Inertio-Elastic Focusing of Bioparticles in a Microchannel
at Ultra-High Throughput
by
Eugene J. Lim
S.B. Electrical Science and Engineering
Massachusetts Institute of Technology 12002
M.Eng. Electrical Engineering and Computer Science
Massachusetts Institute of Technology 12003
SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER
SCIENCE IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY IN ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
AR
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
I MASSACHUSMS T5]NT9:TN
OF TECHNOLOGY
June 2014
JUN 3 0 2014
© 2014 Massachusetts Institute of Technology
All Rights Reserved
LIBRARIES
Signature redacted
Signature of Author..................................
Department of Electrical EnginSering and Computer Science
May 21, 2014
red acted
-------- ....
___
Certified by.Signature
7-)
Certified by............................
Accepted by...............................
Mehmet Toner
Professor of Health Sciences and Technology
Harvard Medical School
Thesis Supervisor
Signature redacted
k>,
Gareth H. McKinley
of Mechanical Engineering
Pre
Massachusetts Institute of Technology
Thesis Supervisor
Signature redacted
,,/j
----.---------.....
Leslie A. Kolodziejski
/T
Chair of the Co imittee on Graduate Students
2
Inertio-Elastic Focusing of Bioparticles in a Microchannel at Ultra-High Throughput
by
Eugene J. Lim
Submitted to the Department of Electrical Engineering and Computer Science
on May 21, 2014, in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy in Electrical Engineering and Computer Science
Abstract:
Many biological and industrial fluids are filled with micro-scale particles that can serve as "state
markers" for real-world issues, such as human health and public infrastructure. In order to
extract this valuable information from such fluids, the controlled manipulation of particles is
often necessary. Microfluidic technologies based on viscosity-dominant flows have achieved
this essential step in small-volume (5 1 ml) fluid samples, while inertial focusing in
microchannels has been used to process large-volume (-0(10 ml)) fluid samples. However,
inertial focusing has primarily been limited to particles suspended in Newtonian fluids. For
example, the extent to which bioparticles can be focused in complex fluids (e.g., whole blood)
not been explored. Using an imaging technique (particle trajectory analysis (PTA)) that
generates non-blurred images of focused bioparticles with velocities up to 2 m.s', we find that
PC-3 (prostate) cancer cell lines undergo a radical shift in equilibrium position when the
suspending fluid is whole blood (as opposed to diluted blood). We also find that the diluted
blood sample exhibits a Newtonian viscosity profile while the whole blood sample exhibits a
non-Newtonian (shear-thinning) viscosity profile. Previous studies of particle focusing in
microchannels have been limited to inertia-dominant or elasticity-dominant flows. Inertia and
elasticity are non-linear effects that tend to destabilize a fluid flow alone, but when
simultaneously important, these effects have been shown to act constructively to stabilize it (e.g.,
turbulent drag reduction in macroscale pipes using high-molecular weight polymer solutions).
We show that in dilute (0.1% w/v hyaluronic acid (HA) in water) polymer solutions, bioparticles
focus (and remain focused) to a single equilibrium position at Reynolds numbers up to Re ~
10,000 (with Weissenberg numbers up to Wi ~ 2,000). We find that PTA (as well as pI-PIV)
can be used to construct particle focusing histograms and fluid velocity profiles based on seeded
particles with velocities in excess of 100 m.s'. We show that viscoelastic normal stresses are the
primary drivers of particle focusing (relative to shear-thinning or secondary flow effects), and
that these effects can be tuned to focus and stretch bioparticles based on fluid rheology. Given
that particle focusing can occur in a previously inaccessible flow regime in which both inertia
(Re >> 1) and elasticity (Wi >> 1) are present, we anticipate the development of: 1) numerical
models to provide insight into the physical basis of this novel phenomenon, and 2) microfluidic
technologies capable of rapidly processing very large volumes (-0(1000 ml)) of biological and
industrial fluids.
Thesis Supervisors:
Mehmet Toner I Professor of Health Sciences and Technology IHarvard Medical School
Gareth H. McKinley I Professor of Mechanical Engineering I Massachusetts Institute of Technology
3
4
Acknowledgements
It has been an immense blessing to work with (my research advisors) Mehmet Toner and
Gareth McKinley. Taking in Mehmet's entrepreneurial spirit and Gareth's intellectual curiosity
on a day-to-day basis gave me the enthusiasm and perseverance to tackle bold scientific ideas
from both a theoretical and practical perspective. They gave me the freedom to work on what I
wanted while providing the necessary resources to help me succeed in my work. I also had the
privilege of working with Thomas Ober and Jon Edd for much of my academic career. They
represent the gold standard for what I would hope for in a teammate, and I wish I could take
them with me as I move onto the next stage of my professional career. I'll be forever grateful to
Terry Orlando and Denny Freeman for helping me absorb (and heal from) the wounds that life
can inflict unexpectedly and forcefully. I also give a respectful nod to the brothers of Phi Beta
Epsilon, who always reminded me that there can be light within the tunnel (as well as at the end
of it).
5
6
Table of Contents
12
1i Overview
1.1 Microfluidic technology for controlled particle manipulation
12
1.2 Inertial focusing for controlled particle manipulation in microchannels
13
1.3 Scope and organization of thesis
14
2 1Controlled particle manipulation in microchannels
16
2.1 Microscale particle mining in a macroscale world
16
2.2 Inertial focusing for controlled particle manipulation in microchannels
19
2.3 Viscoelastic focusing for controlled particle manipulation in microchannels
24
2.4 Microfluidic technologies based on particle focusing
30
2.5 Unexplored aspects of particle focusing in microchannels
32
2.6 Summary
33
3 Bioparticle focusing in microchannels using diluted or whole blood
35
3.1 Introduction
35
3.2 Materials and methods
36
3.2.1 Device fabrication
36
3.2.2 Sample preparation
37
3.2.3 Image capture
38
3.2.4 Image analysis
39
40
3.3 Results and discussion
3.3.1 Image capture of individual particles flowing in blood-based suspensions
40
3.3.2 Quantitative measurements of particle focusing behavior in blood-based suspensions
44
3.3.3 Inertial focusing behavior of polystyrene beads in blood-based suspensions
45
3.3.4 Inertial focusing behavior of white blood cells (WBCs) in blood-based suspensions
46
3.3.5 Inertial focusing behavior of PC-3 (cancer) cells in blood-based suspensions
50
7
3.3.6 Rheological properties of test fluids
52
3.3.7 Bioparticle focusing in complex fluids
53
3.4 Summary
59
4 1Inertio-elastic focusing of bioparticles in microchannels at high throughput
61
4.1 Introduction
61
4.2 Materials and methods
62
4.2.1 Channel fabrication and design
62
4.2.2 Sample preparation
66
4.2.3 Fluid rheology measurements
67
4.2.4 Pressure drop measurements
69
4.2.5 Velocimetry measurements
71
4.3 Results and discussion
74
4.3.1 Flow regime characterization
74
4.3.2 Particle focusing characterization
76
4.3.3 Bioparticle focusing in microchannels
80
4.3.4 Establishing the boundaries of inertio-elastic focusing
84
4.4 Summary
88
51 Summary and outlook
90
5.1 Contributions
90
5.1.1 Tracking focused particles individually using particle trajectory analysis (PTA)
90
5.1.2 Accessing unexplored flow regime where both inertial and elasticity are present
90
5.1.3 Discovering novel focusing mode for bioparticles with ultra-high throughput
91
5.2 Limitations
92
5.2.1 Inertio-elastic focusing knowledge primarily limited to experimental studies
92
5.2.2 Particle isolation using inertio-elastic focusing is more complicated
92
5.3 Outlook
93
8
5.3.1 Establishing the principles of inertio-elastic focusing
93
5.3.2 Observing inertio-elastic focusing in complex microchannel geometries
93
5.3.3 Finding real-world applications for inertio-elastic focusing
94
95
6 1 Appendix
9
List of Figures
2-1
I Microfluidic
technologies used to achieve controlled particle manipulation in a fluid sample
2-2 Principles of inertial focusing in microchannels
2-3
IFundamental
17
20
properties of viscoelastic fluids
25
2-4 Principles of viscoelastic focusing in microchannels
29
2-5 I Microfluidic technologies based on inertial focusing
31
2-6 Visualization of particle focusing landscape
33
3-1
I Imaging techniques
used in inertial focusing studies
36
3-2 Microchannel fabrication using photolithography and soft lithography
38
3-3 IInertial focusing in straight microchannels
42
3-4 Image capture using particle trajectory analysis (PTA)
43
3-5 I Polystyrene bead focusing as a function of flow rate
Q and
3-6 I White blood cell (WBC) focusing as a function of flow rate
3-7 I PC-3 (cancer) cell focusing as a function of flow rate
RBC volume fractionfRB-
Q and RBC volume
fractionfRBc
Q and RBC volume fractionfRac
47
49
51
3-8 IRheometer measurements of diluted and whole blood
54
3-9 I PC-3 cell equilibrium positions in physiological saline and whole blood
58
3-10 1 PC-3 cell identification in whole blood
59
4-11 Particle focusing at high flow rates in Newtonian and viscoelastic fluids
63
4-2 1Rigid microchannel fabrication via hard lithography
65
4-3 1Design parameters for microchannel dimensions
66
4-4 1Shear rheology measurements of hyaluronic acid (H-A) solution
68
4-5 1 Extensional rheology measurements of HA solution
70
4-6 Friction factor in microchannel for Newtonian and viscoelastic fluids
72
4-7 I Obtaining fluid velocity measurements via micro-particle image velocimetry (p-PIV)
73
10
4-8 | Pressure drop measurements in rigid microchannel
4-9
I Particle focusing behavior
in water and HA solution
4-10 IEffect of shear-thinning on particle focusing
4-11
77
78
Direct comparisons of particle and fluid velocity along channel centerline
79
81
4-12 Secondary flow effects in HA solution
4-13
75
Inertio-elastic focusing of bioparticles based on deformability
82
4-14 I Inertio-elastic focusing of bioparticles based on shape
84
4-15 I Relevant scaling laws for inertio-elastic focusing
86
4-16 Operating space of inertio-elastic focusing in straight microchannels
87
6-1
Key parameters of micro-particle image velocimetry (p-PIV)
95
6-2 Inertial focusing as a building block for rare cell isolation
96
6-3 ITechnical barriers to accessing unexplored flow regime
97
6-4 I PC-3 (cancer) cell focusing in physiological saline and whole blood
98
6-5 Polystyrene bead focusing in xanthan gum and polyacrylamide solutions
99
11
Chapter 1 Overview
1.1 Microfluidic technology for controlled particle manipulation
The field of microfluidics can be defined as the science and technology of fluid
management using sub-millimeter scale channels [1]. A typical microfluidic device is an
assembled block of components that can perform the following operations: introduce fluid
samples into the device, manipulate fluid samples within the device, extract information found in
the fluid samples, and preserve information for downstream analysis. The handling of biological
or industrial fluids in microchannels represent a critical aspect of miniaturized device platforms
commonly referred to as lab-on-a-chip (LOC) technologies. Soft lithography (with
poly(dimethylsiloxane) (PDMS) as a substrate) [2] has spurred the development of prototype
devices that can be built rapidly (and cost-effectively) and be treated like "fluidic analogs" of
integrated circuits based on the complex design and precise control that can be achieved. These
device platforms can offer a number of useful features: executing separation and/or detection
steps with high resolution and sensitivity, minimal use of samples and reagents, streamlining
complex assay protocols, and massive scalability based on small footprints [3].
A prominent area of research on microfluidic technologies involves the controlled
manipulation (e.g., displacement, trapping, sorting) of particles found in a biological or industrial
fluid. For example, size-based particle displacement was achieved using a microchannel
containing periodic arrays of rigid obstacles [4]. Particle trapping (and pairing) of different cell
types was achieved using a microchannel containing a dense array of hydrodynamic traps [5].
Continuous cell sorting was achieved using a microchannel containing a fluorescence-activated
optical switch [6]. By effectively putting the lab on a chip, controlled particle manipulation in
microfluidic technologies has led to several critical real-world applications. For example, the
12
isolation of circulating tumor cells (CTCs) from whole blood [7] can enable clinical diagnosis of
cancer as well as direct access to CTCs for cancer biology studies. The sorting of single cells
encapsulated in aqueous droplets [8] can enable identification of bacterial or yeast strains
capable of over-producing or -consuming excreted technologically important metabolites.
Barcoded polymer particles synthesized via flow lithography [9] can enable covertly labeled
pharmaceutical packaging, multiplexed microRNA detection substrates, and embedded hightemperature-cast objects.
1.2 Inertial focusing for controlled particle manipulation in microchannels
Microfluidic technologies can take advantage of fundamental differences in the physical
properties of fluids between macroscale and microscale channels [10]. Perhaps the most critical
difference is the presence (or absence) of turbulence. Fluids mix convectively on large scales
where inertia is often the dominant effect (relative to viscosity). The opposite is true on small
scales such that two fluid streams that merge together in a microchannel flow in parallel without
eddies. In such viscosity-dominant flows, the only mixing that occurs is due to diffusion of
molecules across the parallel fluid interface [11]. Microfluidic technologies were primarily
limited to such flows based on the widely held notion that the small length scales required
operating flow regimes marked by negligible inertia.
Inertia-based particle migration was first observed in macroscale pipes [12], but it was
not until much later that this phenomenon was discovered in microchannels [13]. Randomly
distributed particles migrated to multiple stable (i.e., equilibrium) positions in a straight
microchannel (with rectangular cross-section) and to a single equilibrium position in an
asymmetrically curved microchannel. In straight microchannels, numerical and experimental
13
results suggest the presence of two competing effects (shear gradient lift and wall effect lift) that
are primarily responsible for "inertial focusing" [14]. In curved microchannels, numerical and
experimental results suggest that channel curvature introduces an additional force (Dean drag)
that can bias particle migration to a single equilibrium [15]. Inertial focusing has been used as an
essential component in microfluidic technologies to achieve high-throughput isolation of CTCs
from whole blood [16] and label-free biophysical marker (i.e., cell deformation) quantification
associated with the clinical diagnosis of cancer and inflammation [17].
1.3 Scope and organization of thesis
This thesis explores particle focusing in flow regimes in which both inertia and elasticity
are important. Inertial focusing has been widely explored using different channel geometries
(e.g., straight, asymmetrically curved, complex structures) and different particle types (e.g.,
polystyrene beads, white blood cells (WBCs), hydrogel particles), but the suspending fluid has
been predominantly limited to Newtonian fluids (where elasticity is negligible or non-existent).
Particle focusing has been observed in viscoelastic fluids with non-negligible inertia [18, 19], but
the operating flow regime was dominated by elasticity and well below the threshold for
associated with inertial focusing. Fluid inertia and fluid elasticity are both non-linear effects that
tend to destabilize a flow when acting alone [20, 21], but if they are simultaneously present, then
they can interact constructively to stabilize a given flow [22, 23].
The rest of this thesis is organized into three parts covering relevant background material,
essential technology development, and novel particle focusing observations. In chapter 2, we
provide an introduction to microfluidic technologies with special emphasis on controlled particle
migration. We first discuss microfluidic technologies that achieve controlled particle migration
14
based on viscosity-dominated flows. We then turn our attention to inertia-dominated flows and
discuss inertial focusing from both a theoretical and practical perspective. We also note the
recent work in elasticity-dominated microfluidic flows and identify an unexplored flow regime
(in which inertia and elasticity are important) that merits further investigation.
In chapter 3, we
present an imaging method (particle trajectory analysis (PTA)) capable of capturing fluorescent
images of individual particles traveling at speeds up to 2 m.s-1. We use PTA to characterize the
focusing behavior of polystyrene beads, WBCs, and PC-3 cancer cell lines in the presence of
diluted and whole blood. In chapter 4, we present a fabrication method (hard lithography with an
epoxy substrate) for high-pressure microchannels that can accommodate particle velocities in
excess of 100 m.s-1. We use PTA and other imaging techniques (micro-particle image
velocimetry (pt-PIV), micro-particle tracking velocimetry (p-PTV)) to observe particle and fluid
behavior in the microchannel. The shear and extensional rheology of a viscoelastic fluid are
measured and used to characterize "inertio-elastic focusing" in a previously inaccessible flow
regime marked by significant elastic and inertial effects. In chapter 5, we conclude with a
discussion of the advantages and limitations of inertio-elastic focusing in microchannels along
with suggestions for future work.
15
2 I Controlled particle manipulation in microchannels
2.1 Microscale particle mining in a macroscale world
The mining of microscale particles from large fluid volumes is an essential step in several
real-world macroscale applications. Particles of interest that can be found in biological and
industrial fluids include circulating tumor cells (CTCs) [24] or CD8+ T cells [25] in whole
blood, Escherichiacoli [26] or Nannochloropsis[27] in water, and sand [28] in fracturing fluids.
The detection, isolation, and/or preservation of such particles can be achieved using some form
of controlled particle manipulation. Non-microfluidic technologies built to perform such
operations include fluorescence-activated cell sorting [29], magnetic-activated cell sorting [30],
and centrifugation [31]. However, precise mining of particles in macroscale flows can be limited
in terms of sensitivity, throughput, and cost. Microfluidic technologies have more recently been
developed to achieve similar operations with several advantages, such as minimum use of
samples and reagents, screenings and isolations with high spatial and temporal resolution, and
device scalability for maximum throughput [32].
