parameters affecting the shape of a hydrodynamically focused stream
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RESEARCH PAPER
Parameters affecting the shape of a hydrodynamically focusedstream
Mansoor Nasir • David R. Mott • Matthew J. Kennedy •
Joel P. Golden • Frances S. Ligler
Received: 14 December 2010 / Accepted: 2 February 2011 / Published online: 19 February 2011
� Springer-Verlag (outside the USA) 2011
Abstract Even at low Reynolds numbers, momentum
can impact the shape of hydrodynamically focused flow.
Both theoretical and experimental characterization of
hydrodynamic focusing in microchannels at Reynolds
numbers B25 revealed the important parameters that affect
the shape of the focused layer. A series of symmetric and
asymmetric microfluidic channels with two converging
streams were fabricated with different angles of confluence
at the junction. The channels were used to study the char-
acteristics of Y-type microchannels for flow-focusing.
Computational analysis and experimental results gathered
using confocal microscopy and particle image velocimetry
indicated that the orientation of the sheath and the sample
stream inlets, as well as the absolute flow velocities,
determine the curvature in the concentration distribution of
the focused stream. Decreasing the angle of confluence
between sheath and sample, as well as reducing the overall
Reynolds number, resulted in a flat interface between
sheath and focused fluids. Alignment of the faster flowing
sheath fluid channel with the main channel also reduced the
inertial effects and produced a focused stream with a flat
concentration profile. Control over the shape of the focused
stream is important in many biosensors and lab-on-a-chip
devices that rely on hydrodynamic focusing for increased
detection sensitivity.
Keywords Flow focusing � Angle of confluence �Converging channels � Inertial effects � Laminar flow �Symmetric
1 Introduction
Parallel laminar flow of two or more liquid streams in
microchannels has been studied extensively over the past
decade for use in microfluidic and biomedical applications
such as controlling flow paths (Atencia and Beebe 2005;
Lee et al. 2006; Walsh et al. 2007), patterning of surfaces
(Kenis et al. 1999), diffusional sensors (Brody et al. 1996;
Hatch et al. 2001), flow cytometry on a chip (Golden et al.
2009; Huh et al. 2005; Simonnet and Groisman 2006), and
impedance spectroscopy (Hua and Pennell 2009; Nasir
et al. 2009). In many of these devices, one or multiple
streams focus another stream by influencing its fluidic path.
If the streams comprise immiscible fluids, the flow inter-
actions lead to formation of droplets or bubbles, which
have been studied extensively (Anna et al. 2003; Thorsen
et al. 2001; Whitesides 2006; Ben-Tzvi and Rone 2010).
Herein, we examine the convergence of two miscible flu-
idic streams to understand the dynamics of flow focusing.
The simplest version of this experiment is a Y-junction
channel into which two fluids enter through separate inlets,
converging and then flowing in parallel laminar streams
down a main microchannel. An important subset of
Electronic supplementary material The online version of thisarticle (doi:10.1007/s10404-011-0778-5) contains supplementarymaterial, which is available to authorized users.
M. Nasir � J. P. Golden � F. S. Ligler (&)
Center for Bio/Molecular Science and Engineering,
Naval Research Laboratory, 4555 Overlook Ave. SW,
Washington, DC 20375, USA
e-mail: frances.ligler@nrl.navy.mil
D. R. Mott
Laboratory for Computational Physics and Fluid Dynamics,
Naval Research Laboratory, 4555 Overlook Ave. SW,
Washington, DC 20375, USA
M. J. Kennedy
Chemistry Division, Naval Research Laboratory,
4555 Overlook Ave. SW, Washington, DC 20375, USA
123
Microfluid Nanofluid (2011) 11:119–128
DOI 10.1007/s10404-011-0778-5
Y-junction channels is the T-junction channel where the
junction angle between the two inlet channels is 90� and
the outflow channel is aligned with one of the inflow
streams (Ismagilov et al. 2000; Munson et al. 2004).
