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A modular microscale laboratory

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A modular microscale laboratory

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A Modular Microscale Laboratory

Krisna C. Bhargava

Committee:
Dr. Noah Malmstadt (Committee Chair)
Dr. Richard Roberts
Dr. Yong Chen

Doctoral Dissertation

Mork Department of Chemical Engineering and Materials Science
University of Southern California, Los Angeles, CA
May 2016

1

Table of Contents
1 Introduction ............................................................................................................................................3
1.1 From Chips to Lab-Chips, A Brief History ..................................................................................3
1.2 Context of this Work ....................................................................................................................7
1.3 Organization of this Dissertation ..................................................................................................9
2 Discrete Element Microfluidics ...........................................................................................................10
2.1 Background ................................................................................................................................11
2.2 Results and Discussion ...............................................................................................................14
2.2.1 Design Concept ......................................................................................................................14
2.2.2 Microdroplet Generation ........................................................................................................26
2.2.3 In-Situ Monitoring of Microdroplet Generation ....................................................................30
2.2.4 Manufacturing and Post-Processing .......................................................................................31
2.3 Conclusion ..................................................................................................................................34
2.4 Materials and Methods ...............................................................................................................36
3 Statistical Analysis of Device and Network Performance ...................................................................37
3.1 Background ................................................................................................................................38
3.1.1 Application Circuits ...............................................................................................................39
3.2 Results and Discussion ...............................................................................................................41
3.2.1 Microfluidic Resistor Element Library ..................................................................................41
3.2.2 Determination of Resistor Tolerance from Statistical Methods .............................................43
3.2.3 Circuit Topologies for Parallel and Series Mixing ................................................................46
3.2.4 Network Analysis and Characterization of Performance from Statistical Methods ..............47
3.2.5 Experimental Validation ........................................................................................................50
3.3 Conclusion ..................................................................................................................................54
3.4 Materials and Methods ...............................................................................................................55
3.4.1 Experimental Procedure .........................................................................................................55
3.4.2 Simulation Procedure .............................................................................................................55
3.4.3 Analysis of 2-inlet 1-outlet Fork Circuit Topology ...............................................................56
3.4.4 Analysis of 3-inlet 1-outlet Fork Circuit Topology ...............................................................58
3.4.5 Analysis of 3-inlet 1-output Ladder Circuit Topology ..........................................................59
3.4.6 Experimental Determination of 2-1 Fork Operation ..............................................................60
3.4.7 Experimental Determination of 3-1 Fork Operation ..............................................................61
3.4.8 Experimental Determination of 3-1 Ladder Operation ..........................................................62
4 Thermal Sensing for in-situ Process Management ..............................................................................63
2

4.1 Background ................................................................................................................................64
4.2 Results and Discussion ...............................................................................................................66
4.2.1 Design Concept ......................................................................................................................66
4.2.2 Flow Rate Dependent Response ............................................................................................68
4.2.3 Continuous Flow Titration .....................................................................................................71
4.3 Conclusion ..................................................................................................................................73
4.4 Materials and Methods ...............................................................................................................74
4.4.1 Electronic and Software Interfaces ........................................................................................74
4.4.2 Microfluidic Components and Experiments ..........................................................................75
5 Summary and Outlook .........................................................................................................................80
5.1 Impact .........................................................................................................................................81
5.2 Risks, Trade-offs, and Mitigation ...............................................................................................82
5.2.1 Channel Size Reduction .........................................................................................................82
5.2.2 Input-Dependent Resistance ..................................................................................................84
5.2.3 Complete Coverage of Laboratory Functions ........................................................................84
5.3 Vision for the Future ..................................................................................................................89
6 Acknowledgments ................................................................................................................................90
7 References ............................................................................................................................................91

3

1 Introduction
1.1 From Chips to Lab-Chips, A Brief History
In recent decades, the trend of miniaturizing
electronic systems has been extended to
mechanical and electromechanical devices,
resulting in the development of MEMS
technology, or micro-electro-mechanical-
systems. The invention of integrated circuits of
microscale electronic devices by Jack Kilby at
Texas Instruments in 1958 and Robert Noyce
at Fairchild Semiconductor in 1959 was
largely motivated by the observation that miniaturization resulted in benefits to overall power
consumption, portability, power use, information processing speed, and other performance
metrics.
1,2
Advancements in microelectronics broadly impacted society, resulting in the rapid
growth of old industries such as telecommunications, defense, and finance, as well as in the
creation of entirely new industries such as personal computers and e-commerce and national
projects such as the Apollo Space Program. Witnessing the remarkable pace at which electronic
technological development was occurring and transforming quality of life, academics turned their
eyes to mechanical systems, uncovering analogous scaling laws and theoretical benefits to
performance in miniaturizing machines of all kinds. This sentiment was perhaps most famously
captured in Richard Feynman’s 1959 lecture, “There’s Plenty of Room at the Bottom”,
3
where he
imagined microengineered surgical robots and the forces that would dominantly influence their
operation. Feynman went so far as to offer a set of $1000 prizes for a number of creative endeavors

Figure 1.1
Page from Jack Kilby’s lab notebook describing a flip-
flop (a digital logic device). Image copied from his
personal account on the invention of the integrated
circuit, published in IEEE Transactions on Electron
Devices.
1

4

that would advance the state of micro- and nanotechnology, including the printing of the entire
Encyclopedia Britannica on the head of a pin. Nearly a decade later, Harvey Nathanson reported
the first truly micro-electro-mechanical device, the so-called Resonant Gate Transistor, which
contained a microscale cantilever braced by semiconductor device features.
4
In the following
decades, miniaturized turbines, gyroscopes, motors, and other traditional mechanical and
electromechanical systems were developed, creating the field that is now synonymously referred
to as microsystem design.
5

A variety of specialized manufacturing techniques were adopted in order to process single
crystal wafers into microelectronic systems. Broadly termed “semiconductor processing” or
“microprocessing”, these methods involve selectively adding and removing layers of solid material
from the wafer surface in a layer-by-layer fashion.
6,7
The resulting monolithic devices are often
compositions of transistors, resistors, and capacitors, wired together in a purely planar orientation.
This is distinctly different than the manufacturing of traditional electronic systems, which rely on
thick films of ceramic and metal deposited on fiberglass boards, stitching together discrete
components that are created using typical machining processes (eventually known as “printed
circuit board processing”). Over time, photolithography, chemical and physical vapor deposition,
wet and dry etching, and other microprocessing procedures performed in clean rooms became
common-knowledge in industry and academia alike. As such, they were seen as an immediate
platform on which to develop even more specialized manufacturing techniques for MEMS, which
often require higher aspect-ratio features and exotic materials. The group of modifications and
extensions of microprocessing techniques to MEMS became known as “micromachining”.
8–10

5

Figure 1.2
Cross-sectional and top-down schematics of a
thermopneumatic micropump invented by van de Pol et
al. at the University of Twente in 1989.
11
This is one of
several examples of a growing assortment of MEMS
devices for handling fluids in the early days of µTAS
technology development.

Figure 1.3
Block diagram of Stephen Terry and colleagues’
miniaturized gas chromatograph, invented at Stanford
University’s Electronic Laboratory.
12
Historically, this
development represents the first published example of a
µTAS system.
In 1979, Terry et al. reported the invention of a gas chromatograph micromachined on a
single silicon wafer with significant performance benefits over existing macroscopic
instruments
12
. This system contained thermal conductivity sensors, valves, and a microfluidic
channel in one monolithic package, serving as the earliest application of microsystem technology
to a new domain, analytical chemistry (Figure 1.3). More specifically, Terry showed that the
entirety of a single laboratory process could be reconstructed in a miniaturized setting by
fabricating traditional microelectronic devices alongside MEMS structures. It was not until 1990
that this design concept was clearly defined by Manz et al. as “miniaturized total chemical analysis
systems”, or “µTAS”: the combination of fluid sample handling, processing, and detection in a
single, monolithic device design.
13
A growing assortment of MEMS devices for handling
fluids
11,14–20
set the stage for µTAS and the subsequent growth of the field overall, which
eventually expanded to applications in synthetic chemistry and became known by the more
encompassing name, “lab-on-chip”, or “lab-chip”, technology.
21

6

Academic interest in lab-chips peaked in the 1990’s, with many advancements propelled
by the need for economically reasonable manufacturing methods. Though lab-chips could be
produced using essentially the same capital infrastructure as integrated circuits, their added
complexity and specialized application imposed limitations on scaled manufacturing in an
industrial context. For example, many devices for analyzing medically relevant fluid samples
require disposability in order to prevent unintentional cross-sample contamination or biohazardous
waste. Consequently, the community shifted away from the materials base of semiconductor
processing (i.e. silicon, glass, and other crystal or wafer-cut solids) and towards plastics that were
already common in traditional laboratories (i.e. polystyrene, polydimethylsiloxane). From a design
perspective, this virtually eliminated the possibility of integrating sensors and actuators
traditionally fabricated along-side microfluidic features, but increased focus on manipulating the
underlying physics of microfluidics in order to achieve new and improved sample processing
functionality.
22–24
Methods of fabrication that relied on imprinting,
25
capillary molding,
26
transfer
molding,
27
patterning,
28
and direct micromachining of polymers were developed,
29
dramatically
increasing the disposability of devices while simultaneously increasing their reliance on external
detection systems such as microscopes. Thus, the dream of truly miniaturized total chemical
analysis systems was largely replaced by monolithic microfluidic systems and external detection
systems.
7

1.2 Context of this Work
Microfluidic systems promise to improve the analysis and synthesis of materials, biological or
otherwise, by lowering the required volume of fluid samples, offering a tightly controlled fluid-
handling environment, and simultaneously integrating various chemical processes.
22–24,30,31
In
order to build these systems, designers depend on microfabrication techniques that restrict them to
arranging their designs in two dimensions and completely fabricating their design in a single step.
Furthermore, the reliance of modern microfluidics manufacturing techniques on transparent
plastics limits the ability of designers to include sensors and actuators alongside fluid-handling
elements. Therefore, in order to achieve truly miniaturized total analysis systems, a non-planar
manufacturing approach that still enables sensor and actuator integration and disposability must
be developed.
This work introduces a system of modular, reconfigurable components containing fluidic
and sensor elements adaptable to many different microfluidic circuits (actuators will not be
covered). These elements can be assembled in a plug-and-play, out-of-the-box manner to create
three-dimensional, robust assemblies to automate complex laboratory procedures. This assembly
approach allows for the application of network analysis techniques like those used in classical
electronic circuit design, facilitating the straightforward design of predictable flow systems,
including statistical methods of predicting performance variation in assemblies. Ultimately, the
objective of this work is to reimagine the development cycle of µTAS and lab-chip systems to be
more like electronic printed-circuit board development, where each functionally discrete element
for signal control (e.g. resistors, capacitors, inductors, and op-amps) is a unique module within the
framework of a standardized assembly method. These elements may have different levels of
internal complexity, ranging from simple hydraulic resistors to complex flow distributers
8

analogous to integrated circuits, but are compartmented in a manner suitable to mass
manufacturing and facile description through lumped parameter models. Each element contains
microfluidic features in order to handle sample fluids, as well as an optional electronic or MEMS
features in order to perform detection or actuation.
9

1.3 Organization of this Dissertation
This dissertation is organized into four major chapters, the first three of which are adapted from
scientific papers written by the author and either published or soon to be published:
Chapter 2: Published in the Proceedings of the National Academy of Sciences
“Discrete elements for 3d microfluidics” (Cover Article)
Krisna C. Bhargava, Bryant Thompson, Noah Malmstadt
National Academy of Science, 2014

Chapter 3: Published in Scientific Reports
“Predicting the behavior of microfluidic circuits made from discrete elements”
Krisna C. Bhargava, Bryant Thompson, Danish Iqbal, Noah Malmstadt
Nature Publishing Group, 2015

Chapter 4: Published in Micromachines (MDPI)
“Temperature sensing in modular microfluidic architectures”
Krisna C. Bhargava, Bryant Thompson, Anoop Tembhekar, Noah Malmstadt
Multidisciplinary Digital Publishing Institute, 2015

Each of these chapters is broken into a Background section covering the specific body of work
upon which the research builds, a Results and Discussion section describing the theory and
experiments, a Materials and Methods section with details of procedures used, and a Conclusion
section that provides local context for the advancement made. Chapter 5 proposes several
expansions of the system described in Chapter 2 and presents a boarder vision for laboratory
automation inspired by these works in general.
10

2 Discrete Element Microfluidics
In this chapter, an overall system development strategy that closely mimics the one used in board-
level electronic circuit design and production is demonstrated. Analysis of pressure-flow
relationships within microfluidic circuits composed of discrete elements is simplified using
network analysis based on cataloged component terminal characteristics. System assembly is
shown to be reduced to a hands-on practice similar to assembling Lego™ bricks and aided by
descriptive visual cues on each component in analogy to markings found in standardized electronic
parts. Post-assembly system verification is demonstrated through running test flows, optimizing
operating conditions, and repairing or modifying the assembly and design accordingly. Active
process monitor data are communicated to a computer through a simple microcontroller. Systems
are also shown to be permanently sealed by application of adhesives to the joints or potting a circuit
in its entirety. In this manner, the foundation of a working system of discrete microfluidic primitive
elements is debuted with the predictability, configurability, versatility, and permanence
characteristic of modern board-level electronic components.

