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)

ii

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

iii

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.

iv

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

v

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

vi

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.

vii

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

viii

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

ix

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

x

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

xi

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

xii

List of Tables

Table 4.1. Summary of findings from velocity-force characterization experiments ..................... 72

xiii

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

xiv

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

xv

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

xvi

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.

xvii

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-

xviii

developed the software and firmware. CF performed the duty cycle/velocity characterization

and multi-channel velocity experiments. I performed the software simulations.

1

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

3

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).

4

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).

5

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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