Y-junction, and in particular T-junction, microchannels
have played an important role in microfluidic devices
designed to control diffusion and mixing (Kamholz et al.
1999; Kenis et al. 1999) as well as for applications such as
separation and detection (Hatch et al. 2001; Hofmann et al.
2002; Weigl and Yager 1999). Y-junction microchannels
are typically operated at a low Reynolds number (Re \ 50)
conditions, under which the two merging streams flow
adjacent to each other and the only mixing is due to dif-
fusion of molecules between the two streams. To date,
much of the work on Y-junction channels has focused on
the generation of concentration gradients, including the
effect of the angle of confluence between the two streams
on the diffusion gradient (Yang et al. 2002, 2007).
Recently, the effect of critical parameters such as Re, inlet
geometries, and channel heights on focusing with two side
sheath streams in micron-to-milliscale channels was also
reported (Kim et al. 2010).
The intersection between fluidic channels is also an
important geometric element in nature. For example, the
angle at which capillaries join impacts microcirculation in
the organs (Fujisawa et al. 2006), and the convergent flow
design was used to study the vertebro-basilar junction in
the cerebrovascular circulation system. Ravensbergen et al.
(1996) found that the angle of confluence between the
arteries significantly affected the formation of arteroscle-
rotic plaques in the junction. Converging flows within
tributary streams and river channels have serious impact
on the local environment (Rhoads and Kenworthy
1995), albeit the Re are on the higher end of laminar flow
regime (*1000).
The majority of the aforementioned studies have eval-
uated the merging of two streams with similar flow rates.
Under these conditions, each stream occupies approxi-
mately half of the microchannel volume. However, if one
stream is flowing faster, then the slower stream is confined
or focused against the channel wall. By increasing the flow-
rate ratio between the sheath (higher volumetric flow rate)
and sample (lower volumetric flow rate) streams, the
focusing effect increases. The flow dynamics of merging
streams with unequal flow rates are more complicated, and
the effects of geometric and flow parameters on the shape
of the focused stream remain largely unexplored. Further-
more, previous work has concentrated on symmetric
designs where the two merging channels have the same
angle with respect to the outlet channel (Gobby et al. 2001;
Ismagilov et al. 2000; Kamholz et al. 1999). Asymmetric
junction designs offer certain operational advantages due to
the ease of fabrication as well as the efficient use of real
estate in lab-on-a-chip devices (Nasir et al. 2009; Hofmann
et al. 2002). How these design variations affect the
focusing behavior has not been thoroughly investigated.
In this study, we use simulation and experimentation to
examine flow focusing in microchannels with both sym-
metric and asymmetric junctions. We have previously
shown that increasing the flow rate decreases the diffusion
but also increases the importance of inertial effects (Nasir
et al. 2009). These inertial effects can induce a curvature in
the concentration profile of the focused stream. An
important application of flow focusing is to confine a
sample stream carrying target analyte near a functionalized
sensor surface thereby increasing the target interaction with
recognition elements. However, a curvature in the con-
centration distribution of the focused stream is undesirable,
as a significant amount of the target analyte or assay
reagents is directed away from the sensing surface. For
impedance-based sensors where a conducting flow is
focused over sensing electrodes, cusps in the corner of the
channels can act as high conductivity current pathways that
can lead to a reduction in detection sensitivity (Nasir et al.
2009). A flat focused stream is desirable for both detection
sensitivity and efficiency of target immobilization. Here,
we used the curvature of the concentration profile of the
focused stream as a metric to understand the dynamics of
flow-focusing. We have used numerical and experimental
results to examine channels with symmetric and asym-
metric junctions, the angle of confluence between the
sheath and the sample streams, and operation at multiple
Re conditions.