Controlled particle manipulation using microfluidic technologies has served as a viable
technological platform for several real-world applications. Using a microchannel containing
silicon posts [7] or graphene oxide nanosheets (Fig. 2-1a) [33] coated with an antibody to a
surface maker found on circulating tumor cells (CTCs), efficient isolation of these cells (via
immunoaffinity capture) was achieved from whole blood. Using a microchannel that
compartmentalizes individual cells in monodisperse nanoliter aqueous droplets, the screening of
cells can be achieved based on secretion/consumption of specific products that can be harvested
for drug discovery (Fig. 2-1b) [34, 35] and alternative energy [8]. Using a microchannel that
16
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. . ......
.....
a
oilo
V
...
.....
* -------
a2 II
Jk
yeast Celts
.'
....
-------*---
.......
-
----------- ...
I--
0
reinjected
emulsion
?,:
oil
signal
electrode
ground
electrode
C
(a)
Figure 2-11 Microfluidic technologies used to achieve controlled particle manipulation in a fluid sample.
from
CTCs
isolate
to
used
is
nanosheets
oxide
graphene
with
coated
A microchannel patterned with gold substrates
whole blood. Figure adapted from [33]. (b) A microchannel that encapsulates individual yeast cells in aqueous
surfaces.
droplets was used to screen for mutants expressing variants of the enzyme horseradish peroxidase on their
consumer
tag
to
Figure adapted from [34]. (c) A microchannel that synthesizes barcoded hydrogel particles is used
products with a unique signature that can be read using near-infrared illumination. Figure adapted from [9].
17
synthesizes barcoded hydrogel particles using flow lithography, screening for disease-specific
microRNA [36] and counterfeit-proof labelling of pharmaceutical packaging (Fig. 2-1c) [9] was
achieved. Microfluidic technologies have been able to exploit the presence of laminar flow that
typically exists in microscale flows where viscosity is the dominant effect [1]. In macroscale
flows (where inertia is the dominant effect), fluids mix convectively as a result of turbulent flow
(e.g., milk swirling around a cup of coffee, smoke moving out of a chimney into the open air).
The relative strength of inertia (relative to viscosity) in a fluid can be characterized by the
Reynolds number
Re= pUH
ri
where p is the fluid density, U is the fluid velocity, H is the channel dimension, and
1=
p=
constant is the viscosity for a Newtonian fluid. Fluid flow in microchannels has traditionally
been limited to Re < 1 based on the notion that practically useful effects on such small length
scales can only occur in the absence of inertial effects.
Microfluidic technologies based on viscosity-dominant flows have demonstrated
tremendous potential for achieving controlled particle manipulation in real-world applications
with small ( ; 1 ml) fluid volume requirements. However, other applications (e.g., rare cell
isolation [7], drinking water filtration [26]) demand that higher throughputs be achieved without
sacrificing separation efficiency. Certain methods (e.g., deterministic lateral displacement [4],
membrane filtration [37]) are prone to interparticle disturbances and clogging, while other
methods (e.g., optical traps [38], magnetic selection [39]) will have less effective residence time
in the microchannel. Additional methods (e.g., surface adhesion [40], mechanical traps [5]) will
likely result in damaged or dead cells due to increased flow rates and shear rates that correspond
to less viscosity-dominant flows.
18
2.2 Inertial focusing for controlled particle manipulation in microchannels
Particle migration as a result of fluid inertial effects was first observed in macroscale
pipes [12] such that randomly dispersed particles focused to an annulus (with the distance from
the center equal to approximately 0.6 times the pipe radius). Real-world applications based on
this phenomenon were not explored due to the large scale of the fluidic network as well as the
difficulty of isolating particles from an annulus. It was not until nearly 50 years later when
controlled particle manipulation in microchannels was explored for inertia-dominated flows [13].
In a straight microchannel with square cross-section, randomly distributed particles migrated
laterally to four stable (i.e., equilibrium) positions centered along each wall for Re = 90 and
channel length L ~1 cm (Fig 2-2a). The quality of particle focusing improved with higher Re
and increased distance from the channel inlet.
Previous studies suggested that the inertial lift force on rigid particles consist primarily of
two components: 1) a "wall effect" lift force generated by an asymmetric particle wake near the
wall that is directed toward the channel centerline [41], and 2) a "shear gradient" lift force
generated by differences in the relative velocity for parabolic flow that is directed toward the
channel wall [42]. These studies were limited to simplified model systems (i.e., parallel plates,
circular tubes) with particle confinement ratio a/H « 1 (where a is the particle diameter and H
is the cross-sectional dimension) such that "point-particle" approximations were made. A
numerical model was used in conjunction with experimental observations (in a straight
microchannel with rectangular cross-section) to characterize and predict inertial effects on
particles suspended in a Newtonian fluid [14]. Varying the x-y position in the channel crosssection yielded a distribution of steady-state forces and rotations for a particle held at a given
location. Both experimental and numerical results indicated that particle equilibrium position
19
a
x
0
0.6
1
34
t
C.)
F, c(pU 2 aH
1
F1 OcpU 2 a 6H
4
-9.
-12
00
02
04
Distance (
'
*06
08
equilibrium positions
S)
b
curvature ratio
Dh
-S
2r
Flow
kO*
Flow- P
6=0.0
6Avg=0.0083
N
C
0
0
U
.4_J
Lateral Position (y/w)
Figure 2-2 1Principles of inertial focusing in microchannels. (a) Particles focus to four equilibrium positions in a
straight microchannel (with square cross-section). The disjointed scaling of the lift force FL on the near-wall and
far-wall sides of the equilibrium position suggests the presence of two separate physical effects (i.e., shear gradient
lift and wall effect lift). Figure adapted from [13, 14] (b) Particles focus to a single equilibrium position in an
asymmetrically curved microchannel. Channel curvature alters the velocity field (and the resulting shear gradient
lift) such that particles are exposed to different regions of Dean flow based on particle size. Figure adapted from [13,
15].
20
was strongly dependent on the ratio of particle to channel dimension a/H. For a/H «
equilibrium position
Xeq
1, the
of the particle approached an annular position that was similar to that
previously observed in macroscale pipe flow [12]. However, a shift in Xeq towards the channel
center was observed as a/H increased from 0.1 to 0.9. For the whole range of observed sizes,
particles were found to be off-center but also displaced from the channel wall. Previous
calculations assuming negligible disturbance of channel flow by suspended particles have
yielded a uniform scaling throughout the channel for the lift force FL = fLpU2a 4 H-2 , where fL
is a nondimensional lift coefficient that is dependent on normalized particle position x/h and
channel Reynolds number Rc [43, 44, 45]. However, a disjointed scaling for FL was observed
(FL = fLpU.a
3
H ) for particle positions near the channel centerline versus FL =
fLpUma 6H- 4 for particle positions near the channel wall), which support the idea that two
separate physical effects govern particle behavior in the near-wall region and near-centerline
region (Fig. 2-2a).
In a straight microchannel with square cross-section, long trains of particles with uniform
spacing in the longitudinal direction were observed [13]. Particle-particle distances below a
certain threshold were not favored, and self-ordering in the longitudinal direction (i.e., in the
direction of the main channel flow) was observed. Previous work offered a general scaling for
interparticle spacing and suggested that reversing streamlines played an integral role in particle
train formation, but a more systematic study was not possible with cylindrical channel
geometries [46]. To further study the mechanism of dynamic self-assembly in the simplest
possible system, a straight channel with rectangular cross-section and two-inlet co-flows was
used [47]. The non-unity aspect ratio reduced the number of equilibrium positions from four to
two, and the two co-flows confined particles to one half of the channel so that only one focusing
21
position became accessible. This provided a 1 D system with interparticle spacing as the
dependent variable. Due to differences in speed (since particles entering the channel are
randomly distributed), a faster particle approached a slower particle and formed a particle pair
that moved downstream together. High-speed brightfield images of particle pairs suggested that
dynamic self-assembly is an irreversible process with distinct non-symmetric attractive and
symmetric repulsive interactions. In other words, particle pairs appeared to undergo a variety of
behaviors (including oscillatory motion in the longitudinal direction) prior to reaching a focused
and ordered state. The repulsive interaction was initiated by a viscous disturbance flow (which
became strong at small interparticle spacings) while inertial lift forces pushed the particles back
together. The nonsymmetric nature of the attractive force was consistent with different scaling
of the inertial lift force on different sides of the equilibrium position [14], and the multiple
oscillation cycles were attributed to overshoot of the equilibrium position. Numerical and
experimental methods were used to show the presence of reversing flows regardless of particle
Reynolds number, which suggests that such flows are due to channel confinement (and not fluid
inertia) in rectangular channel flow with parabolic shear.
Additional interactions between particles and the surrounding fluid must be considered
for inertia-dominant flow in curved microchannels. In an asymmetrically curved microchannel,
particle focusing to a single equilibrium position occurred at a lower Reynolds number
(Re ~ 10) and shorter channel length (L ~ 3.5 mm) relative to straight microchannels (Fig. 2-2b)
[13]. Secondary rotational flows caused by inertia of the fluid itself (i.e., Dean flow [48]) can
alter the position of flowing particles. The magnitude of these effects can be characterized in
terms of the dimensionless Dean number
22
De = Re D
2r
where Df is the channel hydraulic diameter, r is the channel radius of curvature, and 6 =
Dh(2r)~' is the curvature ratio. At moderate Dean numbers (De < 50), Dean flow consisted of
two counter-rotating vortices with flow directed toward the outer side wall along the channel
mid-plane and toward the inner side wall along the channel ceiling and floor [49]. The
magnitude of the rotational flow velocity UD scales as UD ~ pDe 2 p-1Dh1, which yields a drag
force attributed to Dean flow that scales as FD ~ pU2 aD2r- 1 . The balance between the inertial
lift force and the Dean drag force determines both the presence (or absence) and preferred
location of equilibrium positions for particles flowing through curved microchannels. Given that
the lift coefficient f, scales with Re' (under the condition that n < 0), the ratio of inertial lift
force to Dean drag forces scales as FL/FD -- S- 1 (a/Dft) 3 Ren [13]. In the limit where S -+ 0
(i.e., straight channels), Dean flow becomes negligible. But in general, this ratio has a strong
third-power dependence on the ratio of particle to channel dimensions. This means that for a
given Re, a larger particle could focus to an equilibrium position while a smaller particle remains
unfocused. However, this ratio also suggests that an upper limit on Re exists above which all
particles (regardless of size) will be defocused by mixing due to Dean flow. This is because the
inertial lift force FL scales with channel velocity squared U2 , but the lift coefficient f, decreases
2
with increasing Re, whereas the Dean drag force FD scales with channel velocity squared U
(without any contribution from f, with increasing Re).
Inertial focusing has also been studied in spiral microchannels with varying channel
widths [50]. Particle focusing was achieved at lower velocities and shorter distances in the
narrower devices. A narrower Re range of stable inertial focusing was observed for wider
23
devices, and the focused streamline shifted away from the inner sidewall at higher average
downstream velocities up to approximately 2 m.s' (where the focusing behavior broke down).
Inertial focusing in spiral microchannels with different curvature radii was then explored in order
to decouple the effects of Re and De for such flows [51]. The size-dependent particle focusing
behavior was characterized in terms of Re, S, and particle confinement ratio A = a/Dh. Two
different regimes of focusing were observed for all particle sizes (with the transition occurring at
approximately A1.s - 2): particles initially focused at the channel center eventually migrate
toward the inner sidewall with increasing Re (i.e., A1--5 > 2), or particles initially focused
within inner half of channel eventually migrate toward the outer sidewall with increasing Re
(i.e.,
A6-O.5
< 2). Numerical methods suggested that an increase in curvature ratio dampened
the shear gradient (due to reorientation of the velocity profile) in the inner half of the channel
(Fig. 2-2b). This effect shifted the vertical position of particles differently (based on particle
size) such that the particles experienced different regimes (i.e., direction and/or magnitude) of
Dean drag forces, resulting in different equilibrium positions that were dependent on both Re
and A.
2.3 Viscoelastic focusing for controlled particle manipulation in
microchannels
Particle focusing has been explored in-depth using different channel geometries (e.g.,
straight, asymmetrically curved, complex structures) and different particle types (e.g.,
polystyrene beads, white blood cells (WBCs), hydrogel particles), but the suspending fluid has
been predominantly limited to Newtonian fluids (where elasticity is negligible or non-existent).
Viscoelastic fluids can differ from Newtonian fluids based on shear rheology and extensional
rheology (Fig. 2-3). For example, a viscoelastic fluid can exhibit a viscosity r7 that decreases
24
a
Particle
Ay--
b
c
P-4
i
[s]
[sa]t
Figure 2-3| Fundamental properties
of viscoelastic fluids. (a) Tunable parameters for particle focusing include
(relative to a weaker viscoelastic fluid)
in response to an applied stress under extensional flows.
channel geometry (e.g., aspect ratio, curvature), particle geometry (e.g., size, shape, deformability), and fluid
rheology (e.g., Newtonian, viscoelastic). (b) A viscoelastic fluid can exhibit a viscosity that increases, decreases, or
time
remains constant over a range of shear rates. (c) A stronger viscoelastic fluid exhibits a longer relaxation
(i.e., shear-thinning) or increases (i.e., shear-thickening) with increasing shear rate f=UHl
under shear flow. In addition, a viscoelastic fluid can exhibit a non-zero relaxation tirme under
25
extensional flow. The progression and magnitude of fluid response to an applied stress can be
characterized in terms of Deborah number De* and Weissenberg number Wi
De* =
-
tp
Wi = A=
AU
H
where A is the stress relaxation time and tp is the observation time. The Deborah number
measures the degree to which the elastic effects have occurred over a given time interval. In
other words, if fluid flow (with steady rate of deformation) suddenly begins at time t = 0, De* =
co but then depends strongly on the fluid relaxation profile at short times. At long times where
the flow approaches steady state, De* -> 0. The Weissenberg number is the ratio of elastic
effects to viscous effects (as opposed to the ratio of inertial effects to viscous effects for the
Reynolds number). When describing flows with a constant stretch history (i.e., simple shear),
the Weissenberg number represents the degree of anisotropy (or orientation) of suspended
polymers generated by the applied deformation.
In fully viscoelastic fluids (with negligible inertia), rigid particles in macroscale pipe
flow were found to migrate in the direction of minimum shear rate (i.e., towards the channel
centerline) [52]. The rate of migration increased with particle diameter and radial distance from
the tube axis. Particles initially located in and around the tube axis did not rotate or migrate
radially. Note that these particles did not exhibit any migration in a Newtonian fluid. A
theoretical analysis based on the second-order fluid model was used to show that particle
migration in a weakly elastic fluid is predominantly dependent on the first normal stress
difference [53]. This effect takes the form of a tension in the longitudinal direction and is
proportional to the square of shear rate. It was suggested that these tensioned streamlines exert a
26
"hoop" stress on a particle, with the net force coming from the side of the particle with the
highest shear rates. Although the analytical model was not strictly applicable to a fully
viscoelastic fluid (which exhibits both shear-thinning viscosity and non-zero normal stresses), it
was inferred that normal stress contributions would dominate particle trajectories in such fluids.
Another theoretical study (based on the Galerkin finite element method) explored the
effects of inertia, shear-thinning and elasticity on particle migration in a two-dimensional
channel [54]. In a generalized Newtonian fluid (which allowed for the possibility of shearRe 5 56.0), shear-thinning effects and the
thinning) at moderate Reynolds number (12.5
curvature of the velocity profile induced strong shear stresses and large slip velocities that caused
particles to migrate toward the channel wall. When the Reynolds number was reduced by an
order of magnitude, inertial effects were not sufficiently large to generate a "particle-free zone"
along the channel centerline. This suggests that shear thinning effects have minimal influence on
particle migration when inertia (or shear rate) is sufficiently small. In an Oldroyd-B fluid (which
allowed for the possibility of both elastic and shear-thinning effects) at low Reynolds number
(0
Re 5 0.2) with elastic effects but without shear-thinning effects, particles migrated
towards the channel centerline due to viscoelastic normal stresses. However, when shearthinning effects were included, elastic normal stresses moved particles toward the channel
centerline while shear-thinning stresses moved particles toward the channel wall (resulting in
particle-free zones at annular positions). In other words, shear-thinning effects moved the
particles away from the channel centerline when inertia or elasticity was sufficiently large.
Particle migration in Newtonian and viscoelastic fluids with negligible inertia was
explored in microchannels with square [55] and cylindrical [56] cross-section. Particle migration
to the channel centerline was observed in the viscoelastic fluid (8% w/v poly(vinylpyrrolidone)
27
(PVP) in water) primarily due to contributions from the first normal stress difference N1 =
(TXX
-
ZqAf2',
with the shear rate being highest near the channel wall (Fig. 2-4a). Note
that the viscosity of PVP was constant over the range of shear rates explored. However, particles
in a shear-thinning fluid (1% poly(ethylene oxide) (PEO) in water) were initially focused along
the channel centerline before becoming radially diffuse with increasing shear rate. In other
words, shear-thinning effects appeared to drive particles toward the channel wall in the presence
of non-negligible inertia (Re ~ 0 (1)).