11

2.1 Background

Figure 2.1
Example lab-on-chip devices sold by Dolomite (a,b) and Micronit (c). The functions of these chips are generally
simple, such as the mixing of two or three reagents, or production of droplets. Chips (a) and (c) are microprocessed
silica and chip (b) is made of silicone elastomer (polydimethylsiloxane, or ‘PDMS’) casted from a microprocessed
mold. The stage in (c) and connector in (d) are examples of chip-to-world interfaces produced by Micronit. Images
from http://www.dolomite-microfluidics.com and http://www.micronit.com

Using discrete components to construct microfluidic circuits offers several advantages over
traditional methods with respect to system cost, planning, and maintenance. In general, two
modular microfluidic design strategies have been proposed previously: systems analogous to
electronic breadboards
32,33
and interconnected monolithic chips.
34–36
Burns et al. demonstrated a
variation of breadboard style systems by fabricating planar microfluidic puzzle pieces with self-
aligned channels.
37,38
Several industrial manufacturers of standard microfluidic integrated circuits,
such as Dolomite and Micronit, offer products which use system-specific chip-to-chip and chip-
to-world interconnects (Figure 2.1). While these solutions promise to expedite the development
12

cycle, they rely on relatively costly and time-consuming microfabrication processes, they do not
generally allow non-planar microfluidic circuit design, and they inherently prohibit designers from
customizing circuits at an elemental level.
Some efforts have been made to alleviate difficulties in constructing microfluidic devices
through centralizing manufacturing in a foundry-like system familiar to that found in the
semiconductor industry. Stanford University and California Institute of Technology both host
microfluidic foundries available to academic and industrial partners alike. Engineers can submit
their fully integrated, monolithic designs, receive active feedback from process engineers, order
disposable polymer chips for fabrication, and order corresponding micromachined molds for
casting their own polymer chips. However, the minimum cost and turn-around time for a single
mold is prohibitive, as are sets of fully fabricated disposable polymer chips. Costs scale with de-
sign complexity, materials selection is limited to polydimethylsiloxane (PDMS), and the design
framework is restricted to a semi-proprietary system defined by work of the Quake Group
(currently at Stanford).
The hydraulic analogy to electronic circuits provides that pressure-driven, low Reynolds
Number flow of an incompressible fluid can be analyzed using Kirchoff’s Laws, enabling the
determination of pressure-flow rate relationships in a complex system based on nodal and loop
techniques.
39
In most microfluidic applications, the primary function of the device can be specified
by a set of intended flow rates, pressure gradients, mixing ratios, or some combination thereof. In
electronic circuit design, these specifications are often referred to as “load requirements” to which
the designer adapts their election of a circuit topology and selection of standardized parts. While
some efforts have been made towards simplifying the microfluidic system design process,
35,40,41

the powerful analysis techniques used in electronics design have not been widely adopted by the
13

microfluidics community largely due to the lack of a standardized parts platform for circuit
construction, inhibiting the exploration of large-scale designs and the growth of the field in
general. In other words, the advent of discrete microfluidic components with standardized
interconnects and dimensional freedom intuitively fits within the framework of design based on
well-defined device terminal characteristics. Merely constructing systems in a modular fashion
does not carry significant design benefits unless certain primitive elements occurring in all lab-
chip systems are identified and compartmented into components on an individual basis. However,
fabricating modules capable of housing a large variety of elements requires significant
manufacturing prowess in three-dimensions.
Recently, additive manufacturing techniques such as high-resolution stereolithography have
been demonstrated as effective tools for the rapid manufacturing of integrated microfluidic
systems without need of a clean room.
42,43
Designers can now create complex channel networks in
three dimensions and choose from a wide selection of material properties, but the cost and time
involved in fabricating a single design iteration is still very high. A simpler approach would be to
batch manufacture a variety of primitive elements from which a designer can assemble a functional
microfluidic system. The iterative process then becomes one of immediate gratification in that the
designer can quickly modify an assembly in response to fundamental design error or replace a
component in order to optimize operation. The devices presented in this report take advantage of
these new manufacturing approaches to produce discrete microfluidic elements with a rich variety
of terminal hydrodynamic characteristics and integrated electronics for in-situ process monitoring.
Additive manufacturing allows the components to be made with high yields, low waste, and high
resolution in three dimensions, enabling the development of an interconnect system which is not
dependent on planar circuit layout.
14

2.2 Results and Discussion
2.2.1 Design Concept

Figure 2.2
(a) CAD assembly drawing of a 1 mm male-male connector aligned with female-type port terminating a 750 µm
microfluidic element of straight-pass type. (b) The flat mating surfaces of the connector pin and port allow for easy
optical inspection of the connector-element channel junction. (c) Chip-to-world interfacing is performed through a
single component that reversibly seals to standardized 1/16'' PEEK tubing.

The fluidic components presented herein were primarily designed to comprise the microfluidic
elements most commonly used to perform passive fluid operations, such as junctions, mixers,
splitters, and chip-to-world interface. All components containing functional elements were built to
a standard, cubic geometric footprint (1 cm side length) and interconnect solution (Figure 2.2) that
lends itself easily towards three-dimensional system configuration. Inlet and outlet elements were
designed to snuggly fit widely available 1/16 in-OD polyether ether ketone (PEEK) tubing in order
to allow users to interface with their devices without having to commit to a proprietary chip-to-
world interconnect solution. The exterior faces of each component were marked with symbolic
cues that correspond to the orientation and type of element within, aiding in rapid assembly based
on diagrammatic expression of the intended system. This is similar to the use of orientation marks
15

on the packaging of fundamental discrete electronic components such as resistors, capacitors,
inductors, and diodes.

Figure 2.3
Micrograph of an interface between a connector pin and straight pass element, both of 750 µm cross-sectional side
length. The tight tolerances associated with stereolithography manufacturing process allow for virtually no
deregistration of channels across the interface relative to their cross-sectional side length.

Elements were terminated on component faces by female-style ports that fit a male-male
style connector by means of an elastic reversible seal enabling plug-and-play operation and
reconfiguration of circuits. The female ports, corresponding male connector pins, and channels
themselves were built with a square shape to ensure optical clarity through their interfaces and
consistent cross-sectional channel orientation between element and connector channels. The
seating of connector pins in ports was designed to ensure self-alignment and continuity between
16

channels (Figure 2.3). Unlike jumper-cable style interconnects, connectors of this style will not
lead to an accumulation of particles or increase requirements for sample volumes by breaking
circuit routing out of a microfluidic environment. Connector channels, designed to have 1 mm in
side length, are larger than the element channels, typically designed with 500-750 µm side length
(Table 2.2, Table 2.3), in order to limit their contribution to hydrodynamic resistance while
ensuring low Reynolds number flow and microliter scale enclosed volumes, preserving the
hallmark conditions for microfluidic flow. Connectors have a spacer between pins to alleviate
difficulties in connecting and disconnecting them from components by hand. The spacers are
cylindrical, and serve as lenses that optically magnify the appearance of flows and aid in post-
assembly test and inspection.
The library of components is shown in Table 2.1; their terminal hydrodynamic properties
are given in Table 2.2. The hydraulic resistance of each element was calculated for use in circuit
analysis assuming low Reynolds number flow, and varied by either modulating the cross-sectional
side length of the channel or the length of the channel segment packed into the component. Each
element was designed using straight channel segments with square cross-sections such that the net
resistance for geometrically complex two-port devices (e.g. helically shaped mixers) could be
computed from series addition of internal resistances. The resistances of segments themselves were
calculated using (2.1), derived from the solution to the Navier-Stokes equation for Poiseuille Flow
in straight channels.
44

𝑅
"#$
=
28.4𝜂𝐿
ℎ
-
(2.1)

17

Table 2.1
Catalogue of components and their associated names, CAD drawings, orientation visual cues, and internal
equivalent circuit diagrams.

18

Table 2.2
Library of constructed circuit elements and their designed segment cross-sectional side-length ℎ, reference label
for circuit analysis, theoretical hydrodynamic resistance 𝑅 as due to designed side-length, and expected resistance
due to manufacturing imperfection 𝑅
./0
(presented with percentile standard deviation). In devices with multiple
outlets, 𝑅 is presented as the internal segment resistance contributed by the equivalent circuit diagram from that
particular element in Table 2.1.The labels used during circuit analysis are placeholders for the numerical averages
presented in their corresponding row values of 𝑅
./0
.

Table 2.3
Comparison of intended and measured side-length of segments (ℎ and ℎ
1.2345.$
respectively) with corresponding
standard deviation. The number of samples measured for a particular category of ℎ is given by 𝑛.

19

Figure 2.4
(a) CAD assembly drawing for a 2-input, 1-output concentration gradient generator in which a single branch resistor
varies the mixing ratio 𝑅
3.7.89
= 𝑅
:,<=>
as shown, see Table 2.2 for explanation of nomenclature and channel
sizes). (b) Equivalent circuit diagram where 𝑅 is the equivalent branch resistance compared to 𝑅
3
, which is inclusive
of control resistor 𝑅
3.7.89
and additional resistance due to structural components such as interface, connector, and
T-junction components.

Here, 𝜂 is the dynamic viscosity of pure water at room temperature (1 mPa-s), 𝐿 is the length of a
segment, and ℎ is the height or width of the (square cross-section) channel. In order to determine
the approximate resistance of the components to use in further network analysis of assembled
circuits, the average cross-sectional side-length of several channels was optically measured (Table
2.3) and the variation from designed values was determined. The expected resistance and tolerance
(Table 2.2) for each element associated with these values was found to deviate within a range
comparable to that of standard discrete electronic resistors. For elements with more than two ports,
an equivalent internal circuit model was constructed and the internal segment resistance is stated
20

explicitly. In elements with bends and corners, the resistance for each straight internal segment
was added in series by assuming low-Reynolds number (i.e. purely laminar) flow.
The accuracy of the element resistance calculations was gauged by constructing a parallel
circuit that compares disparate branch flow rates due to a constant pressure source. The assembly
described in Figure 2.4 was modeled as an equivalent circuit consisting of two branch resistors 𝑅
and 𝑅
3
grounded by two dyed water reservoirs and terminated by outlet resistor 𝑅
?
. Each branch
was designed to differ by only a reference and selected component resistance, 𝑅
5.@
and 𝑅
3.7.89
,
while having identical support components resulting in equal structural resistance 𝑅
395489
. All
resistors in the equivalent circuit model were approximated by series addition of their contributing
element resistances in the actual component assembly (see Table 2.2 for subscript nomenclature).

𝑅 =𝑅
A,<=>
+𝑅
C,<=>
+3𝑅
E,F>>>
+𝑅
G,<=>
+𝑅
HI,<=>
=𝑅
395489
+𝑅
5.@

(2.2) 𝑅
3
= 𝑅
A,<=>
+𝑅
C,<=>
+3𝑅
E,F>>>
+𝑅
G,<=>
+𝑅
3.7.89
=𝑅
395489
+𝑅
3.7.89

𝑅
?
= 𝑅
C,<=>
+𝑅
E,F>>>
+𝑅
A,<=>

The component reference resistor 𝑅
5.@
and variable resistor 𝑅
3.7.89
uniquely control how much
blue and yellow dye enter the outlet T-junction by throttling the action of the pressure source
differently in their respective branches (2.3). This is analogous to the use of a current divider in
electronic circuit design to deduce an unknown resistance with respect to known resistance. Nodal
analysis was applied in the T-junction in order to calculate the pressure where the two dye streams
were combined, such that 𝑄
?
=𝑄
#
+𝑄
L
. The contribution of each dye stream to the outlet streams
was then computed by simple application of Poiseuille's Law, Δ𝑃 =𝑄𝑅, to each branch resistor.
21

𝑄
#
=−𝑃
𝑅
𝑅𝑅
3
+𝑅
?
𝑅
3
+𝑅
?P

(2.3)
𝑄
L
=−𝑃
𝑅
3
𝑅𝑅
3
+𝑅
?
𝑅
3
+𝑅
?P

The volumetric mixing ratio 𝑚
?
of dye streams combined in the outlet resistor was predicted to
have simple dependency on only the selected, reference, and branch structural resistances.

𝑚
?
=
𝑄
#
𝑄
L
=
𝑅
395489
+𝑅
5.@
𝑅
395489
+𝑅
3.7.89
(2.4)

The method of Park et al.
45
was adapted to measure several mixing ratios with varying 𝑅
3.7.89
and
compared to theoretical values calculated from (2.4), validating the simple nodal model with good
agreement (Figure 2.5). Briefly, the resident widths of unmixed collinear dye streams were
measured optically in the junction before diffusive mixing could occur. Assuming that the two
dyed water streams have equal dynamic viscosity, the ratio of their resident widths is then directly
proportional to their flow rates and thus the resistances of their originating branches.

22

Figure 2.5
Comparison of experimental and theoretical mixing ratios for a variety of 𝑅
3.7.89
values (error bars represent the
standard deviation over 12 measurements). Inset images show the co-flowing streams at the T junction; the ratio of
stream widths was used to find the output mixing ratio 𝑚
>
.

With the ability to quickly modify the assembly, this circuit becomes a useful tool for
generating precise mixing ratios based on comparison of select and reference component
resistances. As seen in Figure 2.6, the operational principles of this circuit we expanded by using
it as a module in two-, three-, and four-outlet large-scale tunable mixers by adding or replacing T-
, X-, and XT-junctions near the reservoir inlets. In this manner, the symmetry of the device around
a single axis through which input streams were split was maintained such that the structural
resistance in each new single-outlet sub-circuit was unchanged between configurations. In a planar
setting, this control over parallelization of operation would be impossible due to the need for extra
structural components in order to connect these sub-circuits to the inlets. By driving this circuit
with a constant pressure source, each sub-circuit can be analyzed as a unit with a mixing ratio
23

which is independently controlled by its corresponding branch resistance ratio, as seen in the
equivalent circuit diagrams in Figure 2.7.

