4.22, dashed black line) and its two components: A (Equation 4.20, dashed green line), and B (Equation 4.21, dashed pink line).
It remains to be seen whether the protein-fouling model outlined above will hold
more generally across a wide range of protein-containing liquid/surfactant combinations;
however, it does capture the behavior of all the data we have collected for several different
Pluronic surfactants mixed with sheep blood and with various concentrations of bovine
serum albumin (BSA) in PBS (data not shown). We have also seen clear experimental
evidence of bi-exponential decay for these additional fluids (similar to that depicted in
Figure 4.12a). Future work will examine the effect of different surfactants, proteins, and
various concentrations thereof to see if we can attach any physical meaning to the various
model parameters. Being able to extract specific information about the surface forces
involved in protein adsorption and the rates of these processes makes it possible to
objectively compare the effects of biofouling across different experimental systems (e.g.,
different surface coatings72
) and may provide insight into the underlying mechanisms.
84
To summarize the results presented in section 4.3.4, the drop-velocity
characterization methods described here allowed us to rapidly converge on experimental
conditions (e.g., Pluronic species, concentration, and applied force) capable of manipulating
undiluted blood for up to 15 min per electrode, a significant advance for this “worst-case”
biological sample which has never been reported to move in an air-filled DMF device. In
general, the velocity of protein-containing drops decreases over time, and there exists an
“optimal” fe for slowest decrease of velocity that is just below the point of velocity
saturation. We have developed a simple and automated method for determining this optimal
force and for predicting its corresponding device lifetime. We also presented a theoretical
model describing the time-dependent resistive force dynamics. We anticipate this model
becoming a useful tool in generating greater insight into the processes driving biofouling and
leading to new strategies for combating its effects.
4.4 Conclusion
In conclusion, we have developed and validated a set of fully automated techniques for
characterizing resistive forces on DMF as described by a simplified model including the
parameters fth, fsat,velocity, and kdf. These methods are based on the simple idea of using drop
velocity (determined through dynamic capacitance measurements) as a proxy for the resistive
forces experienced by moving drops. In general, non-protein containing liquids can be
translated repeatedly across a set of electrodes with no appreciable reduction in velocity
when fe < fsat,velocity. Forces in excess of fsat,velocity cause drops to slow down over time, and this
effect appears to be irreversible. For protein-containing solutions, velocity decays under all
force conditions, but the rate of decay varies with fe; in each case, there exists an optimal fe
just below fsat,velocity for which device lifetime is maximized. Thus, for all liquids (with and
85
without proteins) translating drops just below fsat,velocity maximizes both velocity and device
lifetime. The ability to quickly and automatically determine the precise value of fsat,velocity for
any unknown liquid on-chip represents an important technical advance.
We applied these new characterization methods to screen a matrix of experimental
conditions (surface tension, viscosity, conductivity, driving frequency and protein content),
probing their effects on resistive forces. We discovered several interesting trends for two-
plate DMF: (1) increasing driving frequency to > ~2 kHz causes a significant reduction in
kdf, (2) reducing surface tension of a given drop simultaneously reduces fth and fsat,velocity, and
increases kdf, and (3) increasing conductivity significantly lowers fsat,velocity. For all liquids
tested, the maximum velocity was achieved at the highest frequency tested (10 kHz),
suggesting that frequency should always be maximized as long as < c.
Finally, these methods helped us to generate insight into the dynamics of protein-
fouling and to establish experimental conditions allowing the manipulation of undiluted
whole blood on an air-filled DMF device for tens of minutes, a significant advance that paves
the way toward applying DMF for point-of-care diagnostic applications.66,67
As a whole, the contributions described here provide a comprehensive and
quantitative framework for measuring and understanding the resistive forces that act on drops
within a DMF device. Whether these forces are caused by differences in liquid properties,
adsorption of molecules to the device surface, or saturation processes, they can all be
compared within a single, consistent framework and expressed in fundamental units of force
(i.e., N or N/mm). Although these methods ignore certain aspects of the complex fluid
dynamics (e.g., internal circulatory flows, drop deformation, etc.), they capture the dominant
86
effects impacting drop velocity. Because these methods are simple to use and can be
automatically integrated into existing experiments (e.g., as a pre-experiment calibration or as
a means of tracking changes in resistive forces over the course of an experiment), they have
the potential to provide a wealth of data with minimal effort on the part of users. It is our
hope that these methods will make it easier for users of DMF to conduct experiments under
more “optimal” conditions, and perhaps to answer some of the outstanding questions
concerning the underlying physics.
4.5 Experimental
4.5.1 Reagents and Materials
Unless otherwise specified, reagents were purchased from Sigma-Aldrich (Oakville, ON).
Pluronics (BASF Corp., Germany) were generously donated by Brenntag Canada (Toronto,
ON), and Pluronic concentrations are specified as percentages (w/v). All DMF experiments
were carried out using the DropBot hardware and Microdrop software described in Chapter
2. DMF devices were fabricated as in Chapter 2.
4.5.2 Simulations of drop dynamics
All simulations and analyses were implemented with custom Python routines (version 2.7.2,
https://www.python.org/) using the following packages: scipy (numerical integration, signal
processing), numpy (matrix algebra), pandas (time series), shapely (geometric analysis), and
sympy (symbolic math). Numerical integration of Equation 4.1 (using the lsoda method from
the FORTRAN library ODEPACK124
) was performed to simulate the x-position, velocity,
and acceleration of a drop of PBS with diameter 1.2L (~2.7 mm). fe and fth were estimated
using the electromechanical model (Equation 4.6) at = 10 kHz and the device geometry
87
was designed to match the devices used in experiments, with bottom-plate electrode pitch
L = 2.25 mm, inter-plate spacer height h = 180 μm, a 5 μm dielectric layer on the bottom
plate with εr = 3.10, and a 50 nm hydrophobic layer on both the top and bottom plates with
εr = 1.93; this is equivalent to a total dielectric stack capacitance of 5.3 pF/mm2 and an fe of
26.5 μN/mm (assuming U = 100 Vrms). fth was set to 13 μN/mm based on experimental
observations of a threshold of U ≈ 70 Vrms. fclf and fviscous were calculated from Equations
4.14 and 4.15 using ξclf = 0.07 N·s/m2,122
Cv=6 (Poiseuille flow), and μd=1.002 N·s/m2.58
fdrag
was assumed to be 0.