2 Theory
2.1 Flow in rectangular ducts
The Reynolds number (Re) indicates the relative impor-
tance of inertial and viscous effects in a flow, and is given
by
Re ¼ LVql¼ ðinertialÞðviscousÞ ð1Þ
where L is the characteristic length or the hydraulic
diameter, V is the average fluid velocity, and q and l are
the fluid density and dynamic viscosity, respectively. The
hydraulic diameter of a channel with rectangular cross
section is given by 4 * Area/Perimeter. The velocity in this
case is based on the total volumetric outlet flow rate (Qo) in
the focusing part of the channel and is the sum of sample
(Qsa) and sheath (Qsh) flow rates. Using the cross-sectional
area A of the microchannel and flow-rate ratio c (Qsh/Qsa),
the sample flow rate required to produce a specified Re
must satisfy
120 Microfluid Nanofluid (2011) 11:119–128
123
Qsa ¼Re A l
qLð1þ cÞ ð2Þ
and the corresponding sheath flow rate is Qsh = c � Qsa.
Figure 1a shows the top view of a channel where the
sheath stream enters at a 90� angle to the sample stream
and the main channel. The widths w and heights h of all the
channels are assumed to be the same, i.e., the channels
have square cross sections, and c = 25 for this study.
Assuming all fluids to be Newtonian and operating in the
laminar regime, the basic equation for a fully developed
steady flow in the main channel is given by the classic
Poisson equation:
o2u
oy2þ o2u
oz2¼ 1
ldp
dxð3Þ
where p is the pressure, x is the coordinate along the
channel, and the term dp/dx indicates that the pressure
gradient only exists in the direction of flow. Implementing
no-slip conditions on the channel walls, the exact solution
of the Navier–Stokes equation for streamwise velocity
distribution and flow-rate in a channel with square cross
section are given by (White 1991):
uðy; zÞ ¼ 16w2
lp3�dp
dx
� � X1i¼1;3;5;...
ð�1Þði�1Þ=2
� 1� coshðip y=wÞcoshðip =2Þ
� �� coshðip z=wÞ
i3
ð4Þ
Qo ¼4w4
3l3�dp
dx
� �1� 192
p5
X1i¼1;3;5;...
tanhðip=2Þi5
" #ð5Þ
where widths and heights of all inlet and outlet channels
are w and both y and z lie in the range [-w/2, w/2]. In the
case of the flow-focusing channel shown in Fig. 1a, the
flow velocities are specified in terms of the flow-rates and
therefore Eq. 5 can be used to find the pressure gradient in
the sample, sheath, and main channels. Lee et al. (2006)
used a similar methodology to find the velocity distribu-
tions at various points in a rectangular microchannel
where a sample stream was focused from the sides by two
sheath streams. Furthermore, an analytical solution was
found for the width and location of the focused stream.
However, the exact solutions described by these equations
do not give any information about the three-dimensional
concentration profile of the focused stream. Furthermore,
the effects of channel geometry on the shape of the
focused stream are harder to elucidate using theory alone.
Therefore, in order to investigate the fluid dynamics of
flow focusing and the parameters that affect the eventual
shape of the focused stream, we supplemented numerical
techniques with flow experiments in representative
microchannels.
3 Experimental
3.1 Numerical simulations
In order to understand the effect of inlet geometry and
Reynolds number on the concentration profile of the
focused stream, numerical modeling of the flow through
these channels was performed using the COMSOL Multi-
physics finite element analysis package (COMSOL Inc.,
Palo Alto CA) and the Navier–Stokes solver HYTIDE (Liu
et al. 2007). A square geometry (500 lm 9 500 lm) was
used for the sheath and sample inlet channels as well as the
focusing channel. Using Eq. 2, a flow-rate ratio c = 25,
and 500 lm square channels, the sample and sheath flow
rates were 11.5 and 288.5 ll/min for Re = 10 and 28.8 and
721 ll/min for Re = 25. Both symmetric and asymmetric
channels were used (Fig. 1b). For the symmetric design,
the angle between the sheath and sample inlets was 45�,
90�, 135� or 180�, while for the asymmetric design, the
angle was chosen as 45� or 90�. The flow in the channel
was assumed to be incompressible and laminar, with the
no-slip condition imposed on the channel walls. The inlet
flows were specified by choosing appropriate volumetric
flow rates and either imposing a fully developed velocity
distribution (COMSOL) or a uniform velocity that relaxed
to the steady-state distribution prior to reaching the junc-
tion between the two inlet channels (HYTIDE). In addition
to varying the confluence angle, the effects of changing
absolute flow rates (i.e., Re) and sheath-to-sample flow-rate
ratios were evaluated.