The effect of non-negligible inertia on particle focusing was explored in a straight
microchannel with square (50-pm diameter) cross-section [57]. In a viscoelastic fluid (8% w/v
PVP in water) with constant viscosity, particle migration was observed for elasticity-dominant
flow along the channel centerline and channel corners due to normal stress gradients. However,
particle migration was not observed for inertia-dominant flow. For a viscoelastic fluid (0.05%
w/v PEO in water) with shear-thinning, particle focusing shifted from a "quincunx" formation
(i.e., channel centerline and corners) at low flow rates to a single equilibrium position (Re
0.37, Wi = 8.04) at moderate flow rates before steadily decreasing in focusing quality at high
flow rates (Fig. 2-4b). It was suggested that a balance of inertial and elastic effects enabled
three-dimensional "elasto-inertial" focusing to occur. Viscoelastic focusing (with non-negligible
inertia) was further explored in a microchannel with cylindrical cross-section [58]. Using DNA
particles added to a viscoelastic fluid (0.05% w/v PEO in water) as an elasticity enhancer,
particle focusing was observed over a wide range of flow rates (0.018
28
Re
2.3). However,
..
..
. .............................
. .............
a
..............
- ............
. . ......
4
20 pl.min(
100 pl.min-1
.
b
PEO
PVP
. ..........
. .....
.....
......
. ......
0
Re
0.09, Wi= 1.96
S
Re = 0.37, Wi = 8.04
500 pl.min 1
Re= 0.60, Wi= 13.04
E9
S
02
---
elastic
shear-gradient
wall effect
fluid (8% PVP in
Figure 2-4 Principles of viscoelastic focusing in microchannels. (a) Particles in a viscoelastic
from
contributions
to
due
rate
flow
increasing
with
centerline
channel
the
water) with constant viscosity migrate to
viscosity
shear-thinning
with
water)
in
PEO
(1%
fluid
viscoelastic
a
in
Particles
the first normal stress difference.
migrate away from the channel centerline with increasing flow rate due to non-negligible inertia. Figure adapted
position
from [56]. (b) Particles in a viscoelastic fluid (0.5% w/v PEO in water) focus to a single equilibrium
[57].
presumably due to the synergistic effects of inertia and elasticity. Figure adapted from
Wi
El = RRe
particle focusing was optimal at the lowest flow rates and monotonically worsened with
of
increasing Re. The ratio of elastic effects to inertial effects can be expressed in terms
29
.
..
. ....
........................
.
- -- ----------
elasticity number to show that viscoelastic focusing (with or without inertia) in previous studies
has been characterized by El >> 1.
2.4 Microfluidic technologies based on particle focusing
In the case of inertial focusing, a critical feature is the ability to predictably align particles
in a microchannel using passive (and label-free) effects that actually improve with increasing Re.
This phenomenon can achieve controlled particle manipulation at high throughput without
sacrificing accuracy, and it can operate as a stand-alone entity or in tandem with other particle
mining methods (e.g., fluorescence-activated cell sorting, magnetic-activated cell sorting). For
example, a multi-stage microfluidic device consisting of deterministic lateral displacement,
inertial focusing, and magnetic separation steps was used to isolate circulating tumor cells
(CTCs) from whole blood (Fig. 2-5a) [59]. After removing the red blood cells (RBCs) in the
first stage, white blood cells (WBCs) and CTCs were focused to a single streamline (using an
asymmetrically curved microchannel segment) in the second stage. In the third stage, cells
labeled with magnetic beads were deflected from the focused particle streamline (in the presence
of a magnetic field), thus enabling efficient separation of target cells from non-target cells.
Isolated CTCs were found to be viable and possess high-quality genetic information for
molecular analysis. Another microfluidic technology utilized inertial focusing to mechanically
deform single cells using a cross-slot (i.e., 4-way street intersection) geometry [60]. Using an
asymmetrically curved microchannel, focused WBCs and malignant cells were uniformly
delivered to a stagnation point in the cross-slot geometry where they experienced deformation at
high strain rates due to a stretching extensional flow. Based on the resting and deformed state of
cells found in pleural effusions (i.e., an abnormal amount of fluid buildup in the lung), prediction
30
- -
...
.....................
.....
....
....
............
.
1- --
- ......
.
..
.
..
....
. ....
. ................................................
. .......
...............
a
bod ,#1o'iponen
WCTCs
Blood
Red blood cell (8 x 10 9/ml)
WBCs
White blood cell (5 x 10 6/ml)
CTC labeled with magnetic beads (1-100/mi)
*
*
$
Ruing
buffer
Hydrodynamic cell sorting -. Inertial focusing- Magnetophoresis
Inertial
focusing
-n-
-
Inlet filters
Met
Undefiected
Magnetic deflection
b
Flow
Erythrocyte lysis
Pleural effusion
PDMS
microchannel
CMVO
F
3.0
2.6
.0
2.2
b
L
d
FC
a
F
Initial
diameter,d
Deformability,
D = a/b
Malignant
1.8
1.0
cells
5
-1
i
25 Leukocytes
I
I J ,)A
Initial diameter (pm)
Fs
Figure 2-5 Microfluidic technologies based on inertial focusing. (a) Inertial focusing is used in conjunction
with deterministic lateral displacement and magnetic separation to isolate CTCs from whole blood. Figure adapted
from [59]. (b) Inertial focusing is used in conjunction with extensional flows to deform cells found in pleural
effusions. Figure adapted from [61].
31
............
of disease state in patients with cancer and immune activation was achieved. Moreover, the
deformability of specific cells served as an early biomarker for pluripotent stem cell
differentiation and could be related to changes in nuclear structure. This work was explored
further to develop a diagnostic score indicative of malignant pleural effusions obtained from
human subjects (Fig. 2-5b) [61]. Note that microfluidic technologies based on viscoelastic
focusing are limited due to operating flow regimes (Re ; 1) that are well below the threshold for
inertial focusing.
2.5 Unexplored aspects of particle focusing in microchannels
The operating flow regimes associated with inertial and viscoelastic focusing can be
visualized on a Wi-Re state space map (Fig. 2-6). Inertial focusing typically occurs in
Newtonian fluids (with an upper limit observed for Re ~ 1500 [62]), which means that Wi = 0
and El < 1. Viscoelastic focusing typically occurs for Re < 1 [63] but has also been observed
in the presence of non-negligible inertia [18, 19], but El >> 1 in either case. In short, there exists
a vast area of unexplored territory marked by El ~ 1, particularly in the case where Re >> 1 and
Wi >> 1. Elasticity and inertia are non-linear effects that can destabilize a fluid flow when
acting alone [20, 21], but if they are simultaneously present, then they can act constructively to
stabilize the flow [22, 23]. Given the role of high-molecular weight polymers in achieving
turbulent drag reduction in macroscale pipe flows [64], it is conceivable that particle focusing
can occur in "inertio-elastic" flows with sample throughputs that exceed the upper limits of both
viscoelastic and inertial focusing. It is worth noting that inertial focusing has only recently
(within the past seven years) debunked the traditionally held notion that microfluidic flows,
32
. ..
...........
...
.........
.. ....
.....................................
..........
.....
.
Wi
103(19]
102-
[641
10
___ _
*
Al
10-1
-
4-
(151
-4[631
I
U
31
100
10'
102
103
Re
104
Figure 2-6 1Visualization of particle focusing landscape. Observed flow regimes for viscoelastic focusing
(denoted with green line segments) and inertial focusing (denoted with blue line segments) are depicted as a function
of Re and Wi. Each study is referenced by a number in brackets. The orange box represents an unexplored flow
regime in which inertia and elasticity are comparable (with respect to each other).
given their small length scale, require correspondingly small Re flows in order for useful effects
to occur.
2.6 Summary
Controlled manipulation of particles is an essential step in several real-world
applications. Microfluidic technologies based on viscous-dominated flows have demonstrated
effective particle mining from biological and industrial fluids. Inertia-dominated flows can
achieve controlled particle manipulation in microchannels at high throughput, either as a standalone entity or in conjunction with other sorting methods. Elasticity-dominated flows can exhibit
33
different particle focusing modes but at sample throughputs well below the threshold for inertial
focusing in microchannels. An unexplored flow regime exists where both inertia and elasticity
are important. Fluids containing drag-reducing polymers (of high molecular weight) could
enable particle focusing at sample throughputs that exceed the fundamental limits of viscoelastic
and inertial focusing in microchannels. The novelty and importance of this unexplored flow
regime merits further investigation.
34
Chapter 3 1Bioparticle focusing in microchannels
using diluted or whole blood
3.1 Introduction
When inertial focusing in microchannels was first discovered, evidence of particle
focusing was recorded using long-exposure fluorescence (LEF) imaging and high-speed brightfield (HSB) imaging (Fig. 3-1) [13]. LEF imaging can be used to obtain the signal intensity of
all fluorescent particles moving through an interrogation window over a given time interval.
This provides bulk population statistics of particle focusing behavior that be used at high flow
rates (provided that the microchannel can accommodate high-pressure flows without
deformation). However, individual particle statistics (e.g., size, deformation, inter-particle
spacing) cannot be obtained using this imaging technique. HSB imaging is capable of providing
individual particle statistics but is typically limited to particle velocities less than 1 m.s-1 [65]
before significant particle blurring occurs (without the use of a moving microscope stage or a
novel microscopy setup that combines laser illumination with an ultra-fast photodetector [66]).
One imaging approach that has not been widely considered in inertial focusing studies is
micro-particle image velocimetry (t-PIV), which generates velocity fields of seeded particle
flows with micron-scale resolution [67]. The light source is a double-pulsed Nd:YAG laser that
is focused by an epifluorescent microscope with high numerical aperture on a microchannel.
Given the high intensity (Class IV) of laser illumination, very short (5-10 ns) pulse widths are
sufficient to identify the position (and resulting velocity) of fluorescent particles flowing through
the microchannel within a given depth of field. Moreover, the flow behavior of bioparticles in
physiologically relevant fluids has been studied using pt-PIV (or a closely related variation of it)
[68, 69]. In this chapter, we explore the use of an imaging technique (particle trajectory analysis
35
.......
..........
_ ---_._ .__
...
......
.....
....
...
.......
..............
. .....
....
....
. ....
.....
.....
__._..
. ...
Bulk
4
LEF L
I
4
0.1
1
up [m'l
10
100
HSE
PTA
Individual
Top View
up
- 0.1
Mis
Top View
±
up -I m.51
Top View
0
w
HSB
LEF
PTA
Figure 3-1 1Imaging techniques used in inertial focusing studies. Long-exposure fluorescence (LEF) imaging
provides bulk population statistics over a wide range of particle velocities. High-speed bright-field (HSB) imaging
provides individual particles statistics over a short range of particle velocities. Particle trajectory analysis (PTA)
provides individual particle statistics over a much wider range of particle velocities.
(PTA) which is based on p-PIV) to capture images of individual particles flowing through a
microchannel at speeds in excess of 1 m.s 1 . We then use PTA to characterize the focusing
behavior of polystyrene beads, WBCs, and PC-3 (prostate) cancer cell lines in various biological
fluids (i.e., physiological saline, diluted blood and whole blood).
3.2 Materials and methods
3.2.1 Device fabrication
A straight rectangular channel (h =93 mm, w =45 mm, L = 3.5 cm) was formed in
polydimethylsiloxane (PDMS) from a SU-8 master via photolithography and soft lithography
36
.
......
[70] (Figure 3-2). A 4-inch silicon wafer was spin-coated with a 93-pIrm thick layer of negative
photoresist (SU-8 100, Microchem, Newton, MA), exposed to UV-light through a Mylar
photomask (Fineline Imaging, Colorado Springs, CO), and developed (BTS-220, J.T. Baker,
Phillipsburg, NJ). A 10:1 mix of PDMS elastomer and curing agent (Sylgard 184, Dow Coming,
Midland, MI) was poured onto the master mold and degassed for 60 min to remove all trapped
bubbles. The master mold was placed in a 80'C oven for 72 h to thoroughly cure the PDMS. The
cured PDMS replica was peeled away from the master mold before inlet, outlet, and height
calibration holes were punched using a coring tool (Harris Uni-Core, Redding, CA) with a hole
diameter of 1.5 mm. The hole-punched PDMS replica was irreversibly bonded to a glass
coverslip by exposing both PDMS and glass surfaces to 02 plasma for 30 s (Harrick Plasma,
Ithaca, NY).
3.2.2 Sample preparation
Fluorescently labeled polystyrene beads (FluoSpheres, Invitrogen, Carlsbad, CA) were
supplied as stock suspensions in 0. 15M NaCl with 0.05% Tween 20 and 0.02% thimerosal. PC3 human prostate cancer cells (CRL-1435, ATCC, Manassas, VA) were grown in F-12 K
medium (3 0-2004, ATCC, Manassas, VA) containing 10% fetal bovine serum (Invitrogen,
Carlsbad, CA) and 1% penicillin streptomycin (Invitrogen, Carlsbad, CA) at 37'C under 5% CO2
San Jose, CA). The RBC volume fraction (i.e., hematocrit count) in each sample was determined
using a blood analyzer (KX-2 1, Sysmex, Mundelein, IL). WBCs were recovered from whole
blood via RBC lysis buffer (Miltenyi Biotec, Auburn, CA) and fluorescently labeled in PBS
containing 5 mM Calcein Red-Orange AM. Fluid samples with a specific RBC volume fraction
37
a
b
C
e
f
Figure 3-2 Microchannel fabrication using photolithography and soft lithography. (a) SU-8 is spin-coated
and baked onto a silicon wafer. (b) SU-8 is exposed to UV light through a photomask containing the desired
features. (c) Exposed SU-8 is baked and developed to reveal channel features on silicon wafer. (d) Uncured
PDMS is poured over the SU-8 master. (e) Cured PDMS with imprinted features is peeled away from SU-8 master.
(f) Fluid ports are punched into PDMS replica prior to bonding with glass slide via 02 plasma treatment. Tygon
tubing is inserted into fluid ports.
were generated by suspending particles in appropriate amounts of PBS and whole blood. The
particle concentration was set at 3.0 x 106 particles.ml'.
3.2.3 Image capture
The starting sample containing fluorescently labeled particles was injected into the
microchannel using an automated syringe pump (PhD 2000, Harvard Apparatus, Holliston, MA)
at flow rates of Q = 50, 150, and 450 ml.min'. This corresponds to particle velocities of U
0.21, 0.62, and 1.85 m.s 1 . The sample loading system consisted of 5-ml syringe (BD
Biosciences, San Jose, CA), 22-gauge blunt needle (Small Parts, Seattle, WA), 0.02-inch inner
diameter tubing (Tygon, Small Parts, Seattle, WA), and cyanoacrylate adhesive (Loctite, Henkel,
Rocky Iill, CT). Images of particles flowing through the chatmel were cap ured using Nd:YAG
38
laser-light illumination (LaVision, Ypsilanti, MI), an epi-fluorescent inverted microscope (TE2000, Nikon, Melville, NY), and a charge-coupled device camera (PIV-CAM 14-10, TSI,
Shoreview, MN). The laser generated 10-ns pulses of light with an excitation wavelength of 532
nm, and the camera detected light from fluorescent particles with an emission wavelength
exceeding 565 nm. At a stationary location 3.5 cm downstream from the channel entrance,
images were captured at 8 different height positions spaced 6 mm apart. Prior to image capture,
1 0-pm polystyrene beads (FluoSpheres, Invitrogen, Carlsbad, CA) were allowed to settle to the
floor (i.e., y = 0) of the microchannel in order to set imaging locations. For each height position,
a set of 400 images were collected at a rate of 5 frames per second.
3.2.4 Image analysis
ImageJ software (NIH, Bethesda, MD) was used to process raw images and identify infocus particles at each height position. For an in-focus particle at a given height location, images
were taken at multiple height positions in order to observe corresponding changes in
fluorescence signal intensity indicative of an out-of-focus particle. An in-focus particle was
predominantly found to exhibit both a higher mean 8-bit grayscale value and a steeper edge
signal intensity gradient relative to an out-of-focus particle. For each set of 400 images at a
given height location, an image threshold was automatically set using an iterative procedure
based on the isodata algorithm [71]. Using a specific cutoff for particle size based on size
distribution measurements from a cell analyzer, the image filtering technique automatically
generated a table of potential in-focus particles. All particles were marked in the set of images
and referenced numerically in the table, and each particle was characterized based on a userdefined set of parameters (e.g., 2-D particle area, mean signal intensity, x-z position, and
39
circularity). The collection of potential in-focus particles were examined manually to ensure that
in-focus particles were identified and measured properly. For a given flow rate and RBC volume
fraction, quantitative measurements from the collection of in-focus particles were used to
construct surface and scatter plots characterizing various aspects of particle focusing behavior
using MATLAB (Mathworks, Natick, MA).