4.5.3 Benchmarking and calibration of impedance and velocity measurements
The device impedance circuit from Chapter 2 (shown schematically as “version 1” in
Figure 4.13a) was updated for the experiments reported here (shown schematically as
“version 2” in Figure 4.13b). Prior to conducting experiments with DMF devices, the
impedance measurements were calibrated against a test board of capacitors (photograph in
Figure 4.3c). This board contains a range of 20 NP0 capacitors, with nominal values
logarithmically spaced between 1 pF and 1 nF (+/- 5%), and two replicates of each capacitor
on the board, for a total of 40 capacitors. The impedance of each capacitor was measured at
100 Vrms over a range of frequencies, logarithmically spaced between 100 Hz and 20 kHz in
57 steps. Each condition was measured 10 times (10 ms per measurement), resulting in a
total of 22,800 independent data points. The entire procedure was automated and completed
in ~5 min. The resulting data were used to estimate the values of the reference resistors and
parasitic capacitance values in the version 2 impedance circuit (Figure 4.13b) as described in
Chapter 2, with the transfer function modified to match the new circuit topology:
88
2,,
,
21
2
ifbifb
deviceifb
total
fb
CR
CR
U
U
(4.23)
where Utotal and Ufb are the total voltage applied by the amplifier and the feedback voltage
measured by the control board, respectively, Cdevice is the capacitance of the DMF device (or
alternatively, the test board during calibration/benchmarking), and Rfb,i and Cfb,i are the
reference resistance and capacitance when feedback resistor i is selected.
Figure 4.13. Comparison of versions 1 and 2 of the impedance measurement circuit used to evaluate droplet movement in DMF devices. (a) Version 1 impedance circuit introduced in Chapter 2. (b) Improved circuit (version 2) used for results presented in this chapter. In both figures, the gray dashed box represents the circuit model for an electrode on a DMF device. Resistors are used to construct two voltage dividers: one (Rhv, in series with the input voltage) for measuring a scaled-down version of the amplifier output Uhv, and another (Rfb, in series with the device) for measuring the
feedback voltage, Ufb, which is used to estimate the device impedance, Zdevice(). Parasitic capacitors are represented in red.
The capacitances of stationary DI water and PBS drops on DMF devices were
measured as a function of frequency on a 5 mm2 electrode over a frequency range of 100 Hz
to 20 kHz. The drops covered the entire electrode so that the relevant area of the dielectric
was defined exclusively by the size of the electrode.
89
The dynamic capacitances of moving drops of PBS + 0.02% F88 Pluronic on DMF
devices were estimated every 10 ms and converted to x-position and velocity measurements
as in Chapter 2. To calculate the mean velocity of each step, a linear fit was performed on
the x-position versus time data for all points where x < 0.95L. The slope of this line is an
estimate of the mean drop velocity (dx/dt)avg, and this estimate was used to dynamically
adjust the filtering window of a 3rd
-order Savitzky-Golay filter117
to smooth the velocity data.
The filter’s window width was specified by the time it would take for a drop to cover half of
the electrode when traveling at the mean velocity, i.e., 1/5.0
avgdtdxL .
4.5.4 Characterization of non-protein-containing liquids
The liquids evaluated included (1) DI water, (2) PBS, (3) DI water + 0.1 M NaCl + 0.01%
F88 Pluronic, and (4) 70% DI water + 30% glycerol + 0.1 M NaCl. A calibration procedure
was performed on every new liquid and DMF device prior to experiments. For each liquid, a
drop with sufficient volume to completely cover a 5 mm2 electrode was positioned over the
electrode such that the perimeter of the drop was at least 1 mm outside of the edges of the
electrode. Under this condition, the measured capacitance is insensitive to the volume of the
drop and depends exclusively on the area of the electrode. Capacitance measurements were
collected over a frequency range of 100 Hz to 20 kHz. Similar readings were collected over
an empty electrode, providing an estimate of the capacitance of the filler fluid (i.e., air). This
calibration data was used to automatically adjust the actuation voltage to correspond to the
desired force/frequency input using Equation 4.6.
To obtain experimental estimates of the threshold force, saturation force, and
dynamic resistance coefficient, velocity-force datasets were generated by collecting
90
maximum velocity measurements for a unit drop volume (~1 μL) on DMF devices with
applied forces fe ranging from 10 μN/mm to a maximum value fe,max in increments of
5 μN/mm. For each liquid/frequency condition, a single drop was shuttled back and forth
between 2 electrodes, once per force increment; therefore, two maximum velocity
measurements were collected per force step. The initial step duration was set to 2 s (useful
for measuring drops with an average velocity > 1.1 mm/s), but the step durations were
reduced dynamically as the force was increased (which caused drops to complete the
movement routine more rapidly) to reduce the time of the experiments. As long as fe,max was
maintained below the saturation force (see below) for a given liquid and frequency, the
above procedure could be repeated many times on the same set of electrodes with high
reproducibility. For experiments designed to probe the saturation limit (i.e., where fe,max was
set to exceed the saturation force by at least 15–20 μN/mm), a fresh set of electrodes was
used for each test. This entire characterization procedure (including analysis) was fully
automated by a custom software plugin for Microdrop (see Chapter 2).
The saturation force fsat,velocity for each condition was estimated by generating a
velocity-force dataset and dividing it into two parts based on whether the applied force was
above or below an initial guess for the saturation force, f’sat,velocity. Linear fits were performed
to determine the slopes for each of the subsets independently (i.e., the “pre-saturation” range
where fe < f’sat,velocity, and the “post-saturation” range where fe > f’sat,velocity). Uncertainty in
fitted parameters was estimated based on a first-order error propagation of the covariance
matrix. The intersection of the linear fits from the two ranges fintersect(f’sat,velocity), provides an
estimate for the actual fsat,velocity. This procedure was repeated across all possible starting
values of f’sat,velocity, and the reported saturation force was determined as the value of
91
fintersect(f’sat,velocity) for which the difference between f’sat,velocity and the fintersect(f’sat,velocity) was a
minimum. If the difference in slope between the pre-saturation and post-saturation ranges
was less than their estimated uncertainties, fsat,velocity was recorded as being undetermined.
After determination of fsat,velocity, the threshold force fth and the dynamic resistance coefficient
kdf were determined as the x-intercept and the inverse of the slope, respectively, of the linear
fit to the pre-saturation region of the data. Saturation velocity was calculated by solving
Equation 4.20 for dx/dt using the fitted values of kdf and fth, and setting fe = fsat,velocity.