24

Figure 2.6
Single outlet sub-circuits were combined to parallelize operation of the tunable mixer to have (a,b) two, (c,d) three, and (e,f) four outlets. Each sub-circuit is
constructed identically, and arranged around a single inlet splitter such that the mixing ratio at each outlet is independently controlled by corresponding choices
of reference and select resistors.
25

Figure 2.7
Comparison of equivalent circuit models for two-, three- and four-outlet parallelized configurations (top to
bottom) of the tunable mixer system (appearing left to right in Figure 2.6). Each single-outlet sub-circuit is
appended to the inlet reservoirs such that the mixing ratio 𝑚
?,R
of outlet streams 𝑄
?,R
, where 𝑛 = 1, 2, 3, 4, is
independently controlled by the ratio of 𝑅
3,R
/𝑅
R
. The system was constructed with rotational symmetry
around a cylindrical axis so that no additional resistance due to excess components contributed to the branch
resistances despite the expansion of operational capabilities, ensuring that the ratio of select and reference
resistors 𝑅
3.7.89 ,R
and 𝑅
5.@ ,R
remained the only throttles on the distribution of pressures (and thus flow rates)
in single-outlet sub-circuit branches.
26

2.2.2 Microdroplet Generation

Figure 2.8
a) CAD assembly drawing and (b) realization of a T-junction configuration emulsification device. (c) Two dye-
bearing water streams are mixed in a 3-dimensional helical mixer and (d) formed into microdroplets by shearing in
a carrier oil phase. As shown, all connectors are 1 mm and all fluidic elements are 750 µm in cross-sectional side
length.

In addition to being straightforward to analyze in terms of element-by-element hydrodynamics,
modular microfluidic systems offer the advantage of simple configurability. The ability to rapidly
assemble and modify two common microfluidic circuit topologies used to generate droplets was
demonstrated: T-junction and flow-focus (see Park et al. for a review of these methods
45
). In the
T-junction configuration seen in Figure 2.8, a single syringe pump was used to drive two dye-
bearing water streams into the circuit where they were combined, mixed, and emulsified in a carrier
oil stream. The helical mixer component was observed to lose effectiveness at aqueous flow rates
above 2.5 mL/hr, determining the upper bound for the aqueous phase sub-circuit operation. The
27

carrier phase flow rate was held constant at 1 mL/hr while the aqueous phase flow rate was varied,
resulting in well-defined steady-state control of droplet size down to sub-millimeter sizes.

Figure 2.9
(a-b) Realization and (c-d) CAD assembly drawings of a high-throughput T-junction configuration sub-circuit built
in three dimensions. As shown, the channel cross-sectional side length for all connectors is 1 mm and all fluidic
elements is 750 µm.

As seen in Figure 2.9, a 3-dimensional quad-outlet version of the T-junction sub-circuit
was constructed in order to parallelize operation for high-throughput applications. The carrier and
aqueous phases were each split into four streams with cylindrical symmetry around an inlet axis
through which they were introduced. Each new stream was radially transported away from the
axis, and intersected with its immiscible counterpart in T-junctions arranged around the axis. This
“equal path-length distribution” method is similar to that demonstrated in parallelizing operation
of the tunable mixer circuit described above. The potential to produce even smaller droplets while
28

leveraging the ability to construct three-dimensional systems was demonstrated by replacing the
T-junction sub-circuit with a flow-focus sub-circuit (Figure 2.10). The input carrier stream
assembly was built around the aqueous phase flow axis such that carrier phase was transported
vertically down into an X-junction where droplets were formed. The aqueous phase flow rate was
varied once again and the carrier phase flow rate was raised to 5 mL/hr in order to prevent droplet
coalescence in the connector channels near the outlet. The center-channel length of the droplets
outside of the device produced by both circuits was measured optically and shown to reliably
depend on the ratio of aqueous and carrier phase flow rates (Figure 2.11).

Figure 2.10
(A) CAD assembly drawing and (B and C) realization of a flow-focus configuration emulsification device
constructed by replacing a terminal T- junction subcircuit with an X-junction-based module in which the flow
focusing is performed. As shown, the channel cross-sectional side length for all connectors is 1 mm and for all
fluidic elements is 750 µm.

29

Figure 2.11
Droplet length as measured along the center axis of exit tubing for (a) T-junction and (b) flow-focus
circuit sub-systems terminating a two-stream mixer circuit (error bars represent standard deviation over
12 measurements). Note that the flow-focused system allows a smaller droplet size regime to be obtained
despite maintaining equivalent fluid element geometries: the channel cross-sectional side length is 1 mm
for all connectors and 750 µm for all fluidic elements. Inset images are selected examples of images
collected to determining the monodispersity and average values of droplet size distributions.

30

2.2.3 In-Situ Monitoring of Microdroplet Generation
Active elements can be incorporated into the modular packaging described here by building
sensors and actuators into the stereolithographically fabricated parts. Here, we demonstrate the
incorporation an off-the-shelf near-infrared (NIR) emitter-receiver pair into a component designed
for droplet sensing (Figure 2.13). The component was designed such that the diodes fit snugly
into embossed features on the exterior, creating a beam path that intersects a straight pass channel
element. The channel carries water droplets dispersed in a fluorocarbon oil phase formed by an
upstream T-junction circuit. The voltage signal across the NPN phototransistor detector biased in
saturation mode is monitored (Figure 2.12). As droplets of water cross the beam they absorb the
near-infrared light much more than the carrier
oil. The resulting signal is digitized and
communicated to a PC by a microcontroller in
order to determine the droplet production
frequency. The length of the droplets was
deduced from the average flow velocity in the
channel and half-period of the signal (i.e. the
droplet residence time in the beam), and
compared directly with droplet sizes measured
by optical microscopy. The results show good agreement between the two techniques, and suggest
that by incorporating more market-available discrete electronic devices into elements active
process monitoring and feedback control systems can be implemented with ease.

Figure 2.12
Electronic circuit used to detect droplets in a straight
pass channel.
31

Figure 2.13
(a) CAD representation of a component with a straight pass channel of 642.5 µm cross-sectional side length
intersecting the beam created between a discrete near-infrared diode emitter and NPN phototransistor receiver.
Inset is a photograph of the actual block. (b) The component is placed downstream from a T-junction producing
water-in-oil droplets that absorb the beam as they cross its path and (c) generating a periodic signal at the output of
the detector. (d) The residence time of the droplets in the beam and the average velocity of the droplet train are
used to calculate a distribution of droplet lengths, which are compared directly to measurements taken using
standard optical microscopy techniques. Flow rates were set to 5000 µL/hr and 2000 µL/hr for the carrier and
aqueous phases, respectively. Droplet lengths were determined to be 421.22 ± 27.54 µm and 416.90 ± 16.36 µm
by the NIR sensor and optical micrographs, respectively.

2.2.4 Manufacturing and Post-Processing
The material and geometries selected for components and connectors demonstrated excellent wear
resistance. The T-junction emulsification circuit described above was completely disassembled,
reassembled, operated, and cleaned in 28 sequential trials without any leakage. The first two or
three times a connector was attached to a component, removing it was difficult by hand due to the
tight tolerance associated with the connector seating, but could be accomplished by inserting a
razor blade at the joint underneath the spacer and gently prying it loose. Fresh joints between
components and connectors showed no signs of leakage under flow rates as high as 200 mL/hr.
32

Leaks were only observed in connectors where the pin edges had been chipped during rough
disassembly.

Figure 2.14
Contact angle was measured between a water droplet surrounded by oil and an (A) uncoated and (B) coated channel
surface, showing effective modification of the channel hydrophobicity by initiated chemical vapor deposition.

Modifying the surface properties of the channels was explored by coating them with a
fluoropolymer coating via a vapor-phase technique previously demonstrated for modifying
channels in PDMS devices in Dr. Malancha Gupta’s laboratory (USC, Los Angeles).
46,47
In brief,
initiated chemical vapor deposition (iCVD) was used to coat the channels in stereolithographically
fabricated components with poly(1H,1H,2H,2H-perfluorodecyl acrylate-co-ethylene glycol
diacrylate), making the channel walls hydrophobic and increasing the contact angle of a water
droplet in oil from 67.9° to 138.3° (Figure 2.14). The coating did not affect the optical clarity of
the photoresin material.
In addition to reversible assembly techniques, several approaches to permanently sealing
the system for applications where further mechanical, thermal, or chemical durability is required
were explored. Connector-component joints can be sealed with either fast-curing epoxy or silicone
33

pipe sealant via direct application with a cotton-tipped applicator. A microfluidic circuit was also
potted by connecting interface components to breather tubes, completely immersing the assembly
in PDMS, and curing it at 30 °C for 24 hours. The results of these permanent sealing approaches
are shown in Figure 2.15.

Figure 2.15
Potting of joints between components and connectors by direct application of (A) epoxy and (B) silicone pipe
sealant. (C) A T-junction emulsification device was connected to breather tubing and completely encased in
polydimethylsiloxane.

34

2.3 Conclusion
A robust solution for the rapid bench-top assembly of three-dimensional microfluidic systems from
a library of standardized discrete elements was demonstrated. Components were fabricated using
additive manufacturing methods and characterized by their terminal flow characteristics, enabling
the use of circuit theory to accurately predict the operation of a microfluidic mixing system with
scalable complexity in three dimensions. The assembly time (from part selection to initial testing)
for the most complex systems was less than one hour. In addition to being much faster to prototype
than monolithic devices, this system also allows for three-dimensional configurations which were
not previously possible using other modular technologies. By discretizing and standardizing the
primitive elements comprising such systems, newly found design complexity naturally allows for
hierarchal system analysis techniques borrowed from the hydraulic analogy to electronic circuit
design. This in turn allows the designer to have greater focus on satisfying a dynamic set of
operational load requirements rather than working within the restrictively static environment of
planar manufacturing.
The ability to reconfigure systems towards expanded operational capabilities was further
demonstrated by attaching three emulsification sub-circuit modules to a simple mixing circuit in
order to form droplets over a wide range of volumes and generation rates. Despite less need for
analytically predictable operation, piecewise validation was also shown for these canonical two-
phase flow systems by qualifying the mixer sub-circuits and then in turn the emulsifier sub-circuits
for functionality. In a monolithic device, each of the circuits demonstrated would comprise a single
system prone to complete failure due to singular manufacturing error or design error of a single
element. In this system, components in circuit assembly were quickly assessed for their
independent contribution to failure and replaced or modified accordingly. Only after successful
35

test and validation were devices optionally sealed into permanent configurations while maintaining
their optical clarity and ease of interfacing.
The operational performance of one of these circuits was also successfully monitored by
inclusion of a single active component capable of performing in-situ sensing. This implies that the
ability to reconfigure this system is also advantageous from the standpoint of metering systems
before finalization of a design. In addition, the inclusion of active sensing components is
particularly advantageous when considering process monitoring in highly complex systems with
many sub-circuits: densely routed microfluidic systems do not integrate well into standard analysis
tools such as optical microscopes.
This system can make discrete microfluidics a valuable development vehicle for complex
design that has not yet been achieved; with a wider library of passive and active components to
choose from, this system can replace monolithically integrated devices for many microfluidic
applications. In addition, this system will benefit immensely as industrial additive manufacturing
technologies also improve, allowing for the further miniaturization of elements and development
of an even larger selection of elements and materials.

36

2.4 Materials and Methods
Channels in the microfluidic elements have square cross-sections of side-lengths 500, 635, 750,
and 1000 µm. Channels passing through the connectors have a side-length of 1000 µm. 1/16 inch-
OD polyether ether ketone (PEEK) tubing was used to interface with inlet and outlet components
in all circuits. In all droplet studies, flow was driven by Harvard Apparatus 2200 syringe pumps,
assemblies were constructed using ℎ = 750µm components, and Halocarbon 4.2 oil was used as a
carrier phase. Droplets were measured in 1/16'' ID silicone tubing exterior of the assembly.
Components were cleaned between use by flushing their channels with water, soaking them in
isopropanol for 10 minutes, and drying them with pressurized air. All components were designed
using SketchUp 2013 (Trimble Ltd.) CAD software and exported into “.stl” format in preparation
for production using a community-provided software extension. Manufacturing was performed by
FineLine Prototyping Inc. using a stereolithographic process and Somos WaterShed XC 11122
photoresin
42
. NIR process monitoring was accomplished using a SEN-00241 940 nm, 75 mW
Emitter/Detector kit and Arduino Mega microcontroller development board. Data was
communicated directly over USB to a PC and processed off-controller in real time using
Mathworks MATLAB R2014a . Devcon Home 5-Minute Epoxy™ and Permatex Silicone RTV
Adhesive™ were both used to seal component joints for permanent configuration of devices. A
thin layer of 5-Minute Epoxy was spread by hand over unfinished component surfaces with fogged
or opaque appearance in order to enhance their optical clarity.