3.3 Results and Discussion
3.3.1 Image capture of individual particles flowing in blood-based suspensions
Particle trajectory analysis (PTA) was used to identify polystyrene beads, white blood
cells (WBCs), and PC-3 cells over a range of flow rates
fpBc
Q and RBC volume fractionsfiRBc,
where
is the ratio of RBC volume to the starting sample volume. For example, HCT= 45% (i.e.,
whole blood in this study) corresponds tofRBc = 1, while HCT= 15% corresponds tofRBC
0.33
(diluted using PBS). A straight rectangular channel with a 2:1 (h/w) aspect ratio was used to
focus randomly distributed particles to two lateral equilibrium positions centered on the long
face of the channel (Figure 3-3a). These equilibrium positions resulted from a balance of a
"wall effect" lift that acts away from the wall towards the channel centerline and a "particle
shear" lift that acts away from the channel centerline towards the wall (Figure 3-3b). Inertial lift
forces induce lateral migration of particles to stable equilibrium positions at finite particle
Reynolds number RP = Rc(amDh 1) 2 , where R, is the channel Reynolds number, am is the
particle diameter, and Df = 2wh(w + h)- is the hydraulic diameter (with channel height h and
channel width w. Polystyrene beads (mean particle diameter a, = 9.9 pm) used in this study
were monodisperse in nature, while white blood cells (am = 9.0 pm, size range of 7-11 gm) and
40
PC-3 cells (am = 17.8 pm, size range of 10-35 pm) were polydisperse in nature. Note that the
depth of field 6, in a standard microscope objective lens is defined [72] by
6z
nAO
ne
2
NA-M
NA
where n is the refractive index of the fluid, ,o is the wavelength of light being imaged by the
optical system, NA is the numerical aperture of the objective lens, M is the total magnification of
the system, and e is the smallest distance that can be resolved by a detector located in the image
plane of the microscope. For the microscopy system used in this study, the depth of field 5z =
5.8 ptm. In order to reliably differentiate between in-focus particles found at neighboring vertical
positions, the spacing between all vertical positions was set to 6 pm. The imaging locations were
confined to the bottom half of the channel since particle focusing was expected to be symmetric
across the channel mid-plane (i.e., y = 48 pm).
At a given height within the microchannel (e.g., y =48mm), in-focus particles exhibited
peak and uniform fluorescence signal intensity, while out-of-focus particles exhibited suboptimal and radially diffuse fluorescence signal intensity (Figure 3-4a). Using the appropriate
image threshold, it was possible to differentiate in-focus particles at a given vertical position
from in-focus particles at neighboring vertical positions. As a result, in-focus particles found at
all vertical positions were used to make quantitative measurements of particle focusing behavior.
In diluted blood samples where the utility of high-speed bright-field imaging and long-exposure
fluorescence is limited, PTA demonstrated the ability to capture images of individual in-focus
particles moving at ultra-fast velocities (Figure 3-4b). Image capture of individual in-focus
particles (with no evidence of particle streaks) was achieved at flow rates up to
Q = 450 pl.min
in PBS initially, which corresponds to a mean flow velocity of U = 1.85 m.s' and a channel
41
a
b
FL
.00.000
not
0
*00
0**
.2
F
FL
net
FL
0
F
0=
Ft
0
Equilbriumn Positions
Figure 3-3 Inertial focusing in straight microchannels. (a) Randomly distributed particles predominantly focus
to two lateral positions centered on the long face of a straight microchannel with 2:1 aspect ratio. (b) The
equilibrium positions result from a balance of a "wall effect" lift that acts away from the wall towards the channel
centerline and a "particle shear" lift that acts away from the channel centerline towards the wall.
Reynolds number of R, = 158. We limited our study to this range of flow rates, as flow rates
beyond
Q = 450 pl.min'
forfRBc = 1 generated a fluid pressure at the device inlet that exceeded
the critical de-bonding pressure of the PDMS-glass interface. Once PTA-based identification of
individual in-focus particles was established in physiological saline, we repeated these
experiments for polystyrene beads, white blood cells, and PC-3 prostate cancer cells suspended
in diluted blood (Figure 3-4c). AsfRBc increased, in-focus particles exhibited a fluorescence
signal intensity that was weaker and less uniform. However, it was still possible to distinguish
likely in-focus particles from undoubtedly out-of-focus particles for a given
42
Q andfBc.
b
a
PTA
LEF
HSB
0
N
C
0
C
Polystyrene Beads
PC-3 Cells
White Blood Cells
fpsc
fRac
fRec
fMsC
fFMC
fFRC
0
0.07
1
0
0.07
1
fASC
ffec
fROC
0
0.07
1
Figure 3-4 1Image capture using particle trajectory analysis (PTA). (a) Particle focusing behavior is observed
in the x-z plane from eight different vertical positions spanning the bottom half of the channel. Focused particles are
shown to be in focus at y8 =48pm (scale bar = 20 pm). (b) For high-speed bright-field (HSB) microscopy with an
exposure time of 2 ps, individual white blood cells can be identified in physiological saline (fJkc = 0) but not in
diluted blood (fpBc = 0.07). For long-exposure fluorescence (LEF) microscopy with an exposure time of 1 s, a bulk
white blood cell distribution profile can be identified, but the profile cannot be de-constructed based on height
position or particle diameter. For particle trajectory analysis (PTA) with an exposure time of 10 ns, individual white
blood cells re-suspended in physiological saline or diluted blood can be identified at multiple vertical positions in
1
the channel (scale bar = 20 pm). (c) At a flow rate Q = 450 pl.min , PTA images of polystyrene beads (R, = 2.91
forfpBi.c = 0), white blood cells (Rp = 2.41 forfRc = 0), and PC-3 prostate cancer cells (Rp = 9.11 forjfc = 0)
suspended in physiological saline and diluted blood demonstrate that individual in-focus particles can be identified
in starting samples with higher RBC volume fractions (fRac) without significant degradation in fluorescence signal
quality (scale bar = 20 pm).
43
.3.3.2 Quantitative measurements of particle focusing behavior in blood-based suspensions
For a given
Q andfpBc, in-focus particles
from all vertical positions were used to make
quantitative measurements of particle focusing behavior. The distribution of particles in the
channel cross-section (y-z plane) was visualized using an intensity map in which each individual
rectangle represented a possible location for the centroid (y,,z,) of an in-focus particle. The color
scale used to represent the particle frequency nj at a given point in the y-z plane consisted of full
color (for nf> 10), grayscale (for 1 < nf< 10), and white (for nf= 0). Given the polydisperse
nature of white blood cells and PC-3 cells, a scatter plot of lateral centroid coordinate z, versus
particle diameter a was constructed. For a straight rectangular channel with a 2:1 (h/w) aspect
ratio, particle focusing is predominantly reduced to two lateral equilibrium positions centered on
the long face. We evaluated inertial focusing quality of in-focus particles at eight equally spaced
y-positions (spanning the floor and mid-plane of the microchannel). Since no accepted metric
exists to define inertial focusing quality, we established a non-dimensional term "bandwidth
efficiency" 8z that is dependent on mean particli diameter am, the mean lateral distance zn of an
in-focus particle (as an absolute value) from the channel centerline, and the standard deviation az
of in-focus particles in the z-direction (Table 3-1). Bandwidth efficiency was defined as Jz=
Wb am 1 = (4az + am) am-', where Wb is the edge-to-edge bandwidth in the z-direction over which
95% of all in-focus particles can be found. Note that /%is normalized by am, which will vary
depending on the class of particles used. As a result, /2
1 in all cases, with pz > 1 when
particle focusing is nearly perfect (oz ~ 0). Based on the current imaging and device setup,
scanning resolution in the z-direction was comprehensive and continuous, while scanning
resolution in the y-direction was incomplete and segmented. Nonetheless, we established a nondimensional term "focusing utility" PO, to serve as a crude measure of particle focusing fidelity
44
P'let~rene lkeads
5((
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IN
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11.57
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Table 3-11 Quantitative measurements of particle focusing behavior as a function of flow rate Q and RBC
volume fractionfRBc. For a given Q andfRBc, the particle Reynolds number Rp, the mean in-focus lateral distance z.
from the channel centerline, the bandwidth efficiency /, and the focusing utility <P were calculated for polystyrene
beads, white blood cells, and PC-3 prostate cancer cells.
near predicted equilibrium positions in the y-dimension. Given that particle focusing in the
microchannel should result in equilibrium positions near the mid-plane, focusing utility was
defined as
3,
= nfN, where nf is the number of in-focus particles found at the upper four y-
positions and N is the number of in-focus particles found at all eight y-positions. In other words,
since particles were not expected to occupy the lower four y-positions, their presence at these
positions would likely result in reduced recovery of particles downstream.
3.3.3 Inertial focusing behavior of polystyrene beads in blood-based suspensions
Polystyrene beads have been used extensively to study particle focusing behavior in
microchannels [13, 73]. As ready-to-use monodisperse particles exhibiting strong and uniform
45
fluorescence intensity, polystyrene beads were ideal particles. Given the mean particle diameter
and channel dimensions, the particle Reynolds numbers of polystyrene beads in physiological
saline for flow rates
Q = 50,
150, and 450 pil.min' were R, = 0.32, 0.97, and 2.91. Using flow
rates that correspond to Rp < 1, Rp ~ 1, and Rp > 1, polystyrene beads served as a reference
standard for white blood cells and PC-3 cells. For
Q = 50 pl.min'
in PBS (fRBc = 0), bead
focusing in both the z-direction (8z = 1.27) and the y-direction (Py = 0.91) approached optimal
levels (Figure 3-5). WhenfRBc = 0.07, bead focusing decreased moderately in the y-direction (OP
= 0.73) with minimal decrease in the z-direction (8z = 1.35). WhenfpBc = 0.33, bead focusing
was poorly organized in both the z-direction (Jz = 2.86) and y-direction (Py = 0.81). For Q = 150
pl.min' in PBS (fRBC = 0), bead focusing in both the z-direction (#z = 1.08) and the y-direction
(Oy = 1) reached optimal levels. WhenfRBc = 0.07, bead focusing decreased moderately in the zdirection (8z = 1.56) with minimal decrease in the y-direction (Py = 0.96). ForfRBc = 0.33, bead
focusing decreased further in a similar manner (IJz = 1.82, Py = 0.87) but remained largely intact.
For
Q = 450 pl.min'
in PBS (fRBc
(f = 1.45) and the y-direction (y=
=
0), bead focusing became suboptimal in both the z-direction
0.86), as multiple beads occupied a previously unstable
equilibrium position despite a non-unity channel aspect ratio. WhenfRBc = 0.07, bead focusing
decreased minimally in the z-direction (pz = 1.54) but improved minimally in the y-direction (iy
= 0.91). WhenfRBc = 0.33, bead focusing remained largely intact despite a moderate decrease in
the z-direction (fr= 1.79) and a minimal decrease in the y-direction (1i = 0.86).
3.3.4 Inertial focusing behavior of white blood cells (WBCs) in blood-based suspensions
Given significant interest to integrate inertial focusing into more portable and costeffective flow cytometry technologies [65, 74], the focusing behavior (and potential separation
46
f
48
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(VI
Figure 3-5 IPolystyrene bead focusing behavior as a function of flow rate Q and RBC volume fractionfuw.
ForfRBc- = 0, values of Q correspond to Rp = 0.32, 0.97, and 2.9 1. ForfR~gc =0.07, values of Q correspond to Rp
0.26, 0.80, and 2.40. Forf1 c = 0.33, values of Q correspond to Rp = 0.16, 0.49, and 1.46. The in-focus vertical
position yf and in-focus lateral distance zf from the channel centerline for polystyrene beads were used to construct a
8
cross-sectional particle histogram, and calculate the measures , and O, given in Table 1.
efficiency) of white blood cells (WBCs) was investigated. For the mean particle diameter and
channel dimensions used in this study, the particle Reynolds numbers of WBCs in physiological
saline for flow rates
Q = 50,
150, and 450 pi.min' were Rp = 0.27, 0.80, and 2.41. Since WBCs
have a size range of 7-11 ptm, the lower bound of Rp = 0.16, 0.48, and 1.46, while the upper
bound of Rp = 0.40, 1.20, and 3.60. For Q =50 pl.min' in physiological saline (fRBC = 0), WBC
focusing in both the z-direction (#z= 1.43) and the y-direction (<y = 0.79) was weaker relative to
polystyrene beads (Figure 3-6a). In particular, multiple WBCs were found unfocused at the
47
lower four y-positions (i.e., near the floor of the microchannel). WhenfRBc = 0.07, WBC
focusing decreased moderately in both the z-direction (p8, = 1.85) and y-direction (ky = 0.55).
WhenfRBc = 0.33, WBC focusing was poorly organized in both the z-direction (pz =3.13) and ydirection (Ok =0.40). For
Q =150
pl.min' in PBS (fRBc =0), WBC focusing improved in the z-
direction (p6z =1.28) but deteriorated in the y-direction (Py = 0.72) as more WBCs were found
unfocused at vertical positions near the channel floor. WhenfRBc = 0.07, particle focusing
deteriorated moderately in both the z-direction (fz = 1.82) and the y-direction (Py =0.6 1).
However, most WBCs were found near a channel wall to the extent that a loose annulus of
WBCs appeared to form. WhenfRBc =0.33, WBC focusing decreased further in both the zdirection (8, =2.44) and the y-direction (Oy = 0.54) as the annulus of WBCs became more
radially diffuse. For Q =450 pl.min' in PBS (fRBC = 0), WBC focusing decreased moderately the
z-direction (p8z = 1.43) with minimal improvement in the y-direction (Py = 0.75) as WBCs
occupying vertical positions near the channel floor became organized around a previously
unstable equilibrium position despite a non-unity aspect ratio. WhenfRBc = 0.07, WBC focusing
decreased moderately in the z-direction (l, = 1.82) and reversed in the y-direction (Oy = 0.61) as
an annulus of WBCs appeared to form. WhenfRBc = 0.33, WBC focusing decreased moderately
in the z-direction (8z = 2.33) and minimally in the y-direction (Oy =0.5 7) as the annulus of WBCs
became more radially diffuse. Since the WBCs used were polydisperse in nature, we investigated
the relationship between particle diameter a and lateral distance zy of an in-focus WBC (as an
absolute value) from the channel centerline (Figure 3-6b). Despite the narrow size range
observed, larger WBCs were found to be slightly closer to the channel centerline (i.e., smaller zj).
48
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Figure 3-6 1WBC focusing behavior as a function of flow rate Q and RBC volume fractionfRBc. ForfBc = 0,
values of Q correspond to Rp = 0.27, 0.80, and 2.41. ForfRBc = 0.07, values of Q correspond to Rp = 0.22, 0.66, and
1.99. ForfRBc = 0.33, values of Q correspond to Rp = 0.14, 0.40, and 1.21. (a) The in-focus vertical position yf and
in-focus lateral distance zf from the channel centerline for white blood cells were used to construct a cross-sectional
particle histogram. (b) The dependence of particle diameter a on in-focus lateral distance zj can be illustrated using a
particle scatter plot. The dotted line represents the location of the sidewall given a non-deformable microchannel.
49
3.3.5 Inertial focusing behavior of PC-3 cells in blood-based suspensions
Given significant interest to integrate inertial focusing into biocompatible, highthroughput rare cell isolation technologies [75], the focusing behavior (and potential separation
efficiency) of rare cells such as circulating tumor cells (CTCs) in was investigated. We used a
model prostate cancer cell line (PC-3) to assess CTC focusing behavior in blood. Given the
mean particle diameter and channel dimensions, the particle Reynolds number of PC-3 cells in
physiological saline for the given set of flow rates were Rp = 1.01, 3.04, and 9.11. Since the
particle diameter ranged from 10-35 pm, the lower bound of R = 0.33, 0.99, and 2.97, while the
upper bound of Rp = 3.91, 11.76, and 35.26. For Q =50 pl.min' in PBS (fRBc = 0), PC-3 cell
focusing in both the z-direction (fz = 1.47) and the y-direction (Oy = 1) approached optimal
levels (Figure 3-7a). WhenfRBc = 0.07, PC-3 cell focusing was largely unaffected in both the zdirection (#z = 1.56) and y-direction (Oy = 1). WhenfRBc = 0.33, PC-3 cell focusing decreased
moderately in the y-direction (Oy = 0.92) but improved minimally in the z-direction (fz = 1.45).
Since PC-3 cell focusing remained strong, particularly in the z-direction, we repeated this
experiment using whole blood (HCT= 45%). ForfRBc =1,PC-3 cell focusing shifted radically (8,,
= 1.22, Py = 0.17) as PC-3 cells were predominantly found along the channel centerline (z =0)
around a previously unstable equilibrium position (due to the non-unity channel aspect ratio).