The dynamic resistance coefficient kdf was sub-divided into estimates of the fractions
caused by viscous dissipation fviscous and contact-line friction fclf based on Equations 4.14 and
4.13, respectively. Specifically, the viscous fraction of kdf was calculated as:
df
drop
vdfhk
LCkoffractionviscous
2 (4.24)
assuming Poiseuille flow (i.e., Cv = 6), with drop = 1.002 N·s/m2 for DI water, PBS, and
water + 0.1 M NaCl + 0.01% F88119
and drop = 2.501 N·s/m2 for 70:30 water:glycerol +
0.1 M NaCl.121
Contact line friction was assumed to be the source of all remaining
contributions to kdf, such that the contact line friction coefficient was:
h
LCk
L
drop
vdfclf
2
4
1ˆ (4.25)
4.5.5 Characterization of protein-containing liquids
L64 Pluronic was dissolved in whole defibrinated sheep blood (Product #: 610-025, Quad
Five, Ryegate, MT) at 0.1% w/v. In each experiment, a unit drop volume (~1 μL) of this
92
mixture was moved in a circular pattern around four electrodes on a DMF device repeatedly.
A different force was applied on each electrode (15, 20, 25, and 30 μN/mm) at a frequency of
10 kHz and a step time of 2 s. The total experimental time per force condition was 8 minutes
(i.e., 2 min per electrode). Additional experiments at 35 and 40 μN/mm were carried out on
fresh electrodes. For each force condition, a monoexponential decay was fit to the maximum
velocity versus contact time data (where contact time is defined as the total amount of time
that each electrode is in contact with the drop). This normalizes the total time that the drop
was moved during the experiment by the number of electrodes used. Maximum velocities for
each fe condition were interpolated from the monoexponential fits after continuous
movement of the drop for time points of 0, 5, 10 and 15 min. At each of these time points, fth
and kdf parameters were estimated as described above.
93
Chapter 5: Multi-electrode Impedance Sensing
5.1 Introduction
Achieving reliable and fully automated control of DMF chips requires strategies to detect
and recover from the many possible errors that can occur during routine operation, including
fabrication defects (e.g., shorts between electrodes, broken traces, dielectric breakdown), and
surface modifications that occur during use (e.g., biofouling,14,15,113
ionization,31
or charge
trapping102
caused by voltage saturation). These error-conditions can make it difficult or
impossible to achieve any given operation that comprises moving a drop to or from an
affected electrode. In addition, some operations such as splitting and dispensing can be
unpredictable even without defects or surface changes – i.e., the time required to complete
these operations and the final volumes of daughter drops are highly sensitive to the starting
conditions (e.g., the volume and placement of the mother drop,18
surface tension,11
etc.).
Therefore, it is critical that digital microfluidics be paired with a detection system that is
capable of sensing failure modes and also able to provide fast, dynamic control of splitting
operations. Ideally, such a system would be simple, low-cost, and easy to integrate into
existing systems.
Chapters 2 and 4 describe the implementation of an impedance sensing circuit which
has the potential to satisfy most of the above requirements; however, it suffers from one
major limitation: it measures the combined signal from all actuated electrodes
simultaneously and has no means for isolating the effects caused by any single electrode.
Although this system is sensitive to the faults mentioned above (e.g., if one of electrodes
fails, the Chapter 2/4-system measures a decrease in the combined capacitance), it is
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incapable of determining which of the electrodes failed without cycling through them in
series. For DMF to be scalable, the detection system must be able to track multiple drops in
parallel.
There are several possible approaches for implementing multi-electrode, parallel
sensing. Gong and Kim21
described a simple method based on a ring oscillator circuit which
they applied to drop dispensing and splitting under proportional-integral-derivative (PID)
control. They improved the precision of dispensed drop volumes from ±5% to ±1% and
demonstrated the ability to perform non-symmetric splitting. The major limitation to their
method is that it only works with DC actuation, which has several drawbacks relative to AC
operation, including an increased susceptibility to charge trapping and higher resistive forces
as described in Chapter 4. Shin and Lee17
demonstrated a machine-vision approach for
tracking a single drop which could be extended to track multiple drops in theory; however,
such a system would be non-trivial to implement and operate. Image-based methods require
extensive processing, high-speed cameras (if they are to capture drop dynamics), controlled
lighting, and they may be sensitive to the visual appearance of liquids (i.e., color).
Furthermore, it is unlikely that an optically based system could explain a given observed
problem – e.g., dielectric breakdown, shorts, and broken traces may appear the same to an
optical sensor. One system that seems ideally suited for multi-electrode fault detection is the
active, thin-film transistor (TFT) array-based device recently reported by Hadwen et al.26
These DMF devices consist of a 64 x 64 electrode array, each with its own integrated
capacitive sensor that can perform measurements at a rate of 50 Hz. This technology clearly
has great potential, having achieved a scale (in terms of the number of addressable
electrodes) that is orders of magnitude higher than any competing methods; however,
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fabricating these devices requires access to an industrial manufacturing line and therefore
this technology is currently only available to employees of Sharp Corporation (Ichinomoto-
cho, Tenri-shi, Japan) and their collaborators. Further, even when produced at scale, it is not
clear that the manufacturing costs of TFT-based devices will ever reach the point at which
single use (disposable) devices would be practical, an obvious requirement for many
biological applications (e.g., applications involving blood are inherently limited by device
lifetime, as described in Chapter 4). Thus, there is a critical need for an AC-compatible
system for multi-drop manipulation and sensing that is compatible with conventional
devices, including those with extremely low cost described in Chapter 3.
In response to this challenge, we have developed a multi-electrode impedance sensing
method based on time-multiplexing, which can be thought of as “quasi”-parallel
measurement. This strategy is implemented using the same hardware described in Chapter
4, and only requires that impedance measurements be performed quickly relative to the time-
scale of drop movement. The capability to track the position and velocity of multiple drops
simultaneously enables the development of reliable, multiplexed protocols that can
automatically detect points of failure and dynamically reroute drops. The new system can
validate not only drop translation operations, but also splitting and dispensing operations. In
addition, multi-electrode velocity data can be incorporated into the models described in
Chapter 4 to record changing resistive forces (e.g., caused by adsorbed proteins) on a per
electrode basis, and the system can be programmed to adapt accordingly. This work is not
yet complete, but the initial results suggest that the multi-drop sensing and actuation
techniques described here represent an important step towards scalable, fully-automated
digital microfluidic operation.
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5.2 Background and theory
In the standard practice of DMF, the state of each electrode during a protocol step is binary
(i.e., actuated or non-actuated). We refer to this property as the actuation state, and it
specifies whether or not an electrode is intended to generate an electrostatic force to cause a
drop to move. As an extension to this standard framework, we define a second electrode
property, which we call sensitivity (i.e., an electrode can be either sensitive or non-sensitive).
This term defines whether or not the user wants to measure the impedance of an electrode
during a given step. Further, we introduce three levels of time: step (with duration tstep),
measurement period (with duration tmeas.-period), and window (with duration twindow). A fourth
(implicit) division of time for the case when the drop is driven by an AC potential is the
waveform period (where the duration is the inverse of the driving frequency: twave-period =
1/). These levels are progressively smaller – that is, tstep > tmeas.-period > twindow > twave-period.