37

3 Statistical Analysis of Device and Network Performance
Microfluidic devices can be used to execute a variety of continuous flow analytical and synthetic
chemistry protocols with a great degree of precision. The growing availability of additive
manufacturing has enabled the design of microfluidic devices with new functionality and
complexity. However, these devices are prone to larger manufacturing variation than is typical of
those made with micromachining or soft lithography. In this chapter, a design-for-manufacturing
workflow that addresses performance variation at the microfluidic element and circuit level in
context of mass-manufacturing and additive manufacturing is demonstrated. The approach relies
on discrete microfluidic elements that are characterized by their terminal hydraulic resistance and
associated tolerance. Network analysis is employed to construct simple analytical design rules for
model microfluidic circuits. Monte Carlo analysis is employed at both the individual element and
circuit level to establish expected performance metrics for several specific circuit configurations.
A protocol based on osmometry is used to experimentally probe mixing behavior in circuits in
order to validate these approaches. The overall workflow is applied to two application circuits with
immediate use at on the bench-top: series and parallel mixing circuits that are modularly
programmable, virtually predictable, highly precise, and operable by hand.

38

3.1 Background
Additive manufacturing is rapidly becoming a viable alternative to micromachining and soft
lithography for fabricating micro- and milli-fluidic devices.
42,43,48–65
Methods such as
stereolithography (SLA) or extrusion-based processes (e.g. fused-deposition modeling, or FDM)
enable entire devices with non-planar channel geometries to be fabricated rapidly and with less
resources relative to traditional methods. However, additive manufacturing is generally less
precise than micromachining, leading to the possibility of performance errors in microfluidic
systems designed to precisely control fluid transport and mixing. The impact of manufacturing
variability on microfluidic circuit functions has not been explored quantitatively in the literature;
errors in concentration of flows in complex microfluidic networks are generally unpredictable and
must be addressed on a case-by-case, ad hoc basis. Additive manufacturing makes this sort of
quantitative analysis possible by introducing a standardized fabrication technology as well as by
encoding microfluidic system designs as digital, machine-interpreted files.
Chapter 2 introduced a platform of self-aligned discrete microfluidic elements
manufactured using SLA that are reversibly connectable and described by their terminal flow
characteristics much like discrete elements in electronic systems.
66
This system lends itself to the
construction of reconfigurable, modular, three-dimensionally complex, and hierarchically
designed microfluidic devices from a library of standardized components suitable for mass
manufacturing. In this chapter, this system is developed further by demonstrating a virtual
implementation strategy and experimental probing procedure that address predicting variations in
performance This strategy has three parts: (A) definition of a component library of passive
elements qualified by their expected variation due to manufacturing, (B) network analysis to derive
39

mixing operability of some simple microfluidic circuits with useful application on the bench-top,
and (C) prediction of network performance variation using statistical analysis methods.
In (A), an element library that is intuitively compatible with linear circuit analysis and
accompanying statistical analysis techniques is developed; hydraulic resistance values of each
element were selected with convenience for designers in mind. Channel geometry was then
deduced in order to yield these well-defined values of hydraulic resistance. In (B), microfluidic
circuit topologies for source-invariant parallel and series mixing were conceived of and
characterized by simple mathematical rules as a model system for network analysis. Network
analysis is a powerful method for gaining insight into the operation of monolithic microfluidic
circuits (see
35,39–41,45,67–75
for a diverse set of examples), but in general has not been used as a
central tool for design. In (C), a complete virtual implementation of each microfluidic circuit was
devised, including expected manufacturing variation in components, in order to simulate the
realistic scenarios for network performance. This was accomplished through applying mechanistic
understanding of stereolithography to the statistical calculation of hydraulic resistance tolerances
at the module level in (A), and further applying understanding of module level tolerances to the
network analysis performed in (B). Ultimately, experimental realizations of these mixing circuits
were assembled and probed using osmotic solutions in order to validate these models.
3.1.1 Application Circuits
A fundamental process in analytical and synthetic chemistry is the mixing of small quantities of
fluids. Typically, this is accomplished using syringes, pipettes, burettes, and a number of other
glass and plastic tools that are operated by hand to manually withdraw fluids from source
containers and procedurally deposit them into a sample container. The error in the final
composition of a mixture is largely attributed to error in operating these tools, or “source-variant”,
40

and can have serious consequences on the repeatability of procedures critical to research and
clinical activities. Consequently, electronically controlled robotic systems that automate these
procedural tasks have been developed in order alleviate operator-induced error, create better
consistency in the physical operation of instruments, and speed up processing of samples overall.
These systems are often prohibitively expensive, carry a large learning curve, and require
significant infrastructural support. There is therefore a need for hand-held tools for precise,
predictable mixing of low volume solutions that are insensitive to typical operator and instrument
errors, or “source-invariant”. The model circuits presented in this work are designed to serve this
practical need, leveraging the reconfigurable and resistance-centric aspects of our overall discrete
element system, while borrowing inspiration from the large volume of microfluidic mixing circuit
design literature available.
40,67,69,71,73–75
Microfluidic technologies for controlled mixing and
dilution demonstrated in the literature thus far have been focused on the generation of
concentration gradients that mimic biologically relevant fluidic environments. Devices capable of
performing parallel and serial mixing,
70
multi-layer dilutions,
74
and logarithmic concentration
gradients
71
have provided microfluidic chip designers with several strategies for manipulating the
concentration of solutions. While these methods represent a substantial effort to construct
application-specific microfluidic circuits, few of these techniques make it simple for designers to
tune mixing factors in a modular sense.

41

3.2 Results and Discussion
3.2.1 Microfluidic Resistor Element Library
Laminar microscale flows can be analyzed in terms of their hydraulic resistance as determined by
channel size and morphology.
44
In other words, it is possible to develop a set of fluidic elements
with varying channel size that are defined on the basis of total hydraulic resistance per component.
Therefore, a library of microfluidic channel elements categorized by their hydraulic resistance in
a manner that allows designers to rapidly prototype designs on paper was developed (Table 3.1).
Channel sizes were restricted such that the Reynolds Number of each element was strictly
indicative of laminar flow for rates as high as 200 mL/hr. The community practices set by
manufacturers of standardized discrete electronic resistors was adopted, wherein a typical
functional unit of resistance is two to three orders of magnitude larger than that of the so-called
“parasitic” resistance in a wire. Consider the hydraulic resistance of a segment of straight channel
with square cross-section expressed in (2.1). For the purposes of this study, the definition of such
elements is restricted to the flow of pure water, at 20 ⁰C, the temperature of our experiments.
Therefore, a value of 1 mPa-s was used for η throughout. A unit of hydraulic resistance “G” is
defined in short-hand notation for 1 GPa-s/m
3
. This corresponds to the resistance of a reference
channel element of 6 mm length and 642.5 µm square cross-sectional height. This channel height
was selected for its convenience in creating a system of resistors with values on a standard scale
of integers or simple fractions. This approach was borrowed from a similar practice in discrete
electronic components, wherein manufacturers primarily offer electronic resistors with values that
allow for easy combination and selection by designers during the drafting of circuit schematics.
A variety of hydraulic resistor elements were constructed based on the reference 642.5 µm
process height. Resistors larger than 1 G were realized by snaking and coiling longer track lengths
42

into a standardized cubic element footprint. A special class of wire-like components characterized
by a 0.01 G parasitic resistance were developed by increasing the cross-section side length to
2.0317 mm such that flow conditions are still laminar at reasonably high flow rates (e.g. Re ~ 0.1
at 200 mL/hr) in the standard 6 mm reference length. Port elements for interfacing to circuits were
constructed with a special height of 1.1425 mm, resulting in a parasitic resistance of 0.05 G. These
stray millifluidic resistances are sufficiently less than resistor class microfluidic components such
that they need not be considered in microfluidic network analysis during the design phase.

43

Class Name CAD Model Label
Designed R
(G)
Expected R
(G)
Expected
Error (%)
Port
Port

R
P
0.05 - -
PEEK

R
in
3 3.018 10.797 %
Wire
(h = 2031.7
um)
Connector

W
C
0.01 - -
Straight
Pass

W
SP
0.01 - -
L-Joint

W
LJ
0.01 - -
T-Junction

W
TJ
0.01 - -
Resistor
(h = 642.5
um)
Straight
Pass

R
1
1 2.304 7.662 %
Snaked

R
2.5
2.5 0.920 3.305 %
Helix

R
5
5 4.582 2.592 %

R
10
10 9.139 2.244 %

R
25
25 22.824 1.852 %

Table 3.1
Library of constructed discrete elements organized according to their designed hydraulic resistance, with units
denoted as G, short for GPa-s/m
3
. Resistor class components were designed with a 642.5 um channel side-length,
allowing resistance to be manipulated by channel length that is achieved by snaking and coiling channels within
individual resistance components. Expected Resistance and Error (2σ) determined through Monte Carlo Analysis
from measured channel side length, which statistically ensures that 95% of designed components will fall within
the stated resistance tolerance.

3.2.2 Determination of Resistor Tolerance from Statistical Methods
The error in resistance for each element was determined from the errors associated with the
stereolithographic manufacturing process. Consider the hydraulic resistance of a channel segment
of rectangular cross-section height ℎ, width 𝑤, and length 𝐿 given in (2) and derived by solving
the Navier-Stokes equation using a Fourier Series method:
44

44

𝑅
"#$,5.892RU7.
=
12𝜂𝐿
ℎ
W
𝑤
1−
192ℎ
𝑛
=
𝜋
=
𝑤
tanh
𝑛𝜋𝑤
2ℎ
^
R,?$$
_F
(3.1)

Figure 3.1
(a) Port opening with centered channel for a resistance component with 642.5 µm cross-sectional side length
showing the precision in the print plane, xy, and the precision in the print axis, z. Due to the control mechanisms
of stereolithography, precision in the xy and z plane are expected to be different. (b) Total component resistance
was approximated by determining and adding together the resistance of segments respective to the xy-planes
(yellow lines) and z-plane (purple lines). Both planes carry a particular fabrication error, determined by optically
measuring the cross-sectional side length of components and creating distributions of precisions in both orientations
(see Figure 3.2).

The layer-by-layer stereolithographic printing method affects manufacturing tolerances/errors Δ𝑤,
Δ𝐿, and Δℎ due to the direction in which a channel segment is arranged with respect to the printing
process (Figure 3.1). This implies that the error in Δ𝑥𝑦 due to the printing optics and related
control mechanism that affects the so-called “xy print plane” will be different than the error Δ𝑧
due to the mechanism that controls the addition of photoresin layers along the “z print axis”. This
results in channels that are imperfectly rectangular despite their square design. In addition, the
solidification of material during printing and in post-processing may cause further anisotropic
deformation of the channel. These effects appear to be secondary to those resulting from controls
45

mechanisms in the printer, but the characterization procedure described here is translatable across
variety of additive manufacturing processes and materials beyond those demonstrated
experimentally.
Experimental values for the print
plane and print axis tolerances were
determined by constructing a large number
of library components with a model material
(see 3.4.1) and optically measuring their
geometric cross sections (Figure 3.2). These
tolerances were used in a Monte Carlo
simulation to predict the standard deviation
in hydraulic resistance of each element in the
component library (see 3.4.2). Briefly, the
resistance of each channel segment
constituting a given element was computed
using (3.1) with parameters 𝑤, 𝐿, and ℎ
drawn from pseudorandom normal
distributions set by the tolerances Δ𝑥𝑦 and
Δ𝑧 depending on the orientation of that
segment (Figure 3.1). The segment
resistances were added in series such that final resistance for the element was computed for that
particular set of draws. Ultimately, the “manufacturer’s tolerance”, or 2σ, for 5000 draws was

Figure 3.2
Distribution of measured cross-sectional lengths in (a) xy
and (b) z orientation for resistance components of 642.5
um cross-sectional channel side length. Optical
micrographs determined Δxy and Δz to be 659 ± 12.47 um
and 642 ± 4.24 um respectively, for 72 measurements in
each direction.
46

determined such that 95% of constructed resistor elements will fall within the specified range of
values (Table 3.1).
3.2.3 Circuit Topologies for Parallel and Series Mixing

Figure 3.3
(a) Generalized Fork topology where each branch resistance experiences the same pressure drop across and mixing
occurs in parallel between inputs. (b) Generalized Ladder topology where mixing occurs in a serial manner, such
that branch R
1
mixes with branch R
2
, which then passes through a mixing resistance, R
M
, and further mixes with
the next adjacent branch, until branch R
N
is reached.

This study considers two microfluidic circuit topologies, denoted as Fork and Ladder, respectively
capable of parallel and series mixing (Figure 3.3). Reagents are pulled through inlet branches by
a negative flow-rate source, such that they combine at a common junction to yield the target
mixture. Borrowing from the hydraulic analogy to electrical circuits,
39,44
the Fork topology
employs the principles of parallel resistances, wherein the pressure drop seen across each input
branch is equivalent. In turn, the flow rate developed across each branch is due solely to the
selection of branch resistances. This allows for a system where the resulting volume fraction of
each inlet fluid at the outlet is invariant to the flow rate. The Ladder topology enjoys similar
47

independence from source variation, but represents an alternate scenario in which inlet reagents
are mixed serially. Flow through the branch furthest from the source is mixed with the next
adjacent branch, which is then mixed with the next adjacent branch, so on and so forth until the
final mixture is created at the outlet. In other words, the Ladder topology can be thought of as
recursively connected Fork topologies.
3.2.4 Network Analysis and Characterization of Performance from Statistical Methods

Table 3.2
General mixing rules for the 2-and 3-inlet fork microfluidic circuit topology, as well as the 3-1 ladder topology.
The dilution ratio, χ, is designed by selecting microfluidic resistors R
i
(i=1,2,3,M) from a component library such
as presented in Figure 1, and constructed in relation to the appropriate circuit model for that topology (Figures 4-
6).