No PC-3 cells occupied the previously stable equilibrium positions observed at lowerfRBC. For Q
=150 pl.min' in PBS (fRBC = 0), PC-3 cell focusing in both the z-direction (#z = 1.25) and the ydirection (Oy = 1) reached optimal levels. WhenfRBc = 0.07, PC-3 cell focusing was largely
unaffected in both the z-direction (Iz = 1.32) and y-direction (Py = 1). WhenfRBc = 0.33, PC-3
cell focusing decreased moderately in both the z-direction (8I = 1.41) and the y-direction (OP =
50
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7, PM)
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.Pm)
fraction
Figure 3-7 1PC-3 prostate cancer cell focusing behavior as a function of flow rate Q and RBC volume
values of Q correspond to R,
fRBc. ForfBc = 0, values of Q correspond to R, = 0.27, 0.80, and 2.41. ForfBc = 0.07,
(a) The in-focus vertical
1.21.
and
0.40,
= 0.22, 0.66, and 1.99. ForfRBc = 0.33, values of Q correspond to R, = 0.14,
to construct a crossused
were
cells
PC-3
for
position y and in-focus lateral distance zf from the channel centerline
zf for PC-3 cells
distance
lateral
in-focus
on
a
sectional particle histogram. (b) The dependence of particle diameter
a nongiven
sidewall
the
of
location
the
represents
was illustrated using a particle scatter plot. The dotted line
deformable microchannel.
51
I
1). ForfRBc = 1, PC-3 cell focusing again shifted radically (J,= 1.22, Py = 0) as PC-3 cells
predominantly occupied an equilibrium position (centered on the short face of the channel) not
observed at lowerfpBc. For
Q = 450 pl.min'
in PBS (fRBC = 0), PC-3 cell focusing in both the z-
direction (8z = 1.28) and the y-direction (Py = 1) remained at optimal levels due to the lack of
PC-3 cells found at vertical positions near the channel floor (in contrast to the observations for
polystyrene beads and white blood cells). WhenfRBc = 0.07, PC-3 cell focusing was largely
unaffected in both the z-direction (8z = 1.28) and y-direction (Oy = 1). WhenfRBc = 0.33, PC-3
cell focusing decreased moderately in both the z-direction (8.z = 1.35) and the y-direction (P=
1). WhenfpBc
previously for
1, PC-3 cell focusing again shifted radically (#z = 1.32, Oy = 0) as described
Q=
150 pl.min', but PC-3 cell focusing decreased moderately in the z-direction.
Since the PC-3 cells used were polydisperse in nature, we investigated the relationship between
particle diameter a and lateral distance zf of an in-focus PC-3 cell (as an absolute value) from the
channel centerline (Figure 3-7b). WhenfRBc = 0, 0.07, or 0.33, a linear correlation between the
two parameters was observed, such that large PC-3 cells were situated closer to the channel
centerline (z = 0), while small PC-3 cells were situated closer to the channel wall (z = 422.5
mm). WhenfRBc = 1, large PC-3 cells formed a tighter distribution around the channel centerline
relative to small PC-3 cells.
3.3.6 Rheological properties of test fluids
In an attempt to gain insight into the radical shift in PC-3 cell focusing behavior when
fRBC increased from 0.33 to 1, we used a rotational rheometer with a concentric cylinder
geometry to measure the effective viscosity of the test fluid atfRBC = 0, 0.33, and 1 as a function
of shear rate k (Figure 3-8a). The governing equations of motion for a non-Newtonian fluid
52
(such as whole blood) in a rectangular geometry cannot be reduced to simple equations and
solved analytically. However, we used a power-law model to describe the test fluid in the x-z
plane for the ideal case of y = 48 ptm (i.e., the mid-plane of the microchannel) where fluid flow in
the x-direction can be approximated using a simple one-dimensional equation. The viscosity il of
a power-law fluid [76] is defined as 77 = mIkI",
where k is an imposed shear rate, m is a
positive constant called the consistency index (with dimensions Pa-s"), and n is a dimensionless
positive constant. For a fluid whose viscosity is constant regardless of shear rate (i.e.,
Newtonian), n = 1. For a fluid whose viscosity decreases with increasing shear rate (i.e., shearthinning), n < 1. Using a log-log plot of viscosity versus shear rate to calculate n, the test fluid
was found to be Newtonian (n = 1) forfRBc = 0, very close to Newtonian (n = 0.98) forfRBc
0.33, and shear-thinning (n = 0.60) forfRBc = 1. Assuming well-developed flow at y =48 pm, the
equation of motion in the x-direction can be approximated by vx(z) = ((2n + 1)/(n + 1)) UM (1 j2z/Wj("n),
where Un is the mean flow velocity. The shear rate
f(z)
= dvx(z)/dz can also be
calculated from this equation. A plot of vx(z) versus z (Figure 3-8b) and j'(z) versus z (Figure 37c) was constructed forfRBc = 0.33 andfRBC =1. The velocity profile of the test fluid atfRBc =
0.33 is expected to be parabolic, while the velocity profile of the test fluid atfRBc
1 is more
blunted. This results in a sigmoidal shear rate profile for the test fluid atfRBc = 1 as opposed to a
linear shear rate profile for the test fluid atfRBc = 0.33. In particular, there exists a region near
the channel centerline (z = 0) where the predicted shear rate of the test fluid atfRBc = 1 is lower
than the shear rate of the test fluid atfRBc
=
0.33.
3.3.7 Bioparticle focusing in complex fluids
Particle tracking analysis (PTA) was used to identify and characterize individual in-focus
53
..........
.....
--- .-.. ... ..... .............
......
__ -
b
03
--
10
z0(33
.4
102
100
101
10-
101
102
10
3
o
o
d
*
Figure 3-8 1Rheometer measurements of diluted and whole blood. (a) The effective viscosity q for physiological
saline, diluted blood, and whole blood was measured as a function of shear rate f using a rheometer with a
concentric cylinder geometry. (b) Modeling diluted and whole blood as a power-law fluid, the flow velocity vs down
the microchannel for diluted and whole blood at height y = 48 ptm was calculated as a function of in-focus lateral
distance zf from the channel centerline. (c) Modeling diluted and whole blood as a power-law fluid, the shear rate k
for diluted and whole blood at height y = 48 gm was calculated as a function of in-focus lateral distance z from the
channel centerline.
particles in diluted and whole blood. Given the brief (- 10 ns) yet intense pulses of Nd:YAG
laser illumination, individual in-focus particles could be identified (without any visual evidence
of fluorescence streak formation) at mean flow velocities up to 1.85 m.s' (Q = 450 ml.min'), in
test fluids up to HCT= 45% (ARBC = 1), and at multiple vertical positions across the
microchannel. Direct measurements of these particles were used to generate a two-dimensional
(y-z plane) profile of particle focusing behavior and its dependence on particle diameter. This
represents a significant improvement over what has been achieved using high-speed bright-field
(HSB) imaging and long-exposure fluorescence (LEF) imaging. In high-speed bright-field
54
_1___ _._ M
MMMM
o
imaging, quantitative measurements of individual cell properties can only be made in very dilute
(TRBC
< 0.07) blood, as the sheer number of RBCs occludes observation of other cell-sized
particles in the channel. In long-exposure fluorescence imaging, a quantifiable intensity curve
requires an aggregate fluorescence from a population of particles, which means that an ensemble
of particles that are polydisperse in nature cannot be differentiated individually according to size
or vertical position.
PTA was first used to observe the inertial focusing behavior of polystyrene beads in
diluted blood. Polystyrene beads were chosen as an ideal test case (and reference benchmark)
given their monodisperse nature and strong, uniform fluorescence intensity. For particle
Reynolds numbers Rp < 1, Rp ~ 1, and Rp > 1 in PBS, bead focusing behavior using PTA was
largely consistent with previous work in which two microchannels with inverted aspect ratios
were used separately to determine the two-dimensional (y-z plane) profile of bead focusing
behavior [65]. PTA offers a significant advantage in providing three-dimensional scanning
resolution of particle focusing behavior in a single device over a wide range offRBc, and these
particle histograms can be constructed with enhanced detail and accuracy using a high-speed
spinning disk confocal p-PIV system [77]. Assuming that particle focusing behavior is welldeveloped, images of particles in the x-z plane can be taken at kHz frequencies in an automated
and continuous manner in the y-direction with exquisite scanning resolution. PTA image analysis
can also be optimized by inputting collected images into a supervised machine learning system
such as CellProfiler Analyst [78] for automated recognition of complicated and subtle
phenotypes found in millions of particles.
PTA was then used to observe the inertial focusing behavior of white blood cells (WBCs)
in diluted blood. Despite the relative similarity in particle diameter between WBCs (am = 9.0
55
pm) and beads (am = 9.9 pm), WBC focusing in both the z-direction and the y-direction was
visibly weaker atfRBc = 0. PTA demonstrated the ability to deconstruct WBC focusing behavior
based on particle diameter and centroid position of individual particles in the channel crosssection (y-z plane). As a result, the decrease in WBC focusing behavior (relative to beads) could
be partially attributed to smaller WBCs found unfocused at vertical positions near the channel
floor. These results are consistent with the notion that small WBCs experience weaker inertial
lift forces relative to large WBCs since Rp a a2 and are thus more likely to remain unfocused at a
given Rp. PTA also captured the formation of a WBC annulus in the channel cross-section (y-z
plane) atfRBc = 0.07 and 0.33.
PTA was also used to obracila serve the inertial focusing behavior of PC-3 cells in
diluted blood and whole blood. A model prostate cancer (PC-3) cell line was used as a surrogate
for circulating tumor cells (CTCs). CTC isolation poses an immense technical challenge, as
CTCs are present in as few as one cell per 109 haematologic cells in the blood of patients with
metastatic cancer [79, 80]. AtfRBC = 0, PC-3 cell focusing was strong in both the z-direction and
the y-direction. and it remained relatively intact atfRBc = 0.07 andfRBC = 0.33. Since PC-3 cells
are widely polydisperse in nature (a = 10-35 in) and can be much larger than polystyrene beads,
the inertial lift force on a PC-3 cell is expected to be up to an order of magnitude larger.
However, it was unexpected for PTA to not only identify in-focus PC-3 cells atfRBC =1, but to
observe a radical shift in PC-3 cell focusing behavior as opposed to further decreases in both the
z-direction and the y-direction from previously observed equilibrium positions. Despite the
increased RBC concentration in the channel atfRBC = 1, the preferred equilibrium position found
along the channel centerline near the channel floor made it possible to sufficiently resolve infocus PC-3 cells. Long-exposure fluorescence (streak) imaging of PC-3 cells in straight
56
rectangular channels with inverted aspect ratios (h/w = 0.5 and 2) was used to demonstrate that
PC-3 cell focusing behavior in whole blood is symmetric across the center of the channel long
face (Figure 3-9) and is not the result of particle settling or imaging artifacts. However, attempts
to sufficiently resolve PC-3 cells in the upper half of the channel were unsuccessful due to light
absorption and scattering of RBCs (Figure 3-10). The concentration of PC-3 cells spiked into the
suspending fluid was orders of magnitude higher than previously observed concentrations of
CTCs found in cancer patient blood samples. A higher spiking concentration was required to
identify and analyze a statistically significant number of PC-3 cells in a manner that was not
experimentally or computationally prohibitive. The spiking concentration of PC-3 cells should
be varied in future studies to ensure that PC-3 cells can indeed serve as CTC analogs when it
comes to particle focusing behavior. However, self-interactions between neighboring PC-3 cells
in the channel at our spiking level will be negligible (if any) in whole blood, as the volume
fraction of PC-3 cells (0.89%) is almost two orders of magnitude less than that of RBCs (45%).
Bioparticle focusing in microchannels has typically occurred in the absence of RBCs [81,
82] or in heavily diluted blood
(fRBC
! 0.1) [83, 84] due to loss of focusing quality and/or
contamination of target cell populations. Thus, it was quite unexpected when PC-3 cells
experienced a radical shift focusing behavior whenfRBc increased from 0.33 to 1. To gain some
insight into this novel focusing mode, rheology measurements of the test fluid were made atfRBc
= 0.33 and 1. The test fluid was found to be very close to Newtonian atfRBc = 0.33 and strongly
shear-thinning atfRBc = 1. As a result, the flow velocity and shear rate profiles indicated regions
of higher viscosity near the channel centerline for the test fluid atfRBc = 1 relative tofRBc
0.33.
Another parameter to consider is cell deformability, with has been shown to alter equilibrium
positions in the microchannel, particularly if the cell is large and highly deformable [85]. Given
57
a
rf~
=
b
C)
f;.=1
f
Y,
Il
Ii
*
*
Figure 3-9 1 PC-3 cell equilibrium positions in PBS and whole blood. Long-exposure fluorescence (LEF)
imaging was used to verify the focusing positions of PC-3 cells in (a) PBS and (b) whole blood, as observed using
particle trajectory analysis (PTA).
the capacity of PTA to resolve and identify individual particles with velocities typically
associated with inertia-dominant flows, it would be quite useful to characterize the effect of both
inertial lift forces and viscoelastic forces of fluorescently labeled particles (e.g., CTCs, WBCs,
and aqeuous droplets) with varying degrees of deformability in diluted and whole blood.
58
a
b
Q=0
Q>O
**0
.G
e
y &0
y
em;
y
y
S ym.lp
Q> 0
~-0-
K.1.
"''1'"
e
*
*
Lnbound
S
S
Figure 3-10 1PC-3 cell identification in whole blood. (a) A straight rectangular channel with 2:1 aspect ratio was
functionalized with anti-EpCAM antibody, which binds to EpCAM surface markers found on PC-3 cells. After PC3 cells were captured in the channel, images were taken near the channel floor (y = 9 gm) to visualize PC-3 cells
attached to the channel floor (red arrow) and the channel ceiling (green arrow). Images were also taken near the
channel ceiling (y = 81 Vm) to visualize PC-3 cells attached to the channel floor (red arrow) and the channel ceiling
(green arrow). (b) In an unfunctionalized channel, images were taken at y = 18 pm to visualize PC-3 cells flowing
near the channel floor (red arrow) and the channel ceiling (green arrow). Images were also taken at y = 72 gm to
visualize PC-3 cells flowing near the channel floor (red arrow) and the channel ceiling (green arrow).
Moreover, blood analog solutions with shear-thinning behavior similar to that of whole blood,
but with substantially different relaxation times have been shown to generate considerably
different extensional flow patterns [86]. This suggests that the viscoelastic "strength" of the
polymer solution could have a dominant effect on particle focusing behavior.
3.4 Summary
Particle trajectory analysis (PTA) was used to identify and characterize the inertial
focusing behavior of polystyrene beads, white blood cells, and PC-3 cells in diluted and whole
blood. Individual in-focus particles could be identified (without any visual evidence of
1
fluorescence streak formation) at mean flow velocities up to 1.85 m.s (Q = 450 ml.min'), in
59
test fluids up to HCT = 45% (fpBc = 1), and at multiple vertical positions across the
microchannel. Direct measurements of these particles were used to generate a two-dimensional
(y-z plane) profile of particle focusing behavior and its dependence on particle diameter. Of
particular interest is the ability of PTA to not only identify in-focus PC-3 cells atfRBc = 1, but to
observe a radical shift in PC-3 cell focusing behavior (as opposed to complete degradation).
Shear rheology measurements revealed a constant viscosity for diluted blood (fRBc = 0.33) and a
shear-thinning viscosity for whole blood (fRBc = 1), which suggests that the viscoelastic
"strength" of the suspending fluid could have significant implications on particle focusing
behavior in microchannels.
60
Chapter 4 I Inertio-elastic focusing of bioparticles in
microchannels at high throughput
4.1 Introduction
Controlled manipulation of particles from very large volumes of fluid at high throughput
is a critical step for many biomedical, environmental and industrial applications [87, 88].
Microfluidic technologies based on inertial focusing [13] have recently been developed to
achieve rare cell isolation [16] and cell deformability cytometry [60] with high degrees of
sensitivity and throughput. Bioparticle focusing in microchannels have typically involved the
removal [81, 82] or heavy dilution [83, 84] of RBCs in order to achieve the desired performance
metrics. As a result, the suspending fluids are roughly Newtonian (with negligible elastic
effects). However, recent work [89] on the focusing behavior of PC-3 (prostate) cancer cell lines
in whole blood suggests that elastic effects within the fluid could significantly alter bioparticle
focusing in microchannels.
Particle focusing in inertia-dominant flows has been observed in straight [90] and curved
[91] microchannels at moderate Reynolds numbers (Re = pUHy-
1
~ 0(100)), where p is the
fluid density, y is the fluid viscosity (constant for a Newtonian fluid), U is the particle velocity,
and H is the channel dimension (cross-section). The upper bound of inertial focusing in a
straight microchannel is limited by the hydrodynamic transition from laminar flow to turbulent
flow (with focused particles observed up to Re = 1500 [92]), while in curved channels it is
limited by dominant Dean drag forces (relative to inertial lift forces) [73]. Particle focusing in
elasticity-dominant flows has also been observed in microchannels [63, 93] at moderate
Weissenberg numbers (Wi = A
-
0(10), where A is the fluid relaxation time and k = UH-1 is
the characteristic shear rate) but limited to low Reynolds number (Re « 1). Particle focusing to
61
the channel centerline has also been observed in a viscoelastic fluid with non-negligible inertia
[18, 19], but particle focusing destabilized monotonically with increasing Re (particularly above
Re ~0(1)).