Figure 5.1 illustrates these concepts for a single step applied to three different electrodes
(each controlled by a separate channel***
). As shown, during each window, we define
whether or not an electrode is on (that is, driving voltage is applied) or off (that is, driving
voltage is not applied) based on the combination of its actuation state and its sensitivity. If an
electrode is actuated, we would like to maximize the total amount of time that it is in the on
state, and if it is non-actuated, we want to minimize this time. If an electrode is sensitive, it
must be on for at least one window within each measurement period.
***
In practice, multiple electrodes can be “bussed” together (i.e., controlled by a single channel); however, in
the present work, we assume that each channel corresponds to a unique electrode, such that the terms channel
and electrode are interchangeable.
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Figure 5.1. Schematic representation of a single step being applied to three different channels (electrodes). Channels 1, 2, and 3 are represented in blue, orange, and green, respectively. Labels for tstep, tmeas.-period, twindow, and twave-period provide a graphical illustration of these parameters. In this example, there are five windows per measurement period (i.e., tmeas.-period = 5twindow) and two measurement periods per step (i.e., tstep = 2tmeas.-period). Each channel is actuated during the step, with a 60% duty cycle. Each channel is also sensitive during this step, because the states in windows 3, 4, and 5 allow us to uniquely determine their contribution.
Based on these constraints, we define an m × n switching matrix, S, which specifies
the state of all switches during a single measurement period. Each row of S corresponds to a
window within a measurement period and each column corresponds to a sensitive channel.
We iterate through the rows of this switching matrix p times during a single protocol step,
where p = tstep / tmeas.-period. Each entry in this matrix, Si,j, is equal to 1 if the channel in column
j is on during window i, or 0 if it is off, where i is the row index (i = 1, 2, …, m) and j is the
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column index (j = 1, 2, …, n). As an example, consider a switching matrix for the case of
measuring three channels (n = 3) over a measurement period that spans five windows
(m = 5), where all three channels are “actuated” and “sensitive”:
100
010
001
111
111
S (5.1)
This matrix corresponds to one of the two measurement periods depicted in Figure 5.1.
Based on this matrix, each of the channels is on for three out of five windows within each
measurement period. We use the term duty cycle to describe the relative portion of time a
channel spends in its on state. In this example, each electrode has a 60% duty cycle. All
electrodes are on simultaneously during two windows (i = 1 and 2) and each is on
independently for a single window (i = 3, 4 and 5). We define the electrical admittance of
each channel (where admittance is the inverse of the impedance) during each measurement
period using an n × p matrix Y. The following equation defines the m × p measurement matrix
M as the dot product of S and Y:
MSY (5.2)
Therefore, if we can measure M (i.e., the combined admittance of all channels that were in
the on state during each window) over p periods, and we know S (the switching matrix), we
can estimate Y (the admittance for each electrode during each measurement period), by its
linear least-squares approximation:
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MSSSY TT 1 (5.3)
The condition for being able to solve Equation 5.3 is that matrix S must have full column
rank, meaning that m ≥ n, and that there be at least n independent rows. We can ensure that
this condition is met by adding the constraint that for each sensitive electrode, there must be
a single row in S where the electrode is either on while all other electrodes are off, or off
while all other electrodes are on.
Next, consider the case where we want to have a channel that is sensitive (i.e., we
want to know its impedance), but we don’t want it to be actuated. This can be achieved by
designing the switching matrix such that the non-actuated channel has a low duty cycle and
is off for the majority of the time. As an example, we can modify the matrix in our previous
example to:
111
010
001
011
011
S (5.4)
In this case, the two actuated channels (columns j =1 and 2) are on for four out of the five
windows (i.e., 80% duty cycle) and the non-actuated channel (column j = 3) is on for a single
window (i.e., 20% duty cycle). The admittance of each channel can be estimated in the same
way as in the previous example, using Equation 5.3.
This sensing approach makes no assumptions about electrical properties (i.e.,
resistive vs. capacitive), which is why we refer to it in its most general form of impedance
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sensing. If we assume that the impedance of each channel is purely capacitive – which is
usually the case in DMF if we are operating in the electrowetting regime (i.e., << c, see
Chapter 4) – we can convert between admittance, impedance, and capacitance with the
equation:
CZY 2/1 (5.5)
where Z and C are n × p matrices of the impedance and capacitance values, respectively, for
each of the n channels and p measurement periods.
This quasi-parallel sensing approach makes an implicit assumption that all
measurements acquired within a measurement period occur simultaneously, when in fact,
they are collected sequentially. This assumption is only valid if tmeas.-period is very short
compared to the time-scale of drop movement (i.e., tmeas.-period << tstep). To avoid this
requirement, we can add an intermediate step between acquiring the measurements in M and
solving for Y. Since each row in M represents an independent time series in which the same
subset of channels are on, we can perform an interpolation step (e.g., polynomial
interpolation) across each row to shift all measurements to a common timeframe. This
interpolation requires its own assumption that each time series can be approximated (e.g., by
a polynomial function) over the timescale of tmeas.-period.
5.3 Results and discussion
5.3.1 Effect of window length and duty cycle
To understand the performance tradeoffs involved with multi-electrode sensing, we must first
determine the relationship between twindow and the accuracy of our capacitive measurements.
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All other timing parameters are ultimately limited by the length of twindow. For example, the
number of capacitive measurements per channel per unit time (the per-channel sampling rate)
is equal to the inverse of the measurement period (1/tmeas.-period) which is itself equal
to 1/mtwindow. Thus, for any fixed per-channel sampling rate, twindow sets an upper limit on the
maximum number of channels that can be “sensed” simultaneously (i.e.,
n ≤ tmeas.-period/twindow).
We evaluated the root-mean-squared error (RMSE) in measuring a set of known
capacitors with two different window lengths: twindow = 2.7 and twindow = 10.9 ms. Assuming
that the measurement noise is normally distributed, the error is expected to scale with
windowt ; therefore, the shorter window length should have approximately double the RMSE
)27.2/9.10( . The results in Figure 5.2a confirm this prediction for capacitance values
≥ 6.8 pF, where the average measured RMSE was 4% and 1.8% (4/1.8 ≈ 2) for the 10.9 ms
and 2.7 ms windows, respectively. The RMSE for lower capacitance values (< 6.8 pF) are
indistinguishable between the two window lengths, suggesting that for such low capacitance
measurements, errors are non-normally distributed, perhaps as a result of systematic
error/bias (e.g., parasitic capacitance). This reduced performance for low capacitance
measurements (< 6.8 pF) is unlikely to be of practical significance for DMF since the
capacitance of each electrode on a typical device is ~20–30 pF. Furthermore, because multi-
channel sensing involves sampling n electrodes simultaneously, typical capacitance readings
will scale proportionally with n, making low readings less likely. Since drop translation on
our typical DMF devices happens on the order of hundreds of milliseconds, the ability to
sample capacitance values every 2–10 ms should provide sufficient temporal resolution to
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measure tens of drops in parallel, assuming that system noise can be maintained at acceptable
levels.