Nodal analysis was employed to study the operation of 2- and 3-inlet Fork circuits, as well as a 3-
inlet Ladder circuit (see Sections 3.4.3-8). The design objective was stated in terms of 𝜒, the
volume fraction of a given inlet fluid in the outlet mixture. Design rules for 𝜒 for each inlet were
in turn derived, showing how branch resistances can be selected in order to tune operation to
deliver a given mixture of each feed fluid (Table 3.2). Note that the source-invariance of each
configuration is apparent in each mixing rule: 𝜒 only depends on the choice of resistor, and not the
withdrawal flow rate. Each circuit was then constructed using a variety of resistor combinations
(Table 3.3) and tested by running a stock NaCl solution through a single branch of each topology
48

(see Section 3.4.1). The resulting dilutions of the stock solution were tested using osmometry, for
which the stock solution was well suited to provide results with variance far below that of the
predicted manufacturing variance in network operation.
A feature of board-level electronic circuit design that enables efficient and repeatable
design and manufacturing is the use of statistical methods to predict circuit behavior due to error
in terminal characteristics at the element level. Similarly, the tolerance of hydraulic resistors
becomes important for predicting the operation of microfluidic circuits assembled from mass-
manufactured standardized elements. While simple error analysis is sufficient for most circuits
involving few nodes and input reagents, complex networks are hard to analyze by hand. This
analysis can be automated using numerical techniques. The use of Monte Carlo analysis at the
element level was extended to simulate expected performance at the circuit level. More
specifically, bins of pseudorandom normally distributed discrete microfluidic resistors were
generated virtually using the tolerances derived in Table 3.1, and computed the distribution of
possible outlet volume fractions using the rules in Table 3.2. The resulting volume fractions were
analyzed for the inlet of the first branch (Branch 𝑅
F
) of each circuit topology, which was fed by
the stock NaCl solution.

49

Table 3.3
Resistor Combination tables for (a) 2-inlet fork topology, (b) 3-inlet fork topology, and (c) 3-inlet ladder topology,
where the R
1
branch runs a 0.34 M solution, and remaining branches run Milli-Q water, which are mixed and
manually withdrawn at the output end of each topology. The designed mixing ratio that utilizes as-designed
resistance values, Designed 𝜒, and expected mixing ratio from Monte Carlo simulation that takes into account build
error, Expected 𝜒, are calculated by using the respective mixing law shown in Table 1. The expected error is two
standard deviations from the expected mixing ratio.
50

3.2.5 Experimental Validation
The 2, 3-inlet Fork and 3-inlet Ladder circuits were assembled (Figure 3.4-Figure 3.6 respectively)
from the library of modular microfluidic devices (Table 3.1) with the configurations given in
Table 3.3. The volume fraction of inlet reagents was validated for each configuration by
introducing a “probe” solution of measurable concentration to a single inlet, which is then mixed
with diluent from remaining inlets in the circuit, and the outlet concentration is finally measured.
Each circuit was constructed including an inlet resistance determined by 24.4 mm PEEK tubing
(OD 1/16”). The 0.34 M NaCl probe solution was run through the branch denoted as 𝑅
F
in each
circuit and all other inlets were fed by Milli-Q water. After channels were primed by manual
withdrawal, the syringe barrel was interchanged with a clean barrel to collect roughly 0.5 to 1 mL
of resultant mixture. Osmolality of the diluted NaCl solution product was measured, allowing for
determination the volume fraction for each resistance combination, for all topologies, for three
syringe barrel exchanges (effectively three repetitions). Note that the measured output volume
fractions as determined by osmometry to find NaCl concentration in the output fall within the
predicted range of variation from as-designed resistance values. In Figure 3.7, simulated and
experimental volume fraction data are arranged to show the deviation from the designed volume
fraction, whose values for each dilution was calculated by applying the resistor combinations of
Table 3.3 to the mixing laws presented in Table 3.2, for the 𝑅
F
branch of each topology. Note that
many of the experimental values for 𝜒 were found to be greater than those designed, resulting in a
tendency for negative deviations. This seems to occur largely because the mean expected
resistance for many elements is less than their designed value, reflected by an overall higher mean
value for ∆𝑥𝑦 and ∆𝑧 tolerance distribution (or 𝑤, 𝐿, and ℎ channel parameters).

51

Figure 3.4
(a) Circuit diagram of a 2-input, 1-output fork topology where R
1
and R
2
are selectively chosen for desired
operational output. (b) Equivalent hydraulic circuit where only R
1
and R
2
, the selected resistance components
reasonably contribute to mixing ratio and wire elements are construed as “parasitic”, or negligible. Note that the
current source symbol represents a syringe withdrawing solutions through the inlets to the outlet. (c) Equivalent
hydraulic circuit with syringe attached to output end to demonstrate experimental setup.

52

Figure 3.5
(a) Circuit diagram of a 3-input, 1-output fork
topology where R
1
, R
2
, and R
3
are selectively
chosen for desired operational output. (b)
Equivalent hydraulic circuit where only R
1
,
R
2
, and R
3
the selected resistance
components reasonably contribute to mixing
ratio and wire elements are construed as
“parasitic”, or negligible. Note that the
current source symbol represents a syringe
withdrawing solutions through the inlets to
the outlet. (c) Equivalent hydraulic circuit
with syringe attached to output end to
demonstrate experimental setup.

Figure 3.6
(a) Circuit diagram of a 3-input, 1-output
ladder topology where R
1
and R
2
are
selectively chosen for desired operational
output. (b) Equivalent hydraulic circuit
where only R
1
, R
2
, and R
3
the selected
resistance components reasonably contribute
to mixing ratio and wire elements are
construed as “parasitic”, or negligible. Note
that the current source symbol represents a
syringe withdrawing solutions through the
inlets to the outlet. (c) Equivalent hydraulic
circuit with syringe attached to output end to
demonstrate experimental setup.
53

Figure 3.7
Comparison of experimental mixing ratio deviation from designed mixing ratio in comparison to simulated mixing ratio deviation to designed mixing ratio.
For each graph, the upper and lower bound describe a 2σ deviation from the expected mixing ratio, such that the shaded region, effectively the simulated
operating space, is established by the manufacturer tolerance that suggests 95% of the constructed resistor elements will fall within specification.
Experimental data lie within the simulated operational working space for the (a) 2-inlet Fork Topology, (b) 3-inlet Fork Topology, and (c) 3-inlet Ladder
Topology.

54

3.3 Conclusion
This study effectively demonstrated that performance variations in microfluidic systems
constructed using discrete elements could be statistically predicted in context of mass
manufacturing. Device processing and network assembly level error propagation was simulated
using empirically determined process parameters and mechanistic understanding of the SLA
process. Figure 3.7 shows that the measurable performance of real circuits for parallel and serial
mixing constructed from a sample component library reliably perform within virtually determined
bounds of precision. These circuits were useful as a modular, adjustable, and handheld laboratory
tool for creating mixtures with very high levels of precision. Furthermore, the circuit topologies
explored in this work are expandable to an arbitrary number of input solutions; the network and
Monte Carlo analysis techniques presented here reliably enable the determination of performance
of similar systems with scaled complexity.

55

3.4 Materials and Methods
3.4.1 Experimental Procedure
Each circuit topology was tested manually by feeding the 𝑅
F
branch of each circuit with a 0.34 M
NaCl probe solution and running Milli-Q water through the remaining circuit branches. A syringe
was connected at the output end and was manually retracted to prime the circuit branches with
their respective solutions. After priming all branches, a clean syringe replaced the priming syringe
and about 1 mL of diluted mixture was collected. In order to calculate the experimental volume
fraction, an osmometer (Gonotec Osmomat 3000) was used to measure the osmolality of 0.5 mL
of the mixed product. The stock NaCl solution had a measured osmolarity of 0.674 ± 0.0004
osmol/kg; a linear relationship between osmolarity and salt concentration was used to find the
concentrations of the diluted mixtures. All components were fabricated through a contract
manufacturer Fineline Prototyping (Protolabs Inc.) in Watershed 11122 XC photoresin material.
3.4.2 Simulation Procedure
The Monte Carlo simulation was written in Python 3.4.2 using the Anaconda SciPy framework.
Figure 3.8 shows an overview of the procedure. Process data were collected (Figure 3.2) and fit
to a normal distribution, from which the standard deviation and mean values were used to find
expected mean and tolerance values for all members of the resistor component library. A loop with
a maximum count of 5000 tries was constructed, wherein a normally distributed pseudorandom
number generator was called to create a kit of virtual resistors set by the expected values in the
component library in the previous step. The kit was in turn used to calculate expected values for
mixing laws, yielding a predicted 𝜒 value. The resulting 𝜒 values were compared to those expected
from resistors with no manufacturing error, yielding the deviation from intended behavior expected
from mass-manufactured parts.
56

Figure 3.8
Flow of control for Monte Carlo Analysis. Process data informed by SLA manufacturing methods was
used to derive realistic error and mean hydraulic resistances for components used in this study. 10,000
resistor kits were then generated for a given circuit topology, and the performance extrema were derived.

3.4.3 Analysis of 2-inlet 1-outlet Fork Circuit Topology
In electronic circuit theory, circuit subassemblies are often characterized by a simple set of
mathematical rules that relate input and output signal information, treating the circuit as a black
box. Here the concentration of solution is considered to be relevant ‘signal information’ in a
microfluidic circuit subassembly. Specifically, choices in hydraulic resistors are related to inlet
and outlet concentrations. These rules are then validated experimentally by probing a particular
branch of the sub circuits, taking advantage of the ability to neglect flow source variation and treat
flow sources with superposition theorem. The volume fractions of inlet substances 1 and 2 in the
Yes
No
R behavior
xy, z behavior
i = i+1
X behavior
57

outlet solution are derived by first expressing it in terms of constant branch flow-rates, where 𝑄
f

is the flow rate through the N
th
circuit branch (Figure 3.3).
𝜒
F
=
𝑄
F
𝑄
F
+𝑄
g

(3.2)
𝜒
g
=
𝑄
g
𝑄
F
+𝑄
g

The flow rates themselves are derived using the fluidic analogy to Ohm’s Law, the Hagen-
Poiseuille Equation (∆𝑃 =𝑄𝑅), valid in conditions of low Reynold’s Number and laminar flow.
Here, P
0
= 0 to represent atmospheric conditions.
𝑄
F
=
𝑃
>
−𝑃
/
𝑅
F
=−
𝑃
/
𝑅
F

(3.3)
𝑄
g
=
𝑃
>
−𝑃
/
𝑅
g
=−
𝑃
/
𝑅
g

By inserting (3.3) into (3.2) respectively, the flow-rate independent rules for mixing are simply
derived and given by the following:
𝜒
F
=
𝑅
g
𝑅
F
+𝑅
g

(3.4)
𝜒
g
=
𝑅
F
𝑅
F
+𝑅
g

58

3.4.4 Analysis of 3-inlet 1-outlet Fork Circuit Topology
Following the analysis in Section 3.4.3, a 3-input Fork topology follows a similar paradigm
(Figure 3.4). First, the volume fraction of each inlet substance is described in terms of branch flow
rates explicitly.
𝜒
F
=
𝑄
F
𝑄
F
+𝑄
g
+𝑄
W

(3.5) 𝜒
g
=
𝑄
g
𝑄
F
+𝑄
g
+𝑄
W

𝜒
W
=
𝑄
W
𝑄
F
+𝑄
g
+𝑄
W

Next, the Hagen-Poiseuille Law is applied to each branch in order to describe each flow rate in
terms of its respective driving pressure and resistance.
𝑄
F
=
𝑃
>
−𝑃
/
𝑅
F
=−
𝑃
/
𝑅
F

(3.6) 𝑄
g
=
𝑃
>
−𝑃
/
𝑅
g
=−
𝑃
/
𝑅
g

𝑄
W
=
𝑃
>
−𝑃
/
𝑅
W
=−
𝑃
/
𝑅
W

Lastly, the flow rates in (3.6) are used to reduce the expression in (3.5) such that the following
determined volume fraction is shown to be source flow rate invariant, as in the case 2-1 Fork
circuit.
𝜒
F
=
𝑅
F
𝑅
F
+𝑅
g
+𝑅
W
(3.7)
59

𝜒
g
=
𝑅
g
𝑅
F
+𝑅
g
+𝑅
W

𝜒
W
=
𝑅
W
𝑅
F
+𝑅
g
+𝑅
W

3.4.5 Analysis of 3-inlet 1-output Ladder Circuit Topology
Following the analysis in Section 3.4.3, a 3-input Ladder topology follows a similar paradigm (
Figure 3.5). First, the volume fraction of each inlet substance is described in terms of branch flow
rates explicitly.
𝜒
F
=
𝑄
F
𝑄
F
+𝑄
g
+𝑄
W

(3.8) 𝜒
g
=
𝑄
g
𝑄
F
+𝑄
g
+𝑄
W

𝜒
W
=
𝑄
W
𝑄
F
+𝑄
g
+𝑄
W

These expressions are reduced by the Hagen-Poiseuille law, such that:
𝜒
F
=
−
𝑃
g
𝑅
F
−
𝑃
g
𝑅
F
−
𝑃
g
𝑅
g
−
𝑃
W
𝑅
W
=
1
𝑅
F
1
𝑅
F
+
1
𝑅
g
+
𝛼
𝑅
W