Inertia and elasticity are both non-linear effects that tend to destabilize a fluid flow when
acting alone [20, 21], but when simultaneously important, they can act constructively to stabilize
it [22, 23]. Given the turbulent drag reducing properties of high-molecular weight polymer
solutions in macroscale pipes [64], it could be possible to achieve "inertio-elastic" focusing of
bioparticles at throughputs that exceed the fundamental limits of both viscoelastic and inertial
focusing. In this chapter, we explore the possibility of particle focusing in an unexplored flow
regime where both inertia (Re >> 1) and elasticity (Wi >> 1) are present. We propose an epoxybased fabrication of rigid microchannels and explore the use of PTA (and other related imaging
techniques) to characterize particle focusing behavior and fluid velocity profiles based on
individual particle statistics (Fig. 4-1).
4.2 Materials and methods
4.2.1 Channel fabrication and design
For the construction of epoxy devices, channel features were created using computeraided design software (AutoCAD) and printed on a Mylar mask (FineLine Imaging). SU-8
photoresist (MicroChem) was deposited onto a silicon wafer to produce a SU-8 master consisting
of straight channels (L = 35 mm) with square (H= 80±5 ptm) cross-section.
Polydimethylsiloxane (PDMS) elastomer (Sylgard 184, Dow Coming) was poured over the SU-8
master to generate a PDMS replica (Fig. 4-2). The PDMS replica was peeled off and coated with
(tridecafluoro- 1,1,2,2-tetrahydrooctyl)trichlorosilane (Gelest) to produce a hydrophilic surface.
62
...
....
...
.... ...
I,
(W-Plane 13eads
P
I I ii
4)
/
2043(
10 2I
)J
flI
o t Ccup 1C
a a as
lo fs * l
'.
U
U
2oo'
i-
11
A'
24INI. fly
I
I
qWI 1,4(1
e
Ami*
I lud Vebcitv
8
Oim Bead
I' t~ni flBea
-
4)41111
Figure 4-11 Particle focusing at high flow rates in Newtonian and viscoelastic fluids. Imaging techniques used
to observe 8-pim particles (particle velocity and position) and 1-pm particles (fluid velocity) flowing through a rigid
microchannel include long-exposure fluorescence (LEF) imaging, particle trajectory analysis (PTA), particle image
velocimetry (PIV) and particle tracking velocimetry (PTV).
63
coring tool (Harris Uni-Core). One end of a 7-mm strand of 0.028" diameter Teflon cord
(McMaster-Carr) was partially inserted into a 13-inch strand of PEEK tubing (Sigma-Aldrich).
The other end of the Teflon cord was partially inserted into the inlet and outlet holes of the
PDMS master. Epoxy resin (EpoxAcast 690, Smooth-On) was poured over the PDMS master to
generate an epoxy replica. After curing, the epoxy replica was separated from the flexible
PDMS master, and the Teflon plugs were removed from the inlet and outlet holes. A 1-inch by
3-inch glass slide (Thermo Scientific) was coated with a 200-pm thick layer of epoxy resin. The
epoxy replica and epoxy-coated glass slide were irreversibly bonded using mild (50'C) heat from
a hot plate (Thermo Scientific) and gentle pressure using tweezers (Techni-Tool). For the
construction of glass devices, borosilicate glass tubing (VitroCom) with round (50-jim diameter)
or square (50-jim height and width) cross-section was used. PEEK or Tygon tubing was bonded
to a glass slide using an epoxy liquid (Loctite). Each end of the borosilicate glass tubing was
inserted into PEEK or Tygon tubing using an epoxy gel (Loctite). The edges of the glass slide
were covered with air-dry clay (Crayola), and the borosilicate glass tubing was submerged in an
optically matched fluid (Sigma-Aldrich). The height H and width W of the channel cross-section
were chosen to maximize the Reynolds number for a given volumetric flow rate
Q and hydraulic
diameter D = 2HW/(H+W). The channel Reynolds number Re can be expressed as
Re
QD
HWv
_
4Q
a
Dv (1 + a) 2
where v is the kinematic viscosity of the fluid and a = HW is the aspect ratio (with the constraint
that 0 < a < 1). For a constant ratio of QID, the value of Re is maximized when a = 1 (Fig. 4-3 a).
The length L of the channel was chosen to ensure that the flow was hydrodynamically fullydeveloped for all Re over which the flow was laminar. For the flow of a Newtonian fluid in a
64
.
....
........
..
.- ..
. . ........
.
.
..
..........
.
.......
-
--
-----
.
a
b
C
Figure 4-2 Rigid microchannel fabrication via hard lithography. (a) A hard lithography "add-on" method is
used in conjunction with photolithography and soft lithography to build a rigid microchannel (with an epoxy resin as
the substrate). (b) PTFE plugs are used to connect inlet (PEEK) tubing and outlet (Tygon) tubing to the PDMS
master. (c) The epoxy replica is irreversibly bonded to an epoxy-coated glass slide via gentle mechanical pressure
at elevated temperature.
rectilinear duct [53], the hydrodynamic entrance length Le can be expressed as
6
6
Le = D[O.619 1 .6 + (0.0567Re)1. ]1/1-
with the additional condition that Le < L < Ls, where L, is the length of the epoxy-coated glass
slide. The transition to inertially-dominated turbulence is expected to occur at Re ~ 2000, which
suggests that Le = 113D (Fig. 4-3b). For polystyrene beads with particle diameter a = 8 pm, we
set the hydraulic diameter D = W = H = 80 pm such that the ratio of particle diameter to channel
dimension a/D > 0.1. For a straight channel with 80-pm square cross-section, we set the channel
length L = 35 mm, which exceeded the entrance length Le = 0.90 mm for Re ~ 2000.
65
.. ..
. ........
. ............
.
........
........ ......
...
........
a
;o
experlnents
45
0A
. ...................
Figure 4-3 1Design parameters for microchannel dimensions. (a) Plot of channel Reynolds number normalized
for a constant ratio of QID, and friction factor normalized for a constant value of Re, as a function of channel aspect
ratio a = W/H. (b) Hydrodynamic entrance length as a function of channel Reynolds number.
4.2.2 Sample preparation
Hyaluronic acid (HA) sodium salt (Sigma-Aldrich or Lifecore Biomedical) was added to
water (Sigma-Aldrich) for bead suspensions or phosphate buffered saline (PBS) solution (Life
Technologies) solution for cell suspensions and prepared using a roller mixer (Stuart, SigmaAldrich). Polystyrene beads (FluoSpheres, Invitrogen or Fluoro-Max, Thermo Scientific)
suspended in Tween-20 (Sigma-Aldrich) solution (0.1% v/v, water) were diluted in HA solution
(1650 kDa, 0.1% w/v, c/c* = 10 [94], water) at a concentration of 3 x 106 beads.ml'. White
blood cells (WBCs) were harvested from human Buffy coat samples (MGH Blood Bank) via
density gradient centrifugation (Histopaque- 1077, Sigma-Aldrich). WBCs were centrifuged and
suspended in Calcein Red-Orange solution (10 pg.ml', PBS). Fluorescently labeled WBCs were
centrifuged and suspended in PBS, low molecular weight HA solution (357 kDa, 0.1% w/v,
PBS) or high molecular weight HA solution (1650 kDa, 0.1% w/v, PBS) at a concentration of 5 x
106 cells.ml 1 . Anisotropic (cylindrical) hydrogel particles were synthesized via stop-flow
lithography [95] from pre-polymer solutions of 60% poly(ethylene glycol) diacrylate (PEG-DA
700, Sigma-Aldrich), 30% poly(ethylene glycol) (PEG 200, Sigma-Aldrich), 10% 2-hydroxy-2-
66
methylpropiophenon (Sigma-Aldrich), and 3 mg.ml-1 rhodamine acrylate (Polysciences).
Fluorescently labeled PEG particles (20-tm length, 1 0- tm cross-sectional diameter) were
collected and washed in Tween-20 solution (0.1% v/v, PBS) prior to dilution in HA solution
(1650 kDa, 0.1% w/v, water). Microparticles suspended in Newtonian or viscoelastic fluids
were prepared in 100-ml volumes to maximize observation time of particle flow, especially at
the upper limit of flow rates in the rigid microchannel.
4.2.3 Fluid Rheology Measurements
The viscosity of all fluid samples was measured using both a stress-controlled rheometer
(DHR-3, TA Instruments) and a microfluidic viscometer-rheometer-on-a-chip (VROC,
Rheosense) (Fig. 4-4). The DHR-3 instrument imposed an increasing shear rate ramp on a fluid
sample contained within a double-gap cylindrical Couette cell. The viscosity of the fluid sample
was measured on the DHR-3 instrument for shear rates 0.1 < f < 3 x 103 s-1. The VROC
microfluidic chip consists of a borosilicate glass microchannel with a rectangular slit crosssection and a silicon pressure sensor array. The viscosity of the fluid sample was measured on
the VROC device for shear rates 5 x 103
<
f
< 3.3 x 105 s-.
In order to numerically predict the
velocity profiles in the channel, the measured flow curve of the native sample was fit with the
Carreau model
17(f) =
r7.
+ (y7o
- 17.)[1 +
where r7, is the infinite-shear-rate viscosity, qo is the zero-shear-rate viscosity,
f* is a
characteristic shear rate at the onset of shear-thinning, and n is the "power-law exponent". We
measured the fluid viscosity of both native and used samples of HA solution at
Q = 20 ml.min 1
to investigate the role of shear-induced sample degradation. The viscosity of native HA solution
67
.
..
b
a
C
...
........
......
..........
.....
............
.
.........
100
I~~~~
11 ~ IM
11110
11111
Ii 1
0
1111 itII
11 1
t
£R80(1
1o
10
10
-
10
100
10 1
10~
10
10
10
10
Figure 4-4 1Shear rheology measurements of HA solution. (a) Cross-sectional view of rotational rheometers
fitted with Couette cell contains rotating pressure transducer that measures strain given known stress (or vice versa)
by motor. (b) Cross-sectional view of viscometer-rheometer-on-chip contains pressure sensor array that measures
fluid pressure through rectangular slit at increasing distances from microchannel inlet. Flow curve of HA solution
before use ("native") and after use ("used") at flow rates up to Q = 20 ml.minrr. Carreau model fit to unused HA
solution, flo = 230 mnPa.s, r = 0.9 mPa.s, f * = 0.36 s', n = 0.48. Water viscosity (p, = 0.9 mPa.s) is shown by
blue dashed line.
exceeded the viscosity of used HA solution by at least a factor of 2 for shear rates 0.1 <
f
< 103
s- presumably due to the shear-induced disruption of aggregates in the solution. However, the
measured difference in HA viscosity between the samples was minimal and remained unchanged
68
after repeated shearing for the high shear rates (103
<
f
<
10 7 s-1) explored in this study. This
suggests that irreversible polymer degradation had little to no effect on HA viscosity at the flow
rates where particle focusing was observed. The relaxation time A of the native HA solution was
measured based on thinning dynamics in jetting experiments [96]. As a viscoelastic liquid
bridge thins, the diameter of the filament D will decay according to the relation [97]
D oc e- -t/3A
Do
where D, is the initial diameter of the filament. When plotted on semi-logarithmic axes, the
initial slope of filament decay is equal to -1/3k (Fig. 4-5).
4.2.4 Pressure drop measurements
Fluid flow through the microchannel was achieved using a syringe pump (1 O0DX, Teledyne
Isco) capable of a maximum flow rate of 50 ml.min-1, a maximum pressure of 10000 PSI, and a
maximum capacity of 103 ml. A stainless steel ferrule adapter (Swagelok) connected the syringe
pump to the PEEK tubing embedded in the epoxy chip. The syringe pump's internal pressure
transducer was used to obtain pressure drop measurements across the entire fluidic circuit.
However, we found that the hydrodynamic resistance of the microchannel accounted for
approximately 99% of the overall hydrodynamic resistance. As a result, we considered the
pressure drop measured by the syringe pump to be essentially equal to the pressure drop along
the microchannel. The pressure drop AP was an essential parameter in determining the friction
factorf, defined for laminar flow of a Newtonian fluid through a square microchannel as
96
AP
a) 2
0.5 pU 2 (LID) = (1 + a)2
[
--1
tanh(j]/2a)
192
_a
69
jod--=
s5
_
_
1
56.9
--R
b
a
AHA
0.87 ms
Figure 4-5 Extensional rheology measurements of HA solution. (a) Observation of viscoelastic fluid ejected by
a cylindrical nozzle using a Rayleigh-Ohnesorge jet extensional rheometer (ROJER). (b) The dynamics of a
thinning filament bridge was used to determine the relaxation time of the HA solution. Diameter D(t) of a thinning
HA (M, = 1650 kDa) filament bridge as a function of time t. The dashed line in the figure indicates the initial slope
from jetting experiments used to calculate the effective relaxation time. The solid line indicates the visco-capillary
break up profile of a Newtonian liquid. The relaxation time was determined to be k = 8.7 x 10- s.
where U is the mean fluid velocity in the channel, L is the channel length, D is the channel
hydraulic diameter, and Re is the channel Reynolds number. In this operating regime, AP
increased linearly with Q, andf scaled inversely with Re. For Re > 2000 (where the channel flow
is expected to be turbulent),f can be expressed in a microchannel [98] as
raio f
~= kD
wheei th
6n.(
r= [1.
- )+
- 1.81n (Re
<)E1.11]-2
-
3.7)
where e = k/D is the ratio of the average surface roughness on the channel wall k to the channel
hydraulic diameter D. The typical surface roughness was k
0(1 m) for the epoxy channels
used in this study. As a conservative estimate, we set e ~ 0.01 to calculatef as a function of Re.
The characteristic viscosity was an essential parameter for determining the channel Reynolds
number, and the Carreau model was used to calculate the characteristic viscosity as a function of
wall shear rate. For Newtonian flow in a square microchannel (i.e., a = 1), the analytical
solution [98] of wall shear rate w,3D can be expressed as
001-
U
,
= -
Y,D
D
96
22(1
+ a)
[z.ij
j=odd
1
10cosh(jir/2a)
j[
Iw
2
70
192
s
tanh(jw/2a)
.5
d]s
J=odd
U
9.4 -
D
When the characteristic viscosity (based on wall shear rate) is used to calculate Re, the friction
factor of the HA solutionfHA collapses onto the expected curve for a Newtonian fluid (Fig. 4-6).
4.2.5 Velocimetry measurements
Images of fluorescent particles in the microchannel were acquired with a Nd:YAG dual
cavity 90 mJ/pulse laser (LaVision) that was frequency doubled to emit green light at 532 nm, a
1.4-megapixel CCD camera (PIV-Cam 14-10, TSI), and an epifluorescence microscope (TE2000, Nikon). The pulse width for the laser was approximately 6t ~ 10 ns, yielding an
instantaneous power that was approximately 90 MW. The fluorescent signal from the particles is
passed through a barrier filter and dichroic mirror [99]. This allows for the elastically scattered
light from the illumination source (532 nm laser) to be filtered out while leaving the fluorescent
emission (at a longer wavelength) to pass through to the CCD camera virtually unattenuated
[100]. The minimum time between consecutive laser pulses was Atinterpulsemin ~ 200 ns, and the
minimum interframe time (i.e., time between consecutive images) was Atinterfrae ~ 1.2 pis. For a
given flow rate, the time interval between the two consecutive laser pulses was user-defined to
achieve a maximum particle displacement of approximately 8 pixels (which is the optimal
displacement for the correlative PIV algorithm used in this study). For
required between laser pulses
the camera interframe time
(Atinterpulse)
Q < 0.1
ml.min-I, the time
to achieve this optimal displacement was greater than
(Atinterpulse> Atinterframe),
which enabled observation of particle
displacement over two single-exposed images. Therefore at these low flow rates the PIV analysis
was completed in frame straddling mode, which relies on a cross-correlation approach between
the image pair [101] (TSI). Conversely for
Q>
0.1 ml.min-', the time step required for optimal
particle displacement was less than the interframe time
71
(Atinterpulse
< Atinterframe), and
particle
-
10
-a --
-
In
-
10
10
10
10
102
W-te
t 0
10
1010t
R
_
10
pu3 )
Figure 4-6 1Friction factor in microchannel for Newtonian and viscoelastic fluids. Friction factorf as a
function of channel Reynolds number Re based on a shear rate-dependent viscosity evaluated at the characteristic
shear rate at the wall of a microchannel with square cross-section. The gray line indicates the theoretical friction
factor for a Newtonian fluid.
displacement was observed over one double-exposed image. Hence at these higher flow rates,
the PIV analysis was done using an auto-correlation approach (LaVision).