Another important parameter to consider when evaluating different multi-electrode
actuation schemes is duty cycle (i.e., the relative time an electrode is on). If we assume that
inertial effects are insignificant (as described in Chapter 4), we would expect the observed
drop velocity to be directly proportional to duty cycle, and this is indeed what we observe as
demonstrated in Figure 5.2b. This is a useful result – although not featured in this thesis, this
should allow for the use of a very simple control system that outputs a single driving voltage,
with drop velocity (and driving force) modulated simply by changing the duty cycle. This
result is also important in considering the scalability of drop movement and sensing in
parallel.
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Figure 5.2. Capacitance measurement error and relative velocity. (a) Experimentally measured root-mean-squared error (RMSE) in capacitance upon applying 100 Vrms and 10 kHz to the NP0 capacitors on the test board for windows with twindow = 2.7 ms (solid blue) and twindow = 10.9 ms (solid orange). Each RMSE value is based on 10 replicates. The dashed lines with the same colors show the average error for Cnominal > ~6.8 pF. (b) Experimental measurements (blue circles) of relative drop (maximum) velocity on a DMF device as a function of duty cycle (i.e., the percent of time that the waveform is in an on state). The test liquid is PBS + 0.02% F88 at 100 Vrms and 10 kHz.
5.3.2 Scalability
A key requirement of the new method is that it be scalable to many drops in parallel; for
example, if a method allows for simultaneous evaluation of two drops but not ten drops, it is
not scalable and has limited utility. Figure 5.3 demonstrates the scalability of two different
modes of multi-channel sensing, which we refer to as additive and subtractive modes. In
additive mode, the capacitance of each channel is uniquely determined by a single window
per measurement period during which it is on while all other channels are off. In subtractive
mode, the capacitance of each channel is uniquely determined by a single window per period
in which it is off while all other channels are on. As shown, in the case of one- or two-
channel actuation, both modes are equivalent, but when actuating and sensing more than two
channels (i.e., more than two drops moving in parallel), the maximum duty cycle is
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periodmeas
window
t
t
.
1 for subtractive mode, while for additive mode it is )1(1.
nt
t
periodmeas
window.
Figure 5.3d plots the duty cycle for additive and subtractive modes for n = 1–10 and tmeas.-
period = 10twindow, demonstrating the superior scaling of the subtractive mode. Thus, we
adopted the subtractive mode for all of the work described here.
In addition to the scalability of the electrostatic driving force (and the resulting drop
velocity) we also considered the impact of multi-channel sensing on measurement
performance (i.e., the signal-to-noise ratio). Figure 5.3e shows a plot of the root-mean-
squared error in capacitance readings based on simulated data designed to match our
experimental system (e.g., using the noise characterization data from Figure 5.2b). We
found that measurement error increases linearly with the number of channels being sensed
and also with increasing drop velocity (data not shown); the latter is a consequence of the
filtering window width being inversely proportional to the average drop velocity (see
Chapter 4). For typical conditions (e.g., biological buffers with surfactants, where drops
move on the order of ~10 mm/s) the system is capable of measuring capacitance to within
about (2 × n)% – e.g., 10% for n = 5 channels. The relative error in estimating maximum
drop velocity and/or average drop velocity is comparable (2–3 × n)% (data not shown).
While increased error may be undesirable in the context of precise characterization
experiments (e.g., those described in Chapter 4), 20-30% error is suitable for most
applications, where often the only requirement is the ability to determine whether a drop has
reached its destination electrode (i.e., a binary result). In situations where precision is
important, it is straightforward to trade-off reduced parallelism for an enhanced signal-to-
noise ratio. Furthermore, time-series averaging (e.g., if a drop is passed over the same
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electrode multiple times during a mixing or incubation step) can further improve signal-to-
noise, with an increase that is proportional to the square root of the number of averaged
steps. Although some pure liquids (e.g., water) can be moved at velocities approaching 50–
100 mm/s, conditions that would severely limit the number of drops that can be sensed in
parallel, these sorts of liquids tend to move without problems, so they present less of a need
for quantitative sensing; instead, it is slow moving liquids (e.g., protein-containing solutions)
that present the greatest challenge for DMF. For this class of liquids (which often move at
speeds < 10 mm/s), our system should be capable of tracking > 10 drops simultaneously with
measurement error < 30%.
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Figure 5.3. Scalability of multi-drop movement and sensing. (a) Schematic of three drops being actuated toward their destination electrodes (1, 2, and 3, highlighted in blue, orange, and green) simultaneously. (b) Additive and (c) subtractive driving sequences (one measurement period) for each of the three electrodes. Both sequences consist of 10 windows of length twindow (i.e., m = 10), such that tmeas.-period = 10twindow. In the additive scheme, the capacitance of each actuated channel is measured while all other channels are in the off state; therefore, each channel has an 80% duty cycle. In the subtractive scheme, only a single actuated channel is turned off during each window, so each channel has a 90% duty cycle. In this experiment, the number of channels being sensed in parallel is n = 3. (d) Plot of duty cycle (which should translate into drop velocity, as per Figure 5.2b) in the additive (pink circles) and subtractive (brown triangles) mode and (e) root-mean-squared error of capacitance sensing (in subtractive mode) as a function of n for up to 10 channels. Error bars in d are ±1 standard deviation.
5.3.3 Experimental demonstration of parallel sensing for translating drops
To validate the new technique, three drops were repeatedly (and simultaneously) driven onto
adjacent destination-electrodes on DMF devices. Figure 5.4 highlights representative results.
The pink curve shows the sum of the capacitance of all channels that are on during each
window. These measurements are used to estimate the capacitance and velocity of each
channel as a function of time (see section 5.5.6), demonstrating that this technique is indeed
capable of measuring the dynamic capacitance and velocity of multiple translating drops.
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Using these same experimental parameters (twindow = 2.7 ms and tmeas.-period = 27 ms), it is
possible to sense up to 10 channels simultaneously, with measurement noise that scales
linearly with the number of electrodes (see section 5.3.2) . Increasing the number of sensitive
channels beyond 10 requires either a longer tmeas.-period (i.e., a longer time between successive
measurements of each channel) or a shorter twindow.