Simulations for Re [ 0 and including diffusion were
conducted in two steps using COMSOL. First, the velocity
field within the channels was solved using the MEMS
Navier–Stokes module. The flow-field is symmetric about
the plane which bisects both inlet channels, so this sym-
metry condition was imposed and flow in only half of the
geometry was simulated. The fluid in both streams was
assumed to be water at room temperature with a kinematic
viscosity of 1 9 10-6 m2/s. The Chemical Engineering
Module then used the resulting velocity field to predict the
mass transfer due to convection and diffusion according to
Fick’s law (1855) assuming a diffusion coefficient of
1 9 10-10 (m2/s). This value of the diffusion coefficient is
typical of low molecular weight solutes (i.e., \1000 MW)
including the dyes used for flow visualization (Culbertson
et al. 2002). It was assumed that the change in solute
concentration as a result of mass transport did not affect the
density and viscosity of the two fluids. Adaptive meshing
was used to accurately resolve the interface between the
sample and the focusing streams. To assess the effects of
confluence angles, concentration distributions were calcu-
lated for cross sections taken 2 mm downstream from the
junction. The sample stream with the maximum solute
Microfluid Nanofluid (2011) 11:119–128 121
123
concentration was shown in red, and the sheath with zero
concentration was shown in blue. The intermediate colors
reflect the level of diffusive mixing.
Specifying a diffusion coefficient smaller than
1 9 10-10 (m2/s) prevented the numerical simulations
from converging in COMSOL. Since a smaller diffusion
coefficient value (\1 9 10-10 m2/s) was needed to avoid
excessive diffusion for the Stokes flow simulation
(Re = 0), an alternate software was needed for this par-
ticular case. Therefore, HYTIDE solver was utilized
because it allowed visualization of concentration distribu-
tions with zero diffusion coefficient at Re = 0. HYTIDE is
a hybrid flow solver with modules for compressible,
incompressible, and rarified flows, but for this study only
the incompressible solver was employed (Liu et al. 2007).
After HYTIDE was used to solve the velocity field, a
Lagrangian advection routine took points in the outflow
plane and backtracked along streamlines to determine
whether each point originated in the sample stream or in
the focusing stream (Mott et al. 2006).
3.2 Microchannel fabrication and assembly
In order to validate the results of the finite element models
experimentally, Y-junctions with different confluence
angles were micromachined out of Plexiglas (Plexiglas G,
Atofina Chemical, Inc. Philadelphia, PA) using a HAAS
Mini Mill (HAAS Automation, Inc., Oxnard, CA). Since
angled inlets are difficult to machine accurately in a top
down assembly, the junction and the channels were rotated
such that the sheath stream focused the sample stream
along the sidewall and not the bottom surface (Fig. 1b).
Devices where the angles between merging (sheath and
sample) streams and the main channel were the same were
referred to as symmetric, while the devices where the
angles between merging streams and the main channel
were not equal were denoted as asymmetric.
Blank pieces were cut from a 0.25 inch (6.35 mm) thick
PMMA sheet (McMaster-Carr, Elmhurst, Illinois) using a
0.25 inch (6.35 mm) diameter endmill (Harvey Tool,
Rowley, MA). The blank pieces were mounted on a vise,
and a facemill tool (Valenite, Madison Heights, MI) was
used to planarize the milling surface. Thereafter, the
channels were machined using a 0.02 inch (508 lm) end-
mill (Harvey Tool, Rowley, MA). The micromachined
channel width and height were measured to be 600 and
380 lm, respectively. Precision machining techniques
ensured that the variation in channel dimensions of any of
the designs was not more than 10 lm. The same endmill
was also used to mill a glue trench 500 lm wide and
200 lm deep at a distance of 500 lm from the outer edges
of the microchannel and the inlets. This trench prevented
the glue from leaking into the microchannel (Leatzow et al.