Particle velocity measurements were made with 8-pim polystyrene beads (3
x
106
beads.ml-1 water or HA solution), and fluid velocity measurements were made with I -pum
polystyrene beads (3 x 108 beads.ml-1 water or HA solution). At a given x-z plane, micro particle
image velocimetry (p-PIV) was used to record the displacement of 1-pim beads within an array of
interrogation windows over a given time interval (Fig. 4-7). At the same x-z plane, particle
tracking velocimetry (PTV) was used to record the displacement of 8-pm beads in the x-direction
over a given time interval. PTV images were processed in MATLAB (MathWorks) to generate a
set of individual particle velocity measurements. It is worth noting that some particle blurring in
72
0.40
X
0
0.30
0
-z
0
+Z
o0
x)at time t + 't
0. 10
(x, z.) at time t
Figure 4-7| Obtaining fluid velocity measurements via micro-particle image velocimetry (p-PtV). At a given
of interrogation windows
x-z plane, a pair of images are captured of flow tracer particles moving through an array
time interval are
positioned within the microchannel. The particle displacement of all particles over a user-defined
for a given
profiles
velocity
fluid
mean
analyzed using an auto-correlation or cross-correlation algorithm to generate
flow rate.
the fluorescent images can occur at the highest flow rates explored in this study, even with the
extremely short pulse duration of 6t ~ 10 ns. For the microscope objective and camera used in
this work, one pixel corresponds to (eM2= 0.323 x 0.323 ptm2 , hence the fluid velocity
necessary for a particle to traverse one pixel during a single laser pulse (and thus show blurring)
is Ublur, ~ (eM)Sr- = 3 2 m.s-' which corresponds to the maximum fluid velocity for
Q
~6
ml.min-l. For the 1- im particles that were used to measure the fluid velocity profile, a blur
73
length of one pixel is a significant fraction of the particle diameter, which can adversely affect
the accuracy of the correlative PIV algorithm [67]. For this reason, quantitative velocity profile
measurements were not performed at higher flow rates where the blurring would be severe. In a
typical velocimetry measurement, a 1-tm tracer particle travels approximately 4 to 8 pixels
between consecutive laser pulses, which corresponds to a 13% to 25% error. On the other hand, a
typical 8-pm particle used in this study has a diameter of around 25 pixels in a single microscope
image, hence even at the highest velocities considered in this study around U = 130 m.s- (Q =
50 ml.min'), the expected blurring will be approximately 4 pixels which is only 16% of the
particle size.
4.3 Results and discussion
4.3.1 Flow regime characterization
To study particle migration in viscoelastic flows at high Reynolds number, we selected
hyaluronic acid (HA) as a model viscoelastic additive based on its biocompatibility and the
turbulent drag-reducing properties that have been documented in the flow of blood [102] and
synovial fluid [94]. The Reynolds number was calculated based on a shear-rate dependent
viscosity as defined by the Carreau model. This viscosity is evaluated at the relevant wall shear
rate in the fluid given by
= 9.4 U/H, based on the analytical solution for the velocity field of a
Newtonian liquid in a square channel (with cross-sectional dimension H). The Weissenberg
number was calculated based on a fluid relaxation time A= 8.7 x 1 0- s measured experimentally
using the thinning dynamics of a liquid filament [103]. The measured pressure drop AP over the
entire fluidic network was measured by the syringe pump for a given imposed flow rate
Q (Fig.
4-8). For water, APvater first increased linearly with Q before increasing more rapidly at Re ~
74
10
~HA
10
10-_Q
-
1
10
102
10 1
(m)
[m
Figure 4-8 1Pressure drop measurements in rigid microchannel. Pressure drop across the fluidic system for
water and HA solutions. The solid gray line indicates the expected pressure drop for the laminar flow of water in the
microchannel. Inset plot shows pressure drops near the onset of inertially turbulent flow at Q = Q'.
2500±500, which indicated a transition to turbulence. In the HA solution, APHA scaled
sublinearly with
viscosity) for
Q due to shear-thinning effects,
Q < Qt, where Qt
and APHA > APwater (due to the higher fluid
12±2.5 ml.min' is the flow rate at which the flow of water
transitioned from laminar to turbulent. However, for flow rates
sublinearly with
Q>
Qt, APA continued to scale
Q (up to 50 ml.min'), which suggests that the flow of the
laminar even up to Re
HA solution remained
10,000. Using a microfluidic rheometer we also measured the viscosity
of the HA solution (M, = 1650 kDa, 0.1% w/v) before and after sample processing within the
range of shear rates explored in the microchannel (103 < 2 < 107 s-). Over this range of shear
rates the shear viscosities of the native and used samples were found to remain almost
unchanged, indicating that shear-induced degradation of the sample [104] was not a major issue
(Fig. 4-4c).
75
4.3.2 Particle focusing characterization
With the ability to achieve laminar flow in a microchannel at Reynolds number up to
Re ~ 10,000 using a viscoelastic fluid, we investigated the importance of persistent laminar flow
conditions on particle focusing. We first observed the flow behavior of 8-prm beads in HA for
< Qt. At
Q=
Q
0.6 ml.min' (Re = 105, Wi = 17), we observed particle migration towards a single
centralized point along the channel centerline (Fig. 4-9). This focusing behavior was also
observed at flow rates as high as
Q=
6 ml.min'. The results obtained in the viscoelastic HA
solution were in stark contrast to those in a Newtonian fluid. In water, beads initially focused to
four off-center equilibrium positions near each face of the rectangular microchannel at
Q = 0.6
ml.min' (Re = 140) before shifting to a five-point quincunx configuration at Q = 6 ml.min' (Re
= 1400) with equilibrium positions at the centerline and the four channel corners, where the shear
rate is lowest. These experimental observations in water were in broad agreement with previous
numerical studies of inertial migration in Newtonian fluids [105, 14].
Having established that particle focusing can be achieved for
solution, albeit with significant configurational differences, we set
Q < Qt in both water and
Q>
deterministic particle focusing could be preserved in either fluid. For
HA
Q, to determine if
Q>
13 ml.min- in water
(Re > 2000), particle tracking showed that the fluorescent beads were randomly distributed
throughout the channel due to the onset of inertial turbulence, and this critical flow rate
corresponded closely to the critical conditions beyond which APwater increased superlinearly with
increasing
Q.
Surprisingly, for
Q>
Qt, beads in the HA solution continued to focus towards a
centralized point along the channel centerline and we found that particle focusing in HA solution
persisted to Reynolds numbers well above the upper limit that could be attained for particle
focusing in water. These results represent the highest flow rates at which deterministic particle
76
Q = 0.6 ml.min
Q = 6 ml.min I
Q = 20 mi.minI
WatCr
HA
LEF
PTA
LEF
PTA
LEF
PTA
Figure 4-9 1Particle migration behavior in water and HA solution. Long-exposure fluorescence (LEF)
characterizes particle focusing behavior based on aggregate signal intensity of particle populations. Particle
trajectory analysis (PTA) characterizes particle focusing behavior based on individual particle statistics. The hashed
lines indicate the position of the channel walls. At Q = 0.6 ml.min', Re = 140 in water, and Re = 105 and Wi= 17 in
HA. At Q = 6.0 ml.min4 , Re = 1400 in water, and Re = 1270 and Wi = 170 in HA. At Q = 20.0 ml.min-r, Re = 4360
in water, and Re = 4422 and Wi = 566 in HA.
focusing has been achieved in a microchannel and illustrate the precise focusing control that can
be achieved by using only small amounts of a viscoelastic drag-reducing polymeric agent (HA).
In order to provide further insight into the physical basis of inertio-elastic particle focusing
in the HA solution, we carried out a comparative study of water and HA solution within the
laminar regime. We first considered the effect of shear-thinning on particle focusing in HA
solution (Fig. 4-10a). This was motivated by previous work [54, 63] suggesting that shearthinning in the fluid viscosity drives particles toward the wall. At Q = 0.09 ml.min- , we
observed a markedly more blunt fluid velocity profile in the HA solution compared to water (Fig.
4-1Ob), which is consistent with shear-thinning behavior observed at
computational simulations using the Carreau model. At
77
Q
1~
O(104) s-1 and with
6 ml.min-', the characteristic shear
b
a
,=0.09 mI.min
AEii
-1)
10)
-20
~
Hyaluronic Acid (HA)
6 m l.min
()Q2=
M__
1
Water (HO)
Figure 4-10 1Effect of shear-thinning on particle focusing. (a) Based on the shear-thinning regime of hyaluronic
acid (HA), two flow rates were chosen to assess particle focusing in the presence (or absence) of shear-thinning
effects. (b) The fluid velocity profile for water and HA solution are shown at each flow rate. For comparison, the
expected velocity profiles at the mid-plane of the channel (i.e., y = 0 m) for the flow of a Newtonian
fluid and a shear-thinning Carreau model (determined from COMSOL simulations) are shown by the
green and gold curves, respectively. The standard deviation in the velocity measurements are shown by
the error bars in uX, and the width of the interrogation windows are shown by the error bars along the Zaxis.
rate in the fluid increased to j~ O(106) S- where the viscosity varied less strongly with shear
rate. We continued to observe particle focusing towards the center in the HA solution despite
nearly identical fluid velocity profiles (measured using p-PIV with 1 -tm beads) for water and
the HA solution. This result suggests that shear-thinning in the velocity profile did not play a
dominant role in particle focusing under these flow conditions.
Based on PTA measurements of particle focusing behavior at
Q
6 ml.min', we observed
particles in both water and HA solution occupying positions along the channel centerline (Fig. 41 la). This enabled direct comparisons of particle velocity (using 8-um beads) and fluid velocity
78
a
H20
Re= 1270
Wi= 170
Q=6 ml.min'
Re = 1400
30
()
-6-12
20
-18-24
I0
-30
-36
-40
0 0
z (pm)
b
4(
1 0
T
2(0
40
1
4
30F
Ln
10
0I-
40
H20
HA
Q =6 m.min'
Re= 1270
Re= 1400
Wi= 170
-20
0 0
2()
40
z(pm)
Figure 4-11| Direct comparisons of particle and fluid velocity along channel centerline. (a) Cross-sectional1
particle histogram of 8-jim particles in a lower quadrant of the square microchannel at Q = 6.0 ml.min .
(b) Velocity profiles measured in the two fluids (red and blue curves respectively) and the corresponding
velocities of the migrating 8-pim beads (black dots for beads in water and violet dots for beads in the HA
solution) measured at the channel mid-plane (y = 0 pim).
79
(using 1-pm beads) in the two suspending fluids (Fig. 4-11 b). In water, the particles along the
channel centerline translated at up = 28.2±0.9 m.s, which was slower than the local fluid
velocity of uf= 30.2 m.s 1 . However, the measured particle velocity (up = 30.9±0.7 m.s') was
faster than the local fluid velocity in HA solution. These trends are consistent with: 1) a drag
increase expected for a sphere moving in a Newtonian channel flow, given by Fax6n's law for
creeping flow and an Oseen correction for fluid inertia [106, 107], as well as 2) a viscoelastic
drag decrease on a sphere that is initially expected at a moderate particle Weissenberg number
[108, 109].
We also considered the effect of secondary flows on particle focusing in HA solution. This
was motivated by recent work [110, 111] showing that in channels with non-axisymmetric crosssection, normal stress differences in a viscoelastic fluid can drive secondary recirculating flows
that are superposed on top of the primary axial flow field. Comparing the migration behavior of
8-pm beads in a 50-pm square (non-axisymmetric) channel and in a corresponding cylindrical
(axisymmetric) tube, we observed particle focusing toward the centerline in both cases.
Gaussian fits to the LEF intensity profiles observed at x > Lf were indistinguishable to within one
particle diameter (Fig. 4-12), indicating that secondary flows did not play a significant role.
4.3.3 Bioparticle focusing in microchannels
Having eliminated shear-thinning and secondary flows as primary drivers of inertio-elastic
particle focusing, we considered the role of viscoelastic normal stresses on particle in a
microchannel. Previous theoretical work in the creeping flow limit [53] has shown that particle
migration in the direction of minimum shear rate (i.e., towards the channel centerline) is induced
by gradients in the first normal stress difference that are present when the shear rate in the fluid
80
....
..
..
........
..................
ab
.
.....
b
Figure 4-12 I Secondary flow effects in HA solution. Particle distributions across the channel width over a range
of flow rates in; (a) a borosilicate glass microchannel with square (inner dimension =50 sim) cross-section, and (b)
a borosilicate glass microchannel with cylindrical (inner diameter = 50 pim) cross-section. Inset figures show brightfield images of the borosilicate glass microchannels.
varies transversely in the undisturbed flow field around the particle. Numerical simulations of
particle sedimentation in quiescent viscoelastic fluids have also demonstrated that viscoelastic
stresses drive particles towards the centerline of channels and tubes [112, 113]. Given the
"hoop" stress exerted on a particle due to normal stress differences, we used white blood cells
(WBCs) as deformability tracers to visualize viscoelastic normal stresses (which create an
additional tensile stress along streamlines [76]) in a microchannel.
Given the high spatial fidelity and lack of particle blurring provided by pulsed laser
imaging (6t = 10 ns), we were able to make quantitative measurements of individual particle
deformation for shear rates up to
f2
0 (106) s4. The magnitude of WBC deformation was
expressed in terms of a mean aspect ratio AR
=
ax/az (Fig. 4-13a). For WBCs suspended in PBS,
the aspect ratio monotonically increased from AR
1.2 (at
Q=
13 ml.min', Re
=
=
1.0 (at Q = 0.6 ml.min', Re
=
140) to AR
=
3,033) due to the increasing variation in the magnitude of the
viscous shear stress acting across the WBC. By contrast, for WBCs suspended in the 1650 kDa
HA solution, the aspect ratio monotonically increased from AR
81
=
1.4 (at
Q = 0.6 ml.min',
Wi=
a
IfA\27l)
3-
10
1)
FI
Ills
L~1111
J
I IA1
T1'
FJ
1
Figure 4-13 Inertio-elastic focusing of bioparticles based on deformability. (a) Deformation statistics of WBCs
in PBS, a low molecular weight (357 kDa) HA solution and a high molecular weight (1650 kDa) HA solution. The
magnitude of WBC stretching is expressed in terms of aspect ratio AR = al/a,. Scale bar equals 10 ptm. The error
bars indicate the standard deviation in the WBC aspect ratio at each flow rate. (b) LEF and PTA images of WBCs in
PBS, 357 kDa HA solution and 1650 kDa HA solution at Q = 13 ml.minQ.
17, Re = 105) to AR = 2.5 (at
Q=
13 ml.minW, Wi = 368, Re = 2,840). However, we observed a
breakdown in focusing of these deformable particles in both fluids at higher flow rates. For
WBCs in a Newtonian fluid the focusing behavior was lost due to onset of turbulence for Q > Qt.
By contrast, the focusing capacity of WBCs in a viscoelastic fluid appeared to diminish due to a
combination of excessive cell stretching and the corresponding reduction in the hydraulic
diameter of the cells (Fig. 4-1 3b). We have also investigated the role of fluid rheology in
82
manipulating the interplay of particle focusing and particle stretching. In order to reduce the
magnitude of the viscoelastic normal stresses experienced by WBCs, we used a lower molecular
weight (357 kDa) HA solution. From the Zimm scaling for dilute polymer solutions ('~ Mw0 8 )
we can estimate the relaxation time for this less viscoelastic solution to be )357
and the Weissenberg number is reduced to Wi ~ 100 at
Q=
kDa
Z2.6
X
10
S,
13 ml.min 1 . Pulsed laser images
indicate the maximum anisotropy in the cell dimensions was reduced to AR = 1.4 and we
observed enhanced WBC focusing at flow rates beyond
Q=
13 ml.min 1 . These results suggest
that by tuning the nonlinear rheological properties of the viscoelastic working fluid it is possible
to control both particle focusing and particle deformation.
Recent work [114, 115] has suggested that inertial focusing of non-spherical particles
depends on the rotational diameter of a particle, regardless of its cross-sectional shape.
Microscopic video imaging also shows that these particles rotate freely when suspended in a
Newtonian fluid. To investigate the effect of particle shape on inertio-elastic focusing in HA
solution at high Reynolds numbers, we used cylindrical cross-linked PEG particles synthesized
via flow lithography [95]. For a given PEG particle, we measured the lateral position zp (with
channel centerline defined by z = 0 pm) and the instantaneous orientation angle 6, of the particle
(with streamwise alignment defined by 0= 0') in the original HA solution at
Q = 20 ml.min'
(Fig. 4-14). PEG particles in water occupied the entire range of lateral positions (-40 5z < 40
pm) and orientations (-90'
6
90'). By contrast, in the HA solution, the PEG particles
exhibited strong streamwise alignment along the channel centerline with zp -+ 0 and O, -+ 0.
Similar streamwise alignment and migration to the centerline has been predicted in numerical
simulations of the sedimentation of anisotropic particles in viscoelastic suspending fluids [113,
116].
83
a
H2 0.
HAN
b
9()
I
0
.0
45-
*
0
0%
_
)00
0
or
0
-45.
-90
-4)
'
-2()
2()
4()
Figure 4-14 | Inertio-elastic focusing of bioparticles based on shape. (a) PTA images of PEG particles in 1650
kDa HA solution at Q = 20 ml.mirn. Dashed red lines indicate channel centerline. Scale bar equals 30 ptm. (b)
Measurements of lateral position z and instantaneous orientation angle 0 are plotted for each PEG particle in water
(blue) and in the HA solution (green).