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Figure 5.4. Experimental realization of multi-drop moving and sensing. (a) Schematic of three drops being translated toward their destination electrodes (1, 2, and 3, highlighted in blue, orange, and green) simultaneously. (b) Subtractive driving sequence (one measurement period) for three channels. (c) Representative experimentally measured capacitance trace of the sum of all channels that are on (pink) as three drops are driven onto their destination electrodes, and the capacitance estimated for individual channels 1, 2, and 3 (blue, orange, and green, respectively) on the basis of the differently timed windows for each drop. (d) Velocities of drops (generated from the data in c) moving onto electrodes 1, 2, and 3 (blue, orange, and green, respectively). Note that the capacitances (in c) and velocities (in d) for the individual channels were filtered by 3rd-order Savitzky-Golay filters.
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5.3.4 Three-channel splitting simulation
In addition to measuring the dynamic capacitance and velocity of translating drops, multi-
channel sensing has great promise for studying the dynamics of splitting and dispensing and
for validating the completion of these operations during automated experiments. There have
been multiple studies that have investigated the necessary conditions for drop splitting.10,76,125
In general, splitting a drop into two daughter drops requires an increase in the area of the
liquid-air interface, which is energetically unfavorable. Therefore, for splitting to be possible,
driving forces must be applied such that the drop is pulled from two ends (i.e., in opposite
directions) with sufficient magnitude to overcome this energy barrier. The energy barrier can
be reduced by lowering the surface tension, reducing the gap height, or increasing the length
of the “necking” region – i.e., the electrode(s) intermediate to the two ends.10,76,125
As the
drop is stretched, liquid in the necking region pinches together and eventually becomes
unstable and breaks off. Although the basic features and dynamics of this process are well
understood and can be modeled by computational fluid dynamics,126
this process is highly
dependent on surface heterogeneities and is therefore unpredictable. That is, splitting
requires that the mother drop pass through an inherently unstable state, and this limits
reproducibility and volume precision of the daughter drops. Thus, achieving fully automated,
reliable, and precise splitting requires some form of active feedback control.21
Figure 5.5 demonstrates a simulation of how the new multi-drop manipulation and
sensing techniques described here could be applied to drop splitting. As shown, in this
model, a virtual drop is split over three electrodes, with normally distributed noise added to
the capacitance values based on experimentally determined error for twindow = 2.7 ms (see
section 5.3.1). The two outer electrodes were actuated for the entire simulation (90% duty
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cycle), while the center electrode was non-actuated, but sensitive (10% duty cycle). Of
particular interest in Figure 5.5d is the orange trace (channel 2), demonstrating the capability
to measure the volume of liquid in the necking region which is non-actuated. This method
could be useful for verifying the completion of a splitting operation (i.e., the time at which
the necking region on the center electrode breaks off, and its volume reduces to zero). In the
near future, we propose to apply these techniques to control drop splitting and/or dispensing
on device.
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Figure 5.5. Simulation of multi-channel sensing during drop splitting. (a) Schematic of a mother drop (initially centered over electrode 2, orange) being split in two daughter drops (centered over electrodes 1 and 3, blue and green). (b) Subtractive driving sequence (one measurement period) for the three electrodes. Note that in this case, one of the electrodes (channel 2, orange) is not actuated, but is still sensitive, so the capacitance can be measured without applying a significant electrostatic force to it (i.e., a 10% duty cycle). (c) Simulated capacitance of the sum of all channels that are on (pink) as the mother drop is split, and (d) the capacitance estimated for channels 1, 2, and 3 (blue, orange, and green, respectively). Note that the capacitance of the middle electrode (channel 2) decreases until it reaches ~0 pF when the neck pinches off between the two daughter drops. Capacitance data for the individual channels was filtered by a 3rd-order Savitzky-Golay filter.
5.4 Conclusion
We have introduced a new multi-channel impedance sensing technique capable of
simultaneously tracking up to ~10 drops (both position and velocity) with measurement
errors better than ~20% when these drops are moving at speeds < 10 mm/s. The current
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implementation of this technique meets the requirements of most present-day DMF
applications (e.g., on devices with ~100 electrodes). The ability to sense electrodes that are
non-actuated will make it possible to verify the progress and completion of splitting and
dispensing operations, and in future, to provide active feedback to these dynamic processes
to achieve enhanced volume precision. The combination of these features will facilitate the
development of high-level, automated, and fault-tolerant control of digital microfluidics.
5.5 Experimental
5.5.1 Reagents and materials
Phosphate buffered saline (PBS) was purchased from Sigma-Aldrich (Oakville, ON).
Pluronic F88 (BASF Corp., Germany) was generously donated by Brenntag Canada
(Toronto, ON). All DMF experiments were carried out using the DropBot hardware and
Microdrop software described in Chapter 2. DMF devices were fabricated as in Chapter 2.
5.5.2 Hardware and firmware modifications
The DropBot hardware was mostly unchanged from that used in Chapters 2 and 4, with the
exception of the high-voltage switching boards. The switching boards were modified to use
an independent microcontroller unit (ATMega328P, Atmel, San Jose, CA) connected to five
8-bit shift registers to control the state of the high-voltage relays, replacing the previous
design [which uses a 40-channel i2c port expander (PCA9698, NXP Semiconductors,
Eindhoven, Netherlands)]. The new switching boards are shown in Figure 5.6. The firmware
of the control board and switching boards were modified to facilitate rapid switching of the
high-voltage relays based on a predetermined switching matrix, where each column of the
matrix corresponds to a single channel and each row specifies a window within a
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measurement period (see section 5.2 and Figure 5.1). For any given row index, the switching
boards simply update the state of their channels based on this switching matrix. The control
board acts as a coordinator, preloading the switching matrix onto each of the switching
boards at the beginning of a step, and synchronizing changes to the row index for all
switching boards over the i2c network.
Figure 5.6. High-voltage switching board used for multi-electrode impedance sensing. Photographs of the (a) top and (b) bottom of the high-voltage switching board used in Chapter 5. Labels indicate the main components of the board including the input and output connections (the high-voltage signal, +5V power, i2c communication, and outputs to the DMF chip) and the integrated circuits (the ATMega328P microcontroller, 5 8-bit shift registers, and 40 high-voltage PhotoMOS relays).
5.5.3 Benchmarking of impedance measurements
The impedance sensing circuit was tested using a bank of 15 NP0 capacitors with nominal
values spaced logarithmically between 1 and 220 pF at 100 Vrms and 10 kHz. 10 replicates
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were performed for each capacitor with two sampling window times, of twindow = 2.7 and
twindow = 10.9 ms.