2002). The length of the channel from the first inlet to the
Fig. 1 a Schematic shows the top view of an asymmetric junction
channel with the sheath fluid entering at 90� with respect to the sample
and main channels. The sheath stream flow rate Qsh is greater than the
sample stream flow rate Qsa thus focusing the sample stream from
the original height w to a smaller height wf along the wall opposite to
the inlet for sheath fluid. b Symmetric (left) and asymmetric (right)channel designs with angle of confluence a = 90�. c A volume section
of the channel is imaged from the bottom with the confocal
microscope. The inset shows a 3D fluorescent confocal image of the
focused fluid stream. Y–Z cross sections of the imaged sections are
used for comparison of different channel designs in this article.
d Channels used in this study were machined from PMMA substrate
and bonded to a glass slide using UV-curable glue. The metal sleeves
were used to connect tubing to the inlets and outlet
122 Microfluid Nanofluid (2011) 11:119–128
123
outlet was 3 cm. A benchtop drill press was used to widen
the upper half of the inlets and outlet where metal tubing
was inserted and glued into place using 5 min epoxy
(Devcon, Danvers, MA). The PMMA pieces were glued to
standard microscope slides using UV-curable adhesive
(Optical adhesive #72, Norland Products, Cranbury, NJ). A
fully assembled channel is shown in Fig. 1d.
3.3 Confocal microscopy
To visualize the concentration profile from microchannel
cross sections during flow focusing studies, we used a
Nikon Eclipse TE2000-E inverted microscope equipped
with a Nikon D-Eclipse C1si confocal spectral imaging
system (Nikon, Japan). A dual syringe pump (Harvard
Apparatus Model 33) was used to flow sheath and sample
fluids, and confocal images were obtained by scanning in
the region roughly 2 mm downstream from the junction. In
order to visualize the focusing, FWT Red Powder fluo-
rescent dye (Bright Dyes, Miamisburg, OH) was mixed
with deionized water for the sample stream. A 40 mW
Argon laser was used at the 514.5 nm excitation line, and
the spectral detector of the confocal imaging system was
set to detect emission between 583 and 593 nm. Image
stacks were rendered and analyzed in three dimensions
using NIS-Elements AR confocal image processing soft-
ware (Nikon, Japan). Figure 1c shows the channel orien-
tation with respect to confocal scanning. The inset shows
an actual confocal volume-section where the fluorescent
area shows the focused stream.
3.4 Particle image velocimetry (PIV)
Image acquisition was performed using a FlowMaster
MITAS Microscope (LaVision, Germany) equipped with a
dual Nd:YAG laser system (Solo III 15 Hz, New Wave
Research, USA) and a charge coupled device camera with
1376 9 1040 pixels (ImagerIntense, LaVision, Germany).
The microfluidic device was mounted on a stage with
X-, Y-, and Z-translation motors. The stage motors, camera,
and laser system were all controlled using DaVis Imaging
Software. A solution composed of 890 nm fluorescent
microparticles in deionized water was applied to the two
inputs of the microfluidic device using two syringe pumps
(PHD 2000, Harvard Apparatus). Images were acquired
using a 109 objective, which was calibrated using a cali-
bration slide. A z-scan was performed through the depth of
the channel in 5 lm steps to determine the locations of the
bottom and top surfaces, after which the focus of the
microscope was fixed at the middle depth of the channel for
the duration of the experiment. The width of the micro-
channel was observed to be 600 ± 10 lm, and the depth of
the channel was observed to be 370 ± 10 lm. The delay
between laser flashes was set to 300 ls at Re = 25, and
this delay was increased at slower flow rates. The field of
view of the 109 objective was 300 lm 9 250 lm, which
was too small to view the entire region of interest.