4.3.4 Establishing the boundaries of inertio-elastic focusing
Controlled particle manipulation in microchannels using viscoelastic fluids can be achieved
by tuning the channel geometry, particle geometry, and fluid rheology. However, the effective
limits of inertio-clastic focusing are not yet well-defined on the Wi-Re state space. For example,
84
a critical aspect of this study was the observation that 8-tm polystyrene beads achieved particle
migration (which revealed the existence of inertio-elastic focusing) while 1 -pm polystyrene
beads did not (which allowed for fluid velocity measurements). Upon further investigation, 6ptm particles did not achieve complete focusing within the entire length (35 mm) of the
microchannel at Q = 6 ml.min 1 (Fig. 4-15a). Complete focusing (originally observed in 8-pm
particles) persisted for 10-pm particles but not for 24-pm particles. In order to make sense of
this size-dependent observation, it is necessary to recall theoretical scaling laws [43, 53] in the
creeping flow limit associated with inertial lift force F1 , elastic lift force FE, drag force FD, and
thermal force FT
a4
F ~pU2 aj4
FE-
Uza 3
Hu2 H3
kBT
Fv ~ 31T7umiga
FT~
a
where p is the fluid density, 17 is the fluid viscosity, A is the fluid relaxation time, T is the
temperature, kB is the Boltzmann constant, umig is the particle migration velocity, and a is the
particle diameter. The relative strength of elastic effects to other competing effects can be
expressed using the above expressions
FE
F,
27A
paH
FE
2AU 2 a 2
FE
2rIAU 2 a 4
F
3 wrumig H 3
FT
kbTH 3
These simplified expressions begin to offer some insight into the respective boundaries
associated with inertio-elastic focusing in microchannels (Fig. 4-15b). For example, a reduction
in particle size to 6 pm (from 8 pm) affects the elastic force with third-power dependence, while
the (Stokes) drag force is only affected linearly. This would suggest that the migration velocity
is reduced to the extent that complete particle focusing cannot occur in the given microchannel.
However, a further reduction in size to 1 pm resulted in negligible particle focusing without
being significantly affected by thermal forces (as evidenced by accurate flow tracing achieved in
85
a
HA!
Q=6 mlmin-1
Re = 1270
Wi =170
1 pm
b
10 pm
6 pm
1
6
10
24 pm
24
a (pm)
FT
FE
FV
FU
16 m.s 1
Figure 4-15 Relevant scaling laws for inertio-elastic focusing. (a) PTA images of different-sized (1, 6, 10, and
24 pm) polystyrene beads re-suspended in HA solution at Q = 6 ml.min-. (b) Color-coded regions that suggest
increasingly dominant force (i.e., elastic, inertial, drag, thermal) among lesser competing forces.
this study). Conversely, a minimal increase in particle size to 10 tm (from 8 ptm) yielded little
change in particle focusing behavior. However, a further increase in size to 24 tm led to a
breakdown in particle focusing. This suggests that inertio-elastic focusing does not persist
beyond a critical particle diameter due to increasing dominant inertial effects. It should be noted
that this simple analysis becomes more complicated when considering the residence time of
particle focusing in the microchannel (with respect to the fluid relaxation time), which means
that a comprehensive analysis of inertio-elastic focusing should also take into account the
Deborah number (in addition to Reynolds, Weissenberg, and elasticity numbers).
Nonetheless, based on the results in this study, it is possible to depict inertio-elastic
focusing on a Wi-Re state space map and compare it to other instances of particle focusing in
microchannels (Fig. 4-16). Previous studies of particle migration in a viscoelastic fluid (with or
86
103
:
102
10' -
100
10-1
102
101
100
+-
7] [7] Di Carlo etal. (2007)
0[11 Ciftlik
A [14] Leshansky et al. (2007)
*
etal. (2013)
L
103
-+
Inertial Turbulence
t [16] Yang etal. (2011)
[13] D'Avino et al. (2012)
104
Transition to
*
t [17] Kang etal. (2013)
[30] Del Giudice et al. (2013)
Figure 4-16 1Operating space of inertio-elastic focusing in straight microchannels. The parameter
spaces probed by these studies are conveniently located on a two-dimensional plot of the fluid elasticity,
as characterized by the channel Weissenberg number (Wi), and the fluid inertia by the channel Reynolds
number (Re). The slope of a line passing through this space represents the value of the channel elasticity
number (El); which is controlled by variations in the fluid viscosity (qi), the fluid relaxation time (A) and
the microchannel dimensions. A value of El> 1 indicates a primarily elastically-dominated flow on the
length scale of the channel, whereas a value of El < 1 indicates a primarily inertially-dominated flow. The
red bars correspond to the range of Wi and Re explored in this study. Note that the white shaded region
(beginning at Re* ~ 2500) within the red bar on the horizontal axis indicates the regime in which turbulent
flow in the Newtonian fluid was observed. Also note that the studies of [13] and [62] are both in the
Newtonian limit (i.e., Wi = 0).
without inertia) all correspond to highly elastic fluids where particle focusing monotonically
worsened with increasing Re (particularly for Re > 1) [ 18, 19]. These results could be attributed
to the elastic forces on a particle being overwhelmed by the inertial forces, or to onset of elastic
flow instabilities at high Wi [117, 118]. It is worth noting that the deterioration of such
viscoelastic focusing occurs well below the threshold for inertial focusing in a microchannel
87
[13]. In this study, we observed particle focusing in weakly elastic fluids (El
channel centerline over a wide range of Reynolds numbers (10
Re
-
0.1) toward the
10') that actually
improved with increasing flow rate up to Re ~ 0(103). These results were observed in a
previously inaccessible flow regime where both inertia (Re >> 1) and elasticity (Wi >> 1) are
present. Moreover, such controlled particle migration in a viscoelastic fluid occurred at
Reynolds numbers well beyond the upper limit previously observe for inertial focusing in a
Newtonian fluid [62].
4.4 Summary
Using a rigid (epoxy-based) microchannel and imaging techniques derived from microparticle image velocimetry (i-PIV), we observed particle focusing in a previously inaccessible
flow regime where both inertia (Re >> 1) and elasticity (Wi >> 1) are present. Controlled
manipulation of rigid spherical beads, deformable WBCs, and anisotropic PEG particles was
achieved with a high-molecular weight polymer (hyaluronic acid (HA)). We show that there is a
complex interaction between inertial effects in the flow and the viscoelastic fluid rheology that
governs the migration, orientation and deformation of large (non-Brownian) particles suspended
in the fluid. By varying channel geometry, particle geometry, and fluid rheology, we show that it
not shear-thinning or secondary flows in the channel but elastic normal stresses in the fluid that
drive particle focusing to the channel centerline. These discoveries will inform our future work
on the design of particle sorting methods that utilize this previously unexplored flow regime.
With sample processing rates of up to 3 L.hr' (and linear velocities of 460 km.hr') in a single
microchannel, and the ability to parallelize the channel design, inertio-elastic particle focusing
may ultimately be used for rapid isolation of tumor cells from large volumes of bodily fluid
88
samples (e.g., peritoneal washings, bronchoalveolar lavages, urine) [16], high-throughput
intracellular delivery of macromolecules for therapeutic application [119], scanning of
multifunctional encoded particles for rapid biomolecule analysis [36], and removal of floc
aggregates within water treatment systems [120].
89
Chapter 5| Summary and outlook
5.1 Contributions
5.1.1 Tracking focused particles individually using particle trajectory analysis (PTA)
Observation of focused particles in microchannels has achieved predominantly using
long-exposure fluorescence (LEF) imaging and high-speed bright-field (HSB) imaging. LEF
imaging offers excellent bulk population statistics over a wide range of flow rates, but specific
information (e.g., deformation, rotation, depth resolution) cannot be obtained. HSB imaging can
provide this information based on freeze-frame images of individual particles but is limited to a
low range of flow rates before the onset of significant particle blurring. We demonstrated the
use of particle trajectory analysis (PTA) to achieve freeze-frame images of individual
(fluorescently labeled) particles moving at velocities up to 2 m.s-1. Using the fundamental
principles of micro-particle image velocimetry (p-PIV), we captured image slices spanning the
channel height to construct 2-D heat maps that accurately depict the presence (or loss) of
bioparticle focusing in microchannels.
5.1.2 Accessing unexplored flow regime where both inertia and elasticity are present
Particle focusing in microchannels have been limited to inertia-dominant flows and
elasticity-dominant flows. The addition of high-molecular weight polymers have been used to
achieve turbulent drag reduction in macroscale pipes, but controlled particle manipulation in
such fluid flows had not yet been explored in microchannels. One reason for this involved the
technical barriers that had to be overcome in order to access extremely high flow rates in
microchannels. A device fabrication technique was needed to build a rigid microchannel that
(ideally) was optically clear, rapidly prototyped, and cost-effective. Moreover, an imaging
90
technique was needed to capture non-blurred images of individual particles with velocities that
could exceed 100 m.s'. Using hard lithography (with an epoxy resin as the substrate), we built
rigid microchannels that could withstand pressures up to 5000 psi. Using PTA (along with
imaging techniques related to [t-PIV), we obtained quantitative measurements of particle position
and fluid velocity based on individual particle statistics.
5.1.3 Discovering novel focusing mode for bioparticles with ultra-high throughput
In straight microchannels, particle focusing in inertia-dominant flows is limited by the
hydrodynamic transition from laminar flow to turbulent flow, while in curved channels, loss of
particle focusing occurs at lower Reynolds numbers due to dominant Dean drag forces (relative
to inertial lift forces). Particle focusing in elasticity-dominant flows have been limited to much
lower Reynolds numbers that are well below the threshold for inertial focusing in microchannels.
When acting alone, inertia and elasticity are non-linear effects that tend to de-stabilize a fluid
flow. However, when both inertial and elasticity are simultaneously present, these effects can
act constructively to achieve stabilized fluid flow. Using a high-molecular weight polymer
(hyaluronic acid (HA)) with drag-reducing properties, particle focusing to the channel centerline
was achieved at Reynolds numbers up to Re ~ 10,000 (with particle velocities up to 130 m.s'.)
Based on the normal stresses (as opposed to shear-thinning or secondary flow effects) present in
the viscoelastic fluid, we demonstrate that bioparticles can be focused, aligned and deformed
based on precise tuning of fluid rheology. The sample throughputs achieved in the rigid
microchannel via inertio-elastic focusing exceeded the upper limits achieved using viscoelastic
focusing and inertial focusing.
91
5.2 Limitations
5.2.1 Inertio-elastic focusing knowledge primarily limited to experimental studies
Simplified analytical models used in inertia-dominant [43] or elasticity-dominant [53]
flows are not sufficient to understand the physical basis of inertio-elastic focusing. Solutions
based on the full Navier-Stokes equations (or the Cauchy momentum equation) are extremely
difficult to obtain and often require the use of numerical models (e.g., COMSOL Multiphysics,
ANSYS Fluent, Arbitrary Lagrangian Eulerian Method [121]). However, numerical studies on
inertio-elastic focusing are not currently possible since all numerical methods break down when
Wi exceeds a critical value (Wi ~ 0(1)) and typically referred to as the high Weissenberg
number problem [122]). With improved hardware performance and more efficient software
algorithms, it will eventually become computationally affordable to simulate certain aspects of
inertio-elastic focusing (particularly at the lower limits). But for the time being, any information
that helps uncover the principles of inertio-elastic focusing will primarily come from
experimental studies.
5.2.2 Particle isolation in microchannels via inertio-elastic focusing is more complicated
Inertio-elastic focusing can achieve controlled particle migration in a microchannel over
a wide range of Reynolds number. However, the isolation of particles is expected to be more
challenging relative to inertial focusing. For example, while inertio-elastic focusing itself can be
considered "label-free", the suspending fluid itself is "labeled" with a high-molecular weight
polymer. The viscoelastic properties of the resulting polymer solution will alter the flow field in
any device expansion/contraction regions [123], and the presence of elastic normal stresses could
compromise downstream sorting methods (e.g., magnetic-activated cell sorting (MACS)).
92
Moreover, the viscoelastic fluid should be bio-inert (i.e., not initiate a response or interact with
living entities) and not interfere with any reagents used to manipulate and analyze bioparticles
found in the fluid sample.
5.3 Outlook
5.3.1 Establishing the principles of inertio-elastic focusing
Inertio-elastic focusing in a rigid microchannel was achieved using a particle suspension
containing a high-molecular weight polymer (HA) with turbulent drag-reducing properties. It
would be useful to identify a common rheological "signature" (based on shear and extensional
rheology) that a viscoelastic fluid would need to exhibit in order to observe this phenomenon.
For example, a broad sweep of various parameters (e.g., particle size, flow rate) could offer
insight into assembling a state-space map of inertio-elastic focusing similar to the one developed
for inertial focusing in asymmetrically curved microchannels [13].
5.3.2 Observing inertio-elastic focusing in complex microchannel geometries
Given the wide-spread use of curved (e.g., asymmetrically curved, spiral) microchannels
to achieve controlled particle manipulation, it is only fair to explore inertio-elastic focusing in
such channel geometries. Given the constructive (or destructive) relationship between inertial lift
and Dean drag forces, it is of significant interest to see if an "elastic analog" of this relationship
exists as well. Note that viscoelastic focusing (with negligible inertia) has been observed in
spiral microchannels such that elastic forces drive particles to center while Dean drag forces
migrate laterally to different equilibrium positions based on particle size [124]. Inertio-elastic
flows should explored in microchannels with complex geometries (i.e., channel
93
expansions/contractions [125], physical barriers [126]) to determine whether particle focusing
(or other useful effects) can occur.
5.3.3 Finding real-world applications for inertio-elastic focusing
The ultra-high throughput of inertio-elastic focusing in microchannels has been featured
heavily in this work. However, inertio-elastic focusing is not merely limited to such high values
of Re and Wi, and it is in more moderate flow regimes where additional useful effects can occur.
One aspect of inertio-elastic focusing that offers practical value is the controlled stretching of
deformable particles in a microchannel. A similar effect was observed in microchannels with
narrow constrictions and used to achieve intracellular delivery of macromolecules (i.e., carbon
nanotubes, proteins, small interfering RNA) into multiple cell types (including embryonic stem
cells and immune cells) [119, 127]. By tuning the rheological profile of the (biocompatible)
viscoelastic fluid, it could be possible to transfect plant or mammalian cells in quantity and rate
of production that significantly exceeds the current limits of cell transfection/transformation
technologies.
94
Chapter 6 1Supplementary Figures
(5zm: depth of measurement
''I
6z
. ..
=
I
.. I .." 1., 1, 11_
3nA0
)2+
(NA) 2
-
,
8zf: depth of field
, ; :I- .
I I-
2.16d
tan0
6z = NA) 2 +
S(NA)2
PG
ne
(NA)M
Nd:YAG Laser
A =532 nm
8t 10 ns
Figure 6-11 Key parameters of micro-particle image velocimetry (p-PIV). The depth of measurement is twice
the distance from the center of the object plane beyond which fluorescent particles will not significantly influence
the fluid velocity measurement. The depth of field is twice the distance from the center of the object plane beyond
which the object is considered unfocused based on image quality.
95
Inlet
Out
Blood
tCTC
(Waste)
Figure 6-2 Inertial focusing as a building block for rare cell isolation. Fluorescently labeled PC-3 cells bound
to superparamagnetic beads were spiked into diluted blood (fRuc = 0.33) and processed in a multi-stage device at
Re ~ 100. After the PC-3 cells were focused in the inertial focusing stage, the two focused streamlines where split
and exposed to a NdFeB magnet array. PC-3 cells were sufficiently displaced in the magnetic deflection stage to
enable collection in the cell capture stage, which contained another magnet array (amidst reduced fluid flow).
96
. ...
..............
..
..............
.
. ...
. ........
. ........
......
......
......
.....
. . .........
-. 11-.1
............................
. .......
__
Wi
A
L
10 -4-
8 PDMS
PTA
102
-
10'
-
z
100 4-
I
10-'
100
I
I
10'
102
103
+-*
Re
104
Figure 6-3 1Technical barriersto accessing unexplored flow regime. The idea of particle focusing in an
unexplored flow regime where both inertia (Re >> 1) and elasticity (Wi >> 1) are present was motivated by: 1) cells
focusing to completely different equilibrium positions in whole blood (relative to diluted blood) [89], and 2)
significant energy savings in macroscale pipe flow due to the presence of high-molecular weight drag-reducing
agents [64]. However, in order to investigate particle focusing in this flow regime, microchannels made of
polydimethylsiloxane (PDMS) will heavily deform (if not delaminate), and the image quality of focused particles
using particle trajectory analysis (PTA) has not been studied.
97
45Jm
(
90 pi
I
-V
Q = 450
Q = 50 pl.min-i
pl.min'
Figure 6-4 1PC-3 (cancer) cell focusing in physiological saline and whole blood. Streak images of PC-3 cells (a)
physiological saline (fB( = 0) and (b) whole blood (/?g(: = 1) were taken at Q = 50 pl.min-' and 450 pl.min-'. Note
that channel bulging becomes evident at the higher flow rate, particularly in whole blood.
98
WXliole Blood
Xanthian Gtum
Polyacrylamide
Figure 6-5 1Polystyrene bead focusing in xanthan gum and polyacrylamide solutions. Streak images of 10-pim
polystyrene beads re-suspended in (a) whole blood (fRBC = 1), (b) xanthan gum (1800 kDa, 125 ppm, water) solution
and (c) polyacrylamide (5000 kDa, 500 ppm, water) solution were taken at Q = 150 [l.min-'.
99
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