5.5.4 Velocity versus duty cycle measurements
A single drop of PBS containing 0.02% w/v F88 was driven back and forth between two
electrodes at 100 Vrms and 10 kHz. For each step, the capacitance of a single channel (the
actuated destination electrode) was sampled once every twindow = 2.7 ms over a total step
duration of tstep = 1 second. Each set of measurements was divided into repeated blocks of 10
windows each (where the time of each block is analogous to tmeas.-period = 10twindow but without
any multi-channel sensing since there was only a single actuated channel per step). The
number of windows for which the electrode was in its on state was varied between three and
ten per block, equivalent to duty cycles ranging from 30 to 100%. Drop velocity was
estimated from capacitance measurements for each duty cycle condition using the method
described in Chapter 4 (i.e., not using the new multi-channel sensing scheme). The only
difference relative to this previously described method is that we ignored capacitance
measurements collected when the actuated channel was in its off state (e.g., in the case of a
30% duty cycle, we ignored seven out of every ten readings).
5.5.5 Noise-scaling simulation
Drop position/velocity versus time was simulated by numerical integration as in Chapter 4
using the same device geometry and drop shape. The max velocity of the drop was 10 mm/s
(approximately matching the velocity of the PBS + 0.02% w/v F88 actuated at 100 Vrms and
10 kHz, used for the experiments in this chapter). fe, fth, and kdf were set to 23 μN/mm,
13 μN/mm and 1.0 μNs/mm2, respectively. Random multiplicative and normally distributed
noise was added to the simulated data (standard deviation was 4%, corresponding to
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twindow = 2.7 ms, and tmeas.-period = 27 ms) and tstep was set to 1 second. The simulation was
repeated for n = 2–10 channels with 5 replicates of each. Each row in the measurement
matrix M was “shifted” to a common timeframe by linear interpolation prior to estimating the
capacitance and velocity using Equation 5.3 and filtering with a 3rd
-order Savitzky-Golay
filter as in Chapter 4. The root-mean-squared error in capacitance was calculated from the
noise-free, simulated data.
5.5.6 Experimental demonstration of parallel sensing for translating drops
Three drops of PBS containing 0.02% w/v F88 were driven onto three different destination
electrodes simultaneously at 100 Vrms and 10 kHz (twindow = 2.7 ms and tmeas.-period = 27 ms).
Each channel was on for nine windows per measurement period (i.e., a 90% duty cycle).
Interpolation, capacitance estimation and filtering were performed as above.
5.5.7 Three-channel splitting simulation
The capacitance versus time of a three electrode splitting operation was simulated at 10 kHz
and 100 Vrms by assuming a mother drop that initially covered the center electrode (channel
2) and half of its neighboring electrodes on either side (channels 1 and 3) at time t = 0. The
capacitances of channels 1 and 3 (the destination electrodes of the two daughter drops) were
assumed to increase linearly from t = 0 to 0.5 s. For t ≥ 0.5 s, the destination electrodes were
completely covered by the drop and the capacitance of all channels was at equilibrium. The
capacitance of each of the channels was calculated based on its covered area (assuming
2.25 mm x 2.25 mm electrodes) multiplied by the device capacitance, cdevice = 5.3 pF/mm2.
The capacitance of channel 2 (i.e., the center electrode), was calculated based on the total
initial capacitance of all three channels minus the capacitance of channels 1 and 3. 4%
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multiplicative Gaussian noise was added to the sum of the admittance for all active channels
during each window (calculated using Equation 5.2). The capacitance for each channel was
then estimated using linear least-squares (Equation 5.3), and filtered as above.
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Chapter 6: Conclusion and Future Directions
6.1 Conclusion
When I commenced work on this thesis in 2009, digital microfluidics was still very much in
its infancy, and research in the field was primarily focused on developing new protocols and
demonstrating “proof-of-concept” applications. While a few labs (including the Wheeler lab)
had built simple, computer-controlled automation systems, these systems were often not very
capable (e.g., no closed-loop feedback) and difficult to use, and they were mostly
inaccessible to those without the knowledge and skills to build such systems. At that time,
the majority of the experiments conducted in the Wheeler lab (and other top labs in the field)
relied on manual control (i.e., drops were manipulated by manually probing contact pads
with high-voltage probes). While these methods and this stage of technology development
were certainly useful for demonstrating the exciting possibilities available with DMF, the
lack of a simple-to-use and accessible control instrument was clearly limiting serious
progress in the field.
This situation inspired the development of DropBot (described in Chapter 2). This
control instrument and its accompanying software were designed to be easy-to-use by non-
experts, and we decided to share the hardware designs (e.g., CAD files, PCB schematics) and
source code with the community as open-source hardware/software
(http://microfluidics.utoronto.ca/dropbot). Since that time, we have built seven of these
systems in the Wheeler lab (where they are used on a daily-basis), and we have assisted other
labs from around the world to build (as of August 2015) an equal number of systems,
including labs at the University of Helsinki, the University of California at Los Angeles,
118
Stanford, Lawrence Berkley National Labs, the Karlsruhe Institute of Technology, and the
South University of Science and Technology of China (SUSTC) in Shenzhen; a clear sign
that we are not alone in recognizing the potential of this technology.
The DropBot system precisely controls the driving force applied to drops with
integrated compensation for parasitic and device capacitance, and amplifier-loading effects.
This feature is extremely important for achieving reproducible operating conditions. By
controlling the applied force (instead of specifying operational conditions in terms of
voltage), the system is able to enable consistent drop velocity on devices that were formed
with drastically different structures (differing dielectric materials and thicknesses, etc.).
DropBot also provides sophisticated impedance sensing, which facilitates the
characterization of drop position, instantaneous drop velocity, and device capacitance. These
quantitative characterization features provide important tools for internal quality control of
DMF devices, comparing results across multiple users and labs, and for addressing
outstanding challenges in the field (e.g., improving device reliability and resistance to
biofouling).
Another significant challenge when I entered the field was a lack of access to
inexpensive DMF devices. Device fabrication typically requires access to cleanroom
facilities and is prohibitively expensive, both in material and labor costs. This situation
motivated the work of Chapter 3, in which we demonstrated the potential for inkjet printing
to significantly reduce fabrication costs and improve accessibility. While the devices
described in this work still require traditional dielectric and hydrophobic coatings, we
estimate that replacing this single photolithography step results in a device cost reduction of
> 50% and removes the need for a cleanroom facility. This development is also significant in
119
that it suggests a fabrication method that can be scaled to a roll-to-roll process, providing the
clearest example yet of an industrial-scale manufacturing strategy capable of producing DMF
devices with equivalent performance to devices made using small-batch photolithography.
The development of DropBot and its combined capabilities for carefully controlling
the applied force and measuring the resulting velocity, provided a unique opportunity to
study questions underlying the fundamental physics of drop movement. Multiple researchers
in the Wheeler lab (and elsewhere62,65,79
) seem to have empirically settled on driving
frequencies in the 7–10 kHz range, but this preference is not explained by existing theories.