(3.9) 𝜒
g
=
−
𝑃
g
𝑅
g
−
𝑃
g
𝑅
F
−
𝑃
g
𝑅
g
−
𝑃
W
𝑅
W
=
1
𝑅
g
1
𝑅
F
+
1
𝑅
g
+
𝛼
𝑅
W

𝜒
W
=
−
𝑃
W
𝑅
W
−
𝑃
g
𝑅
F
−
𝑃
g
𝑅
g
−
𝑃
W
𝑅
W
=
𝛼
𝑅
W
1
𝑅
F
+
1
𝑅
g
+
𝛼
𝑅
W

60

Where 𝛼 =𝑃
W
/𝑃
g
. Then through nodal analysis, one is able to find the relative pressures in the
circuit. Two equations can be used to describe the conservation of flow in the node nearest to the
outlet:
𝑃
g
−𝑃
W
𝑅
:
−
𝑃
W
𝑅
W
=𝑄
(3.10)
−
𝑃
g
𝑅
F
−
𝑃
g
𝑅
g
−
𝑃
W
𝑅
W
=𝑄

Such that,
𝛼 =1+𝑅
:
1
𝑅
F
+
1
𝑅
g
(3.11)

Giving a final expression for the volumetric mixing ratio for each branch:
𝜒
F
=
𝑅
g
𝑅
W
𝑅
g
𝑅
W
+𝑅
F
𝑅
W
+𝑅
F
𝑅
g
+𝑅
:
𝑅
F
+𝑅
g

(3.12)
𝜒
g
=
𝑅
F
𝑅
W
𝑅
g
𝑅
W
+𝑅
F
𝑅
W
+𝑅
F
𝑅
g
+𝑅
:
𝑅
F
+𝑅
g

𝜒
W
=
𝑅
F
𝑅
g
+𝑅
:
𝑅
F
+𝑅
g
𝑅
g
𝑅
W
+𝑅
F
𝑅
W
+𝑅
F
𝑅
g
+𝑅
:
𝑅
F
+𝑅
g

3.4.6 Experimental Determination of 2-1 Fork Operation
Consider a small volume, 𝑑𝑉
W
, of concentration 𝑐
W
at the outlet resulting form the mixing of two
small volumes having run through branch 1 and 2 of the 2-inlet Fork circuit.
61

𝑐
W
𝑑𝑉
W
=𝑐
F
𝑑𝑉
F
+𝑐
g
𝑑𝑉
g
(3.13)

Which can be rewritten in terms of continuous flow, following 𝑄 =
$m
$9
,
𝑐
W
𝑄
W
=𝑐
F
𝑄
F
+𝑐
g
𝑄
g
(3.14)

From superposition theorem, one treats the flow rates as current through each branch, and proceed
to divide both sides of this equation by the total flow rate, giving:
𝑐
W
=𝑐
F
𝜒
F
+𝑐
g
𝜒
g
(3.15)

Assuming that the concentration of solute in branch 2 is set to zero and the stock NaCl solution is
to run through branch 1, the operation of the circuit can be verified using the measured values of
output and stock NaCl solutions simply, such that:
𝜒
F
=
𝑐
W
𝑐
F
=
𝑐
?49049
𝑐
39?8n

(3.16)

3.4.7 Experimental Determination of 3-1 Fork Operation
One follows the same methodology as in Section 3.4.7 to experimentally determine the volume
fraction NaCl through branch 1.
𝑐
-
𝑄
-
=𝑐
F
𝑄
F
+𝑐
g
𝑄
g
+𝑐
W
𝑄
W
(3.17)
𝑄
-
=𝑄
F
+𝑄
g
+𝑄
W
(3.18)
62

𝑐
-
=𝑐
F
𝜒
F
+𝑐
g
𝜒
g
+𝑐
W
𝜒
W
(3.19)
𝑐
g
=𝑐
W
=0 (3.20)
𝜒
F
=
𝑐
-
𝑐
F
=
𝑐
?49049
𝑐
39?8n

(3.21)

3.4.8 Experimental Determination of 3-1 Ladder Operation
Again, one reduces the volume fraction, 𝜒, to a ratio of output concentration to stock concentration
as shown in Section 3.4.7.
𝑐
-
𝑄
-
=𝑐
F
𝑄
F
+𝑐
g
𝑄
g
+𝑐
W
𝑄
W
(3.22)
𝑄
-
=𝑄
F
+𝑄
g
+𝑄
W
(3.23)
𝑐
-
=𝑐
F
𝜒
F
+𝑐
g
𝜒
g
+𝑐
W
𝜒
W
(3.24)
𝑐
g
=𝑐
W
=0 (3.25)
𝜒
F
=
𝑐
-
𝑐
F
=
𝐶
q49049
𝐶
H9?8n
(3.26)

63

4 Thermal Sensing for in-situ Process Management
The technique of integrating market-available discrete electronic sensors into discrete microfluidic
elements introduced in Section 2.2.3 is further explored in this chapter. A discrete microfluidic
element with integrated thermal sensor was fabricated and demonstrated as an effective probe for
process monitoring. Elements were constructed using stereolithography and market-available
glass-bodied thermistors within the modular, standardized framework of previous discrete
microfluidic elements demonstrated previously. Flow rate-dependent response due to sensor self-
heating and microchannel heating and cooling was characterized and shown to be linear in typical
laboratory conditions. An acid-base neutralization reaction was performed in a continuous flow
setting to demonstrate applicability in process management: the ratio of solution flow rates was
varied to locate the equivalence point in a titration, closely matching expected results. Ultimately,
this element is shown to potentially enable complex, three-dimensional microfluidic architectures
with real-time temperature feedback without application specificity or restriction to planar channel
routing formats.

64

4.1 Background
Thermal sensing plays a vital role in chemical engineering systems by providing quantitative, non-
specific monitoring of process reactions and conditions. Traditionally, devices for real-time
temperature measurement are immersed in bulk quantities of reagent as they are combined in batch
or continuous flow reactors. Unpredictable transport and mixing behavior of macroscopic fluid
systems can affect both the predictability of processes as well as the reliability of data collected by
immersed thermal probes. Micro- and millifluidic systems handling liquid reagents can eliminate
artifacts in fluid handling by linearizing transport and mixing behavior, as well as taking advantage
of a variety of other physical phenomena specific to low-Reynolds number flows.
21–24
However,
existing thermal probes for microfluidic systems are often either highly application specific or
limited to planar manufacturing formats derivative of thin-film semiconductor processing
technology. One such example is the use of liquid phase temperature-sensitive indicators that
produce low-resolution visible light signals, such as fluorescent dyes.
76–81
These probes are limited
in their application by the potential for unintended reactivity with processing reagents and are
therefore ill-suited for use as a general solution. Methods of thermal detection that do not require
reaction indicators have also been demonstrated, including infrared thermography
82,83
and direct
integration of electronic temperature sensors with microfluidic channels. Thermography requires
specialized optical equipment and provides relatively low resolution, making it unsuitable for real-
time monitoring of complex systems. It also requires direct line-of-sight to the channel being
integrated, limiting system complexity. Sensor integration avoids these constraints, and devices
such as thermocouples/thermopiles,
84–89
thermistors,
90–93
and resistance temperature detectors
94–97

have been successfully fabricated alongside microfluidic channels. These devices require
specialized thin-film manufacturing practices such as micromachining that are costly and limit
65

their format to planar design, making them better suited as instruments for purely analytical
activities (e.g. microcalorimetery).
In this chapter, the library of elements is expanded to include a thermal probe for monitoring
continuous flows of process reagents or assessing unknown flow rates. The element was designed
by employing the technique of integrating market-ready discrete electronic devices with the
discrete microfluidic element framework. More specifically, a device in which a glass-bodied
thermistor is reversibly sealed within a microfluidic channel element such that it was maximally
submerged by inlet flows is successfully demonstrated. The resulting discrete microfluidic element
serves an accurate, precise, modular and low-cost temperature sensor that is deployable for in-line
monitoring of temperature without limited chemical application or planar format specificity.

66

4.2 Results and Discussion
4.2.1 Design Concept

Figure 4.1
(A) Exploded-view CAD model and (B) assembly of the device demonstrated in this work. (A) depicts the insertion
of a radial-style thermistor inserted into a microchannel element through a single face and sealed by PDMS gaskets
with two slits for electrical leads.

There are several discrete electronic elements for thermal sensing commonly available on the
market, each with its own unique set of advantages and disadvantages. Thermistors were selected
to be integrated into the discrete microfluidic elements platform for their fast response times, high
sensitivity, generally good accuracy, and low cost compared to resistance temperature detectors or
thermocouples. However, thermistors are not particularly linear or stable over long periods of use.
These were considered as acceptable trade-offs; a secondary objective for design of discrete
microfluidic elements is to ensure they are semi-disposable and easily replaceable. Furthermore,
high-precision thermistors are readily accessible, ensuring that empirical calibration procedures
should be applicable over a broad number of duplicate devices.
Thermistors are internally composed of a chip of ceramic or polymer that is connected at
two terminals to electrodes. The chip is then coated with relatively thermally conductive glass or
epoxy, forming its external packaging. Non-specialized, glass thermistors are generally available
Cap
Thermistor
Body
Gasket
A B
67

in two packaging geometries herein dubbed “radial” and “bead”. Cylindrically shaped radial
thermistors are generally larger than bead thermistors and have stiffer electrodes with tight
manufacturing tolerances informed by their use in printed circuit board design. They typically have
a lower surface-area-to-volume ratio than semi-spherical bead packages, implying a qualitatively
more sluggish response to temperature changes. Nevertheless, their geometry is critically easier to
integrate with microfluidic components that are assembled by hand, and were therefore selected
as the packaging of choice in the design presented in this report.
The discrete microfluidic element shown in Figure 4.1 was constructed such that glass
body of a radial thermistor was submerged in the microfluidic channel, maximizing contact area
for heat conduction between fluid and the thermistor surface. This was accomplished by
fabricating each component in two parts, allowing for simple, bench top-level assembly. These
parts, dubbed the “body” and “cap”, of the element were self-registered by a pin-and-socket
interference fit similar to that used in larger assemblies of discrete microfluidic elements. Where
electronic leads were drawn out of the body and cap, small silicone gaskets were inserted. Upon
assembly of the cap and body, the gaskets compressed to seal unintended gaps for leaks and isolate
the leads electrically. The combination of self-alignment between the cap and body as well as the
friction between the thermistor and gasket held the thermistor approximately in the center of the
microchannel element in the body. The result was a channel area roughly 200 µm wide around the
thermistor packaging. No leaks were detected from this channel through the cap-body interface at
continuous flow rates of deionized water as high as 50 mL/hr. A small amount epoxy was used
between the cap and body to improve the leak proofing to flow rates as high as 150 mL/hr.
68

4.2.2 Flow Rate Dependent Response
Thermistors summarily behave as temperature-dependent, nonlinear resistors. Consequently,
electrical current developed through a thermistor will cause Joule heating of the device. This heat
can offset the absolute measurements of the temperature if the thermistor is unable to dissipate
power effectively. In microfluidic channels, substantial hydraulic resistances 𝑅
"#$
relative to
macroscopic, traditional channels may also result in the generation of heat from viscous flows. For
a device such as that shown in Figure 4.2 to achieve a steady-state measured temperature (𝑇
1
), a
balance between heat generated due to self-heating of the thermistor and microchannels and heat
dissipated by the circuit overall must be established. This is expressed mathematically in (4.1) by
balancing power generated by an electrical resistor 𝑃
.P
and hydraulic resistor 𝑃
"P
with a general
expression for power dissipation 𝑃
8
.
𝑃
.P
+𝑃
"P
=𝑃
8

(4.1)
𝑉
g
𝑅
+𝑄
g
𝑅
"#$
=ℎ(𝑄)(𝑇
1
(𝑅)−𝑇
@
)

Here, 𝑉
g
/𝑅 is the power through the thermistor due to the voltage 𝑉 across its leads. 𝑇
@

represents the actual temperature of surrounding fluid intended to be measured. In the device
presented in this report, both the measured temperature 𝑇
1
and the power dissipated by the
thermistor are dependent on its resistance 𝑅. ℎ is a dissipation constant that accounts for the ability
of the fluid, surrounding packaging, and laboratory environment to remove heat generated in the
thermistor and microfluidic circuit. Heat is removed convectively from the thermistor by
microfluidic flows, implying that ℎ will be dependent on the flow rate 𝑄 through the device. In
addition, ℎ is a function of the surface area of the thermistor-fluid interface, geometry, type of
69

fluid, and other device design and operation specific parameters (all constant for the experiments
described in this section). An analytical solution to (4.1) is unlikely, considering the complex
dependency of power balance on flow rate, making an empirical assessment of measurement
nonlinearity the ideal approach to characterizing device response.

Figure 4.2
Microfluidic assembly composed of the discrete elements in Table 4.1 used to perform the characterizations
reported in this work. For each flow rate, the test device was allowed to reach a steady state measurement. The
temperature of the syringes and test device were then recorded over 30 seconds, approximately once a second. The
resulting offset between the test device reading and average of the syringe readings was then computed.

In applications where the device is used to measure the temperature of a microchannel
flow, the flow-rate dependent offset between measured temperature and the fluid temperature is
required in order to gather the most accurate result. For the device presented in this report, heat
Q
A
, T
1

Q
B
, T
2

T
Sense

Q
70

dissipation from the thermistor in typical laboratory conditions and working flow rates was found
to be independent of flow rate below 2 mL/hr and approximately linear thereafter (Figure 4.3).
Figure 4.2 describes the experimental setup used to perform the measurement.