We also routinely experienced decreasing device performance (i.e., drops became
increasingly difficult to move) as a function of increased use, but the specific cause was often
unclear. This degradation was often blamed on protein-adsorption (i.e., biofouling), but we
began to suspect that “saturation” effects played a significant role. These observations and
the lack of understanding around resistive forces in general motivated the work in
Chapter 4.
In Chapter 4, we developed a set of fully automated methods for characterizing
resistive forces on DMF and uncovered several interesting findings. We discovered that
resistive forces have a strong frequency dependence, and this effect is dominated by a
reduction in the dynamic friction coefficient kdf for driving frequencies > ~2 kHz, providing
the first direct evidence for the rationale for using high frequencies to drive drop movement
in two-plate DMF devices. The results of this work also helped us to appreciate the important
effects of surface tension – reduction of which simultaneously reduces threshold force fth and
velocity-saturation force fsat,velocity, and increases kdf. We discovered that when non-protein-
containing drops are moved with applied forces below fsat,velocity, they can be translated
120
repeatedly over the same electrodes with no appreciable reduction in velocity. We also
demonstrated that for drops containing proteins, although their velocity decays under any
applied force, there exists a force (just less than fsat,velocity) for which device lifetime is
maximized. The ability to easily identify fsat,velocity for any unknown liquid through a simple
on-chip characterization routine is an important technical advance that will enable users to
achieve maximum device lifetime under any experimental conditions. Using these
techniques, we also discovered conditions supporting the first reported manipulation of
whole blood in air on DMF. The fact that this “worst-case” biological sample can be handled
for > 15 min per electrode suggests that DMF may be capable of working with more
“challenging” samples than was previously believed.
Finally, Chapter 5 illustrates a method for extending the capabilities described in
Chapters 2 and 4 such that they can be applied to multiple drops in parallel during the
course of an experiment. We also described a method for sensing non-actuated electrodes,
making it possible to verify the completion of splitting and dispensing operations. These
features provide the foundational components necessary for developing high-level,
automated, and fault-tolerant control of digital microfluidics.
6.2 Future directions
6.2.1 Hardware
From a functional perspective, DropBot should be capable of running most practical DMF
applications (in research laboratories working with devices bearing ~hundreds of electrodes)
into the foreseeable future. The most obvious areas for improvement include the
development of add-on modules to support additional functionality (e.g., temperature control,
121
integrated sensors, etc.). To make the system more portable and suitable for in-the-field
operation (e.g., point-of-care diagnostics), it would be worthwhile to develop an integrated
amplifier (the system currently relies on an external amplifier). The current design is also
relatively expensive (several thousand dollars); reduction in this cost would make the
technology available to more users.
6.2.2 Devices
The inkjet printing technique described in Chapter 3 relies on a research-grade printer (the
Dimatix DMP-2800), which costs tens of thousands of dollars to purchase. Adapting this
method to work with a standard, office-grade printer (< $100) would make this technique
more widely accessible. It may also be possible to print the dielectric and/or hydrophobic
layers which would facilitate a simplified, all-in-one fabrication process. There are many
other possible strategies for improving the fabrication of DMF devices (which may reduce
cost and/or increase performance) and I expect that as more people adopt this technology, we
will see more developments in this area. The ability to quantitatively characterize devices
using the methods described in Chapter 4 should facilitate these activities.
Another significant device-related challenge is figuring out how to scale beyond
~100s of electrodes. Single-plane wiring methods (used for all devices described in this
thesis) require routing between adjacent electrodes to access electrodes deep within an array.
Because the gaps between electrodes must remain small (< 100 μm) for drops to cross, this
limits the number of wires that can fit within this space, and therefore the depth of electrode
arrays along a single dimension (e.g., our current photolithography procedure is limited to 4
rows, with typical array sizes of 4 × 15). Strategies for multi-layer routing with through inter-
layer vias are one possible technique to overcome this limit. Such methods are commonly
122
used in PCB fabrication, but the surface of PCB-based DMF devices is not sufficiently flat
for reliable operation. Multi-layer photolithography on glass/silicon is also possible,127
but
this adds additional fabrication time and cost to an already tedious and expensive process.
Other strategies for overcoming this limitation include optoelectrowetting,128
cross-
referencing schemes,129
and thin-film transistor based devices,26
though these strategies have
yet to gain widespread use.
6.2.3 High-level programming
Chapter 1 introduced the concept of an abstraction layer hierarchy, a concept that is further
described in Figure 6.1. All of the work reported in this thesis has operated on the lowest
level of this hierarchy (i.e., direct control of the electrode switching sequence). Working at
this level places an inherent limit on the scalability and complexity of the applications that
can be practically attempted with DMF.†††
The developments described in this thesis (e.g.,
automated control, quantitative on-chip characterization of multiple electrodes in parallel, an
improved understanding of the physics of drop movement) set the stage for the development
of the second layer in this hierarchy: automated planning, control, and validation of basic
fluidic operations. Some of these operations (e.g., translation, merging and mixing) should be
straightforward to implement based on the findings of Chapter 4. Others (e.g., splitting and
dispensing) will be more challenging as they will require better characterization to facilitate
automatic selection of the force, timing, and geometry (e.g., length of “necking region”) for
successful execution. The advances described in Chapter 5 should make these operations
tractable as well.
†††
Imagine how difficult it would be to perform any meaningful computation by explicitly programming the
on/off state of a network of transistors.
123
Figure 6.1. Abstraction layer hierarchy. Description of four layers of abstraction starting from the highest-level: (1) human readable protocol, (2) a dependency graph, (3) basic fluidic operations, and the finally, the low-level (4) electrode switching sequence. Level 1 and 2 can be thought of as existing in the software domain, while level 3 and 4 are in the hardware domain. Transitions between levels require parsing and translation (level 1→2), placement and scheduling of operations (level 2→3), path routing and timing (level 3→4). The rightmost column shows examples (i.e., text and graphical schematics) representing each layer.
While our development efforts have largely focused on a bottom-up perspective
(hardware domain), other labs (mostly from computational fields) have attacked this
hierarchy from a top-down approach (software domain).130–134
Only when these two lines of
development meet in the middle will DMF be able to achieve its true potential.
6.2.4 Applications
Based on rapid progress over the past six years, I believe that DMF is coming of age and it
will be exciting to witness the transition beyond “proof-of-principle” demonstrations to the
solving of real-world challenges. The key will be to identify those applications that take
124
advantage of DMF’s inherent strengths (reconfigurability, ability to work with solid samples,
ease of sensor integration, etc.). The current rate of growth (e.g., the number of new research
groups and commercial players converging on this field) leads me to believe that DMF has a
bright future ahead.
125
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