Figure 4.3
Device response with respect to flow rate. The difference ∆𝑇 between the temperature recorded by the device and
the average syringe temperature was computed for across a range of flow rates 𝑄 of deionized water in the assembly
shown in Figure 2. Data were shifted by the difference measured in the condition of no flow ∆𝑇 0 𝑚𝐿/ℎ𝑟 ,
providing an empirical assessment of the flow rate-dependent offset between measured temperature and fluid
temperature. The thermistor appears to perform with little variation to measured temperature at low flow rates.
Microfluidic flow appears to cool the thermistor starting around 2 mL/hr. Error bars shown represent the standard
deviation of data collected during the recording period.

Two syringes (A and B) with measured temperature 𝑇
F
and 𝑇
g
were used to drive deionized water
through the device from a single syringe pump such that 𝑄
u
=𝑄
v
. The flow rate-dependent
temperature measured in the test device 𝑇
3.R3.
(𝑄) was recorded alongside 𝑇
F
and 𝑇
g
in order to
compute the temperature difference ∆𝑇
w
=𝑇
3.R3.
−〈𝑇〉 where 〈𝑇〉 is the average of the syringe
temperatures at steady state. The experiment was repeated across a range of total flow rates 𝑄 =
𝑄
u
+𝑄
v
. During data processing, ∆𝑇
w
was shifted by its value in a stopped-flow condition
∆𝑇
w
(0 𝑚𝐿/ℎ𝑟) in order to effectively ‘zero-out’ the difference between the syringe temperatures,
T (°C)
Q(mL/hr)
71

experimental device temperature, and calibration errors due to intrinsic variations in their
associated thermistors and self-heating conditions. The final offset ∆𝑇 =∆𝑇
w
−∆𝑇
w
(0 𝑚𝐿/ℎ𝑟)
serves as consistent method of assessing device response in real laboratory conditions.

4.2.3 Continuous Flow Titration

Figure 4.4
Two solutions, an acid and base, with approximately equal normality were combined in the microfluidic circuit
shown in Figure 2 to perform a continuous-flow titration. Their volumetric mixing ratio 𝑄
u
/(𝑄
u
+𝑄
v
) was varied
by parametrically by increasing the flow rate of acid solution while decreasing the flow rate of base solution such
that the total flow rate 𝑄 = 𝑄
u
+𝑄
v
in the sensor was always 5 mL/hr. The change in temperature before and after
mixing ∆𝑇 was measured in a similar manner used to characterize device flow rate dependent response, predictably
locating the equivalence point at a volumetric mixing ratio 0.5. The resulting data were shifted by the average value
due only to device behavior, or when only acid or base solution was present. Error bars shown represent the standard
deviation of data collected during the recording period.

In order to demonstrate the ability of the device to act as an effective in-line process monitor, we
performed a set of simple continuous flow neutralization reactions. The microfluidic circuit shown
in Figure 4.2 was driven by two independent pumps with flow rates 𝑄
u
and 𝑄
v
representing acid
T (°C)
Q
A
/ (Q
A
+Q
B
)
72

and base solutions of equal concentration respectively. These solutions were combined in the T-
junction, mixed through diffusion in a long length of channel, and probed with the thermal sensor
microfluidic element. The difference in steady state temperature reading before and after mixing
∆𝑇
w
was computed and recorded in the same manner as used in assessing the flow-rate dependent
nonlinearity of the test device. The volumetric mixing ratio 𝑄
u
/(𝑄
u
+𝑄
v
) was parametrically
varied, allowing for the construction of the titration curve shown in Figure 4.4. The sum of their
flow rates 𝑄
2
+𝑄
L
was held constant throughout the experiment so as to prevent flow-rate
dependent nonlinearity from contributing unexpected offsets to individual data. Note that ∆𝑇
w
was
shifted by the average of offsets in a no-reaction condition, or where the volumetric mixing ratio
was 0 and 1. The resulting curve reflects the expected behavior of the reaction conditions, showing
maximal heat release when equal volumes of acid and base solution with equivalent normality mix
in the microfluidic circuit. Thus ∆𝑇 is symmetric around the volumetric mixing ratio 0.5, reflecting
acid-limited and base-limited conditions in the reaction to the left and right of this value
respectively.
73

4.3 Conclusion
A new discrete microfluidic element for in-line thermal sensing and process management was
successfully demonstrated. A market-available glass-bodied thermistor with radial packaging was
aligned within a microfluidic channel element using the same self-registering interference fit
methods otherwise used to interconnect discrete microfluidic elements at an assembly level. The
device shows good predictability in typical laboratory conditions: the flow rate dependent response
is nearly linear at working flow rates, enabling potential use even as a single-ended flow rate
sensor. Furthermore, the device predictably locates the equivalence point in a continuous flow
acid-base titration, showing its effectiveness at detecting changes in temperature in processes
involving even low concentrations of reagents. Ultimately, this device is free of format or
application specificity, and is easily deployed in complex, three-dimensional microfluidic
assemblies composed of discrete elements. This approach to integration of off-the-shelf electronics
in 3D-printed microfluidic elements provides a general template for the creation of microfluidic
sensing and actuation modules. Such an approach can capture the full range of functionality
provided by commercial microelectronics without requiring any specialized microfabrication
procedures.

74

4.4 Materials and Methods
4.4.1 Electronic and Software Interfaces

Figure 4.5
Electronic schematic of the circuit used in this study to collect thermistor data.

Radial-style glass bodied thermistors (US Sensor 103JG1F, 10k 1%, Digikey) were used for all
temperature measurements in this study. Thermistor leads were connected in a voltage divider
scheme to a microcontroller development board with an on-board 10-bit ADC (Arduino Mega), as
seen in the electronic schematic given by Figure 4.5. The internal ADC voltage was referenced to
the 5 V line for convenient accurate reading of the range. Controller software was written to read
the temperature-dependent voltage drop across the thermistor, compute its resistance, and calculate
the temperature using the Steinhart-Hart Equation.
98
More specifically, ten readings were taken in
1 ms intervals and averaged when the controller was commanded to return a result; the ADC
measurement takes approximately 100 µs. This reading was in turn communicable over standard
serial to a computer or other data recorder. Precision resistors (0.25%) were used to divide a 5V
line voltage with the thermistor, though their actual values were measured to the milliohm level
75

and stored on-board in the controller software to minimize their contribution to errors in accuracy.
Coefficients for the Steinhart-Hart Equation were pre-computed from resistance-temperature
tables provided by the thermistor manufacturer using matrix inversion and also stored on-board.
The resolution of temperature readings is directly limited by the resolution of the ADC. For the
device demonstrated in this study, the smallest readable change in signal is approximately 4.878
mV, corresponding to approximately 0.089 °C; the minimum resolution is artificially enhanced
using averaging, assuming no significant changes in temperature occur in the 10 ms sampling
period.
4.4.2 Microfluidic Components and Experiments
All microfluidic components were fabricated from transparent photoresin (Accura ClearVue Free)
by stereolithography in a manner similar to that previously used to construct discrete microfluidic
elements.
66
Holes were fabricated as part of the design to route thermistor electrical leads away
from detectable flow areas. A thin layer of PDMS was cut using a hole punch and a razor blade to
act as a gasket to seal thermistor leads away from fluid flow and prevent leaks. More specifically,
a thin cut was introduced into the PDMS slab using the corner of a razor where a lead was intended
to be threaded. Upon assembly of the cap and body (Figure 4.1), the gaskets expanded radially to
form seals around the leads due to the axial compression from by-hand press fitting. A good seal
was indicated by sudden optical clarity of the gasket. In some devices, a small drop of fast drying
epoxy (Loctite 5-minute Epoxy) was dragged around the center pin of the cap before assembly.
The library of discrete microfluidic elements utilized in this study is provided in Table 4.1. The
flow-rate dependent behavior of the thermal sensor elements was determined by connecting the
test assembly shown in Figure 4.2 to a syringe pump (Harvard Apparatus PHD 2000) loaded with
30 mL syringes of deionized water. Measurements were collected after allowing at least 8 minutes
76

of steady state flow in order to thermally stabilize the system conservatively (stability in the
measurement typically occurred within 1 minute). Approximately 30 seconds of temperature data
were recorded and averaged for each flow-rate variation (timing curves are provided in Figure
4.6). The average coefficient of variance for these measurements was 0.1565%, indicating good
reliability of the timing parameters used in this experiment. The continuous-flow titration
experiment was performed in the same manner, except with two independent syringe pumps
(Harvard Apparatus 22), one loaded with a 30 mL syringe of acid solution and another loaded with
a 30 mL syringe of base solution (timing curves are provided in Figure 4.7). 8 mM solutions of
HCl and NaOH in deionized water were used as a model solutions of equal normality, giving the
expectation that a volumetric mixing ratio of 0.5 would release the most heat. The measured pH
of base solution was 11.48 (expected was 11.9) and the measured pH of acid solution was 2.05
(expected was 2.10).
77

Table 4.1
Library of discrete microfluidic elements used in this study. All channels had square cross-sections and were 642.5
µm wide (as designed). In keeping with the standard geometric constraints of discrete microfluidic elements
previously demonstrated, each component was a constrained to a single cube of 1 cm side width. Connectors were
6 mm long and the mixer was 2.6 cm long, the equivalent length of two standard cubes and one connector.

Name CAD

Connector

Port

T-Junction

Mixer

Temperature Probe

78

Figure 4.6
Temperature recordings over the steady state measurement period in the experiment described in Results and
Discussion to measure device nonlinearity as a function of flow rate.

0 mL/hr
1 mL/hr
2 mL/hr
3 mL/hr
4 mL/hr
5 mL/hr
7 mL/hr
9 mL/hr
Temperature (°C)
Time (s)
5 10 15 20 25 30
24

23

22

21

20
Temperature (°C)
Time (s)
5 10 15 20 25 30
24

23

22

21

20
Temperature (°C)
Time (s)
5 10 15 20 25 30
24

23

22

21

20
Temperature (°C)
Time (s)
5 10 15 20 25 30
24

23

22

21

20
Temperature (°C)
Time (s)
5 10 15 20 25 30
24

23

22

21

20
Temperature (°C)
Time (s)
5 10 15 20 25 30
24

23

22

21

20
Temperature (°C)
Time (s)
5 10 15 20 25 30
24

23

22

21

20
Temperature (°C)
Time (s)
5 10 15 20 25 30
24

23

22

21

20
Syringe 2 Device Syringe 1
79

Figure 4.7
Temperature recordings over the steady state measurement period in the continuous flow titration experiment
described in Results and Discussion. The equivalence point in the titration occurs in the condition 𝑄
u
= 𝑄
v
. This
is seen when the difference between the average syringe temperature and the device temperature is minimal across
a range of volumetric mixing ratios, reflecting maximal device heating.
Q
A
=5 mL/hr | Q
B
=0 mL/hr
Time (s)
5 10 15 20 25 30
24
23
22
21
20
Q
A
=0 mL/hr | Q
B
=5 mL/hr
Q
A
=1 mL/hr | Q
B
=4 mL/hr
Q
A
=2 mL/hr | Q
B
=3 mL/hr
Q
A
=4 mL/hr | Q
B
=1 mL/hr
Syringe 2 Device Syringe 1
Temperature (°C)
Time (s)
5 10 15 20 25 30
24
23
22
21
20
Temperature (°C)
Time (s)
5 10 15 20 25 30
24
23
22
21
20
Temperature (°C)
Time (s)
5 10 15 20 25 30
24
23
22
21
20
Q
A
=2.5 mL/hr | Q
B
=2.5 mL/hr
Temperature (°C)
Time (s)
5 10 15 20 25 30
24
23
22
21
20
Temperature (°C)
Time (s)
5 10 15 20 25 30
24
23
22
21
20
Q
A
=3 mL/hr | Q
B
=2 mL/hr
Temperature (°C)
Time (s)
5 10 15 20 25 30
24
23
22
21
20
80

5 Summary and Outlook
The objective of this study was to create the framework required for a comprehensive system of
microfluidic elements, each satisfying some primitive operation involved with microflow transport
and analysis. The first system of this kind was demonstrated in Chapter 2, enabling the
engineering of microscale laboratories for synthetic and analytical wet chemistry with arbitrary
complexity and scalability. The many intricate features and sophisticated geometries required to
encapsulate functional elements such as straight passes, junctions, and mixers were achieved by
leveraging existing high-precision additive manufacturing available through centralized
prototyping services. This same flexibility was shown to be useful in integrating commodity
discrete electronic devices directly with microfluidic elements. These functions were inherently
compartmentalized as mass-manufactured discrete elements and interconnects with standardized
form-factors, allowing for complex networks to be assembled. Companion virtual implementation
methods for predicting the fluid-handling behavior of networks composed from discrete elements
in an out-of-the-box manner were developed in Chapter 3. Statistical analysis was shown to be a
powerful tool for analyzing the effect of process variation on element terminal characteristics, and
then the functional behavior of some model microfluidic circuits. In Chapter 4, a new process
monitor element for in-line temperature measurement was introduced by further developing the
method of integrating discrete electronic elements with microfluidic elements. In this particular
case, a high level of performance was achieved in real, variable laboratory conditions by
incorporating a thermal sensor directly within a microfluidic channel. The device was designed
with two levels of modularity: the sensor could be readily swapped from within the discrete
microfluidic element, and of the element itself was inherently modular with respect to the assembly
of complex networks.
81

5.1 Impact
Sophisticated protocols for synthetic and analytical chemistry often require a significant number
of process reagents. Though an analogy to electrical circuit design is often appropriate when
considering fluid transport in microfluidic devices, the uniqueness and variety of reagents handled
in a device adds a layer of complexity to their geometric arrangement. In other words, in order to
route an arbitrary number of reagents in a microfluidic setting, a designer must escape the planar
format of traditional micromachined, monolithic devices and have access to constructing systems
in three-dimensions. This in turn eliminates the ability of designers to probe their devices using
another traditional device, the microscope, which fully depends on planar formats in order to
generate meaningful data. Instead, in-situ process monitors must be used. The resulting devices
may resemble something like a chemical processing plant: pipes and sensors are arranged in the
manner that best suits process conditions and specifications, rather than the limitations implied by
the manner of system fabrication. The system presented in this report allows engineers to do just
that at the microscale: design for process specifications, with the freedom to work in three
dimensions.

82

5.2 Risks, Trade-offs, and Mitigation
5.2.1 Channel Size Reduction
Several limitations in the system reported here are present but eminently solvable. The most
immediately important of these is the reduction of channel size. One of the largest benefits of
microfluidic systems is the reduction of overall reagent volume required to perform analytical
chemistry protocols compared to traditional macroscopic methods (i.e. “test-tube” chemistry).
Reagents are often rare or expensive, and large channel sizes increase the resident volume of
microfluidic networks, implying greater wastage of reagent. The channels presented in this report
are larger than 500 µm, compared to the typical range of 10-500 µm afforded by micromachining.
This limitation resulted from those inherent to stereolithography, the method of choice for
fabricating discrete microfluidic elements. Therefore, channel size acts as a qualitative trade-off
to three-dimensional channel complexity in that micromachining restricts geometries to a planar
format. However, as stereolithography tools and translucent photoresins improve, it is likely that
sub-500 µm features with non-planar geometries will be possible to fabricate. One direct solution
in the present is to fabricate many simpler discrete microfluidic elements (i.e. straight passes and
junctions) using microCNC and laser ablation approaches, since they do not require fully-enclosed
changes in channel direction.
55

The reduction of channel size in devices fabricated by stereolithography also poses another
tradeoff with hydraulic resistance tolerance. Consider the relationship given by (2.1), where the
hydraulic resistance of a square channel is inversely proportional to the fourth power of the width
of the channel cross-section. This relationship is plotted for several constant channel lengths and
inlet viscosities in Figure 5.1. For low nominal values of channel width (i.e. below 500 µm), a
small manufacturing error easily produces a large error in hydraulic resistance. In order for channel
83

sizes to be reduced, the tools for stereolithography must improve in positional accuracy of write-
heads and calibration against surreptitious deformation and morphological changes to fabricated
parts. The latter strategy has been demonstrated in many tools for classical photolithography
through the use of stepper motors.
6,7
The former has been demonstrated through so-called two-
photon absorption stereolithography for building sophisticated photonic devices from photoresins
common to semiconductor processing methods.
99–103
Future stereolithography approaches to
constructing discrete microfluidic elements would benefit from adopting these advancements
simultaneously.

Figure 5.1
Hydraulic resistance for various microchannels with lengths typical to straight passes and T-junction devices. The
resistance changes rapidly as channel sizes decrease below 500 µm, implying that small manufacturing errors can
result in gross tolerances in resistance. Note that the dashed lines represent channels that are not generally
manufacturable using currently available stereolithography technologies.

84

5.2.2 Input-Dependent Resistance
A risk to the further development of a comprehensive workflow for microscale laboratories lies in
the input-dependency of hydraulic resistance: the viscosity of the fluid changes the resistance of
the channel in which it flows. In other words, the functional description of each discrete
microfluidic element purely based on hydraulic resistance to pure water flows falls short of being
applicable for all laboratory functions. Strategies must be developed for describing components
comprising networks in which flows may have multiple viscosities (e.g. blood plasma and water)
and or are immiscible (e.g. oil and water). In the case of miscible flows with multiple viscosities,
this problem is further complicated where reagents mix, resulting in new viscosities dynamically
generated within a network. In the case of immiscible flows, droplet size and surface tension may
introduce network-configuration dependent changes to individual element behavior, analogous to
unintended feedback in electrical networks. Evidence of chaotic and organized behavior of droplet
trafficking has already been provided through studies of simple resistive networks,
104–107
forming
a base of work for translating such relationships to discrete microfluidic elements. Therefore, a
potential strategy of dealing with both of these issues is to empirically analyze transport
phenomena in many discrete microfluidic elements in simple test networks and construct models
that relate them to one another purely empirically.
5.2.3 Complete Coverage of Laboratory Functions
At a broad level, a risk in the further development of this system as a complete solution to
miniaturizing laboratory processes is in the creation of discrete microfluidic elements that
comprehensively cover all basic transport, sensing, and actuation tasks, spanning multiple channel
size standards and materials requirements. Within the realm of transport, mixers that are qualified
85

with respect to the fluid properties of their inlet
flows must be developed. A similar empirical
approach as described for the multiple viscosity
and immiscibility problems in Section 5.2.2
might be appropriate here. An example of one
such device is provided in Figure 5.2, where
collinear streams are separated, split, and
rejoined in order to artificially decrease the
diffusion length of transported molecular
species. This technique is referred to as
lamination,
108–113
and lends itself well to both
network analysis in terms of terminal hydraulic
characterization as well as a semi-empirical description of its mixing efficiency over a variety of
flow rates and diffusion constants. A new realm of actuators will also be necessary, covering
valving and pumping of fluids, as well as for dealing with separations of solid precipitates from
flows and active mixing through stirring. In addition, a richer variety of optical sensors (low and
high power, alike must be developed to deal with quantitative analysis of chemical indicators, such
as those used in colorimetric, fluorescent, and chemiluminescent assays. Label-free methods of
analysis must also be incorporated into the system through discrete microfluidic elements
constructed with electrodes and improved thermal sensors. A variety of sketches for hypothetical
discrete microfluidic elements are provided in Figure 5.2-Figure 5.8.

Figure 5.2
CAD model of a discrete microfluidic element for
mixing by lamination. An inlet flow comprised of two
substances intended to be mixed are separated from
one another, split into multiple streams, and
recombined in a single outlet. The diffusion length of
species in the flow is therefore reduced, while the
outlet flow-rate is maintained as constant.
86

Figure 5.3
Cross-section sketch of a discrete microfluidic element with imbedded electrodes. This component could be used
for impedance spectroscopy, focusing of ionic species, capacitive measurements of active reactions, or even electro-
osmotic pumping when in conjunction with a second module of similar kind in an assembly.

Figure 5.4
Cross-section sketch of a discrete microfluidic element for capturing solid precipitates or particles in flow using
dielectrophoresis. Patterned electrodes are incorporated into a microchannel such that they create a
nonhomogeneous electrical field in direct proximity of the particles, generating a net force towards or away from
the electrode surface.

87

Figure 5.5
Cross-section sketch of a discrete microfluidic element fabricated using an opaque material for measuring optical
absorbance of inlet flows. The S-shaped channel acts to block rays that are not paraxial, enabling the use of the
Beer-Lambert Law in calculating the concentration of an attenuating solution. This same device can be used to
quantify the results of a colorimetric, fluorescent, or chemiluminscent assay.

Figure 5.6
Cross-section sketch of a discrete microfluidic element valve. An imbedded permanent magnet coated with an inert
polymer is propelled to or away from the inlet microchannel by wire-wound electromagnets. In the “off” state, the
magnet is set against a barrier that is part of the printed structure. In the “on” state, the magnet is lifted away from
the barrier and towards the inlet channel.

88

Figure 5.7
Cross-section sketch of a discrete microfluidic element similar to the one described in Chapter 4. A thermistor is
imbedded in the insulating build material such that only one surface is exposed to the fluid flow. This surface can
host solid-phase reactions if it is pre-coated with a substrate molecule. Alternatively, this element can act as an in-
line temperature monitor with standard 1G hydraulic resistance.

Figure 5.8
Cross-section sketch of a discrete microfluidic element for active mixing. A permanent magnet coated with an inert
polymer sits in a well below the microchannel. The magnet is actuated by external electromagnets, essentially
stirring the fluid as it enters the element.

89

5.3 Vision for the Future
The broader vision for the future of this work is to create a universal workflow for microscale
chemistry systems. Virtual design of complete laboratory protocols as microfluidic circuits from
the network to physical assembly level would be managed in software, allowing for engineers to
rapidly iterate designs for optimized performance and manufacturing yield. A rich library of
transport, mixing, process monitor, and actuator discrete elements would be available, each
modeled by its terminal hydraulic characteristics, process functionality, material of construction,
and surface chemistry. Among the process monitors, every sensing modality typical to a wet
laboratory environment would be available: optical, mechanical, chemical, and thermal. The
devices would be simple to assemble and test, owing to a universal controller box and software
readout system, and even simpler to dispose of. Ultimately, bins of discrete microfluidic elements,
and hierarchically more complex modules, would become as common-place to the laboratory
environment as plastic pipette tips and petri dishes – scientists and engineers would lean on this
system as a first-stop for performing new experiments or designing new instruments. Assembly
designs would be distributable as files, allowing for maximum translatability of research between
academic laboratories.
90

6 Acknowledgments
The tragedy of all scientists and engineers is how rare it seems that simple solutions actually solve
complex problems. Though the idea of discrete microfluidic elements continues to strike me as
“too simple”, a comprehensive solution to constructing arbitrary microscale laboratories was far
from “easy”. This work required the inspired contributions of several people, who must be
acknowledged here. Chief among them is Bryant Thompson, whom I thank for pouring countless
hours into helping me to validate my ideas, develop them further, filter out the less reasonable
ones, and advance the vision. Along with Bryant, I would like to acknowledge Danish Iqbal,
Anoop Tembhekar, Nareh Movsesian, Jordan Tse, Kristof Toth, Peichi Hu, Dr. Kristina Runas,
Dr. Carson Riche, and Roya Ermagan for helping to execute many of these ideas. I thank Dr. Noah
Malmstadt, my PI, for his support over the last three years. Noah’s uncanny ability to remind me
of the forest when lost in the trees enabled our team to accomplish a large body of work in a
relatively short span of time. I thank my sister, Verna Bhargava, for reminding me that design and
aesthetics can and should permeate all levels of our engineering conscience. I thank Clark Willison
for our many stimulating conversations spanning subjects from circuit design to biology, and
comforting me to keep thinking out-of-the-box whenever I felt boxed in. I thank my past mentors
in industry for teaching me how to think calmly, draw analogies, and boldly attack problems using
knowledge that is already there. I thank Ashley Gordon at USC for providing the excellent sketches
converted out of my lab notebook in the concluding chapter of this report. And last, but not least,
I thank my parents, Satiesh and Rupa Bhargava, who have patiently supported me not only through
the course of my doctoral program, but in the nonlinear way I seem to have found to this point in
my life.

This work was supported by the National Institute of Health (Award 1R01GM093279) and Viterbi
Doctoral Fellowship (USC).
91

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Abstract (if available)

Abstract Microfluidic systems promise to improve the analysis and synthesis of materials, biological or otherwise, by lowering the required volume of fluid samples, offering a tightly controlled fluid‐handling environment, and simultaneously integrating various chemical processes. In order to build these systems, designers depend on microfabrication techniques that restrict them to arranging their designs in two dimensions and completely fabricating their design in a single step. Furthermore, the reliance of modern microfluidics manufacturing techniques on transparent plastics limits the ability of designers to include sensors and actuators alongside fluid‐handling elements. Therefore, in order to achieve truly miniaturized total analysis systems, a non‐planar manufacturing approach that still enables sensor and actuator integration and disposability must be developed. ❧ This work introduces a system of modular, reconfigurable components containing fluidic and sensor elements adaptable to many different microfluidic circuits (actuators will not be covered). These elements can be assembled in a plug‐and‐play, out‐of‐the‐box manner to create three‐dimensional, robust assemblies to automate complex laboratory procedures. This assembly approach allows for the application of network analysis techniques like those used in classical electronic circuit design, facilitating the straightforward design of predictable flow systems, including statistical methods of predicting performance variation in assemblies. Ultimately, the objective of this work is to re‐imagine the development cycle of μTAS and lab‐chip systems to be more like electronic printed‐circuit board development, where each functionally discrete element for signal control (e.g. resistors, capacitors, inductors, and op‐amps) is a unique module within the framework of a standardized assembly method. These elements may have different levels of internal complexity, ranging from simple hydraulic resistors to complex flow distributers analogous to integrated circuits, but are compartmented in a manner suitable to mass manufacturing and facile description through lumped parameter models. Each element contains microfluidic features in order to handle sample fluids, as well as an optional electronic or MEMS features in order to perform detection or actuation.

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Asset Metadata

Creator Bhargava, Krisna C. (author)

Core Title A modular microscale laboratory

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Materials Science

Defense Date 12/03/2015

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag analytical chemistry,biochemistry,bioMEMS,fluids,lab‐chip,lab‐on‐chip,MEMS,microfluidics,microtechnology,miniaturization,miniaturized total analysis systems,OAI-PMH Harvest,sensors,soft matter,uTAS

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Malmstadt, Noah (committee chair), Chen, Yong (committee member), Roberts, Richard W. (committee member)

Creator Email kcbhar@gmail.com,kcbharga@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-217611

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Legacy Identifier etd-BhargavaKr-4180.pdf

Dmrecord 217611

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