Therefore, an X–Y scan was performed in which images
were acquired at 15 locations, taking 5 steps in the
X-direction and 3 steps in the Y-direction. At each
X–Y location, 50 sets of images were acquired. After all
image acquisition was complete, each set of 50 images was
processed using the sum of correlation method within the
DaVis Imaging Software to yield a representative vector
field. Finally, the 15 vector fields corresponding to each
X–Y location were exported as text files and then digitally
stitched together in MATLAB for visualization. The
velocity field measured in the regions outside of the
microfluidic channel consisted of randomly oriented vec-
tors of small magnitude, and these regions were digitally
removed for clarity.
4 Results and discussion
4.1 Effect of angle of confluence
Flow simulations and confocal studies were conducted in
microchannels with 45�, 90� and 180� as the angle of
confluence a between sheath and sample streams. In our
initial study, all channels were symmetric. The focusing
characteristics were studied for Re = 10 and Re = 25.
These Re were chosen not only because they are typical of
many flow-focusing devices (de Mello and Edel 2007;
Hairer and Vellekoop 2009) but also because the relative
importance of inertial effects at such low Re is not gener-
ally appreciated (Di Carlo 2009; Squires and Quake 2005).
In order to maintain a flow-rate ratio of 25, the sheath and
sample flow rates were adjusted accordingly. Using Eq. 2
and the actual dimensions of the channel described in Sect.
3.2, the sample and sheath flow rates, respectively, were 11
and 283 ll/min for Re = 10 and 28 and 707 ll/min for
Re = 25. The results (Fig. 2) indicated that curvature in
the interface between the sheath and focused fluid, and the
resulting cusps of fluid at the channel corners, increased
both with increasing Re and the angle of confluence. Since
the channel dimensions and flow-rate ratios were the same
in each design, any change in the focused stream profiles
for a particular Re was strictly due to the angle of conflu-
ence. The sheath stream flowed faster than the sample
stream and pushed the latter stream toward the channel
sidewall opposite to the sheath fluid inlet. Due to the par-
abolic velocity profile of the sheath stream, the sample
stream was not focused uniformly along the interface
between the two streams. To varying extents, the imping-
ing of the sheath stream caused the focused stream to curve
Microfluid Nanofluid (2011) 11:119–128 123
123
or cusp along the adjacent surfaces (top and bottom sur-
faces in this particular channel). As the angle increased, the
cusps in the focused stream also became more prominent.
Increasing the Re from 10 to 25 drastically increased the
cusp formations. The results were confirmed with both
simulations and experiments.
A qualitative understanding this trend can be gained by
considering the velocity profile of the sheath fluid just before
it enters the channel junction. The fully developed flow has a
parabolic velocity profile in which the center of the parabola
has the highest velocity. At shallow angles (a = 45�), the
component of sheath fluid velocity normal to the flow in the
main channel was small. However, as the angle a increased,
the angle at which the sheath stream impinged on the sample
stream also became steeper and resulted in an increase in
curvature of the interface between sheath and focused
streams (Fig. 2). The component of the sheath fluid velocity
normal to the flow in the main channel was maximized for the
180� case and correlated with the largest observed cusps. At
higher Re, the sheath fluid velocity was greater and conse-
quently the cusps were more pronounced with steeper slopes
(Electronic Supplemental Information (ESI), Fig. S1). It
should be noted that increasing the Re alone does not auto-
matically cause the formation of cusps. If the sheath and the
sample flow rates were the same, then the boundary between
the sheath and sample streams remained flat at all Re (ESI
Fig. S1). The formation of cusps was a direct result of the
mismatch between the velocities of the merging streams in
combination with the angle of confluence.
Interestingly, both simulations and confocal images
showed that the slope of the cusps decreased near the
channel wall. Presumably, this effect was due to the no-slip
boundary condition which applied to both sheath and
sample streams. Within a finite distance from the channel
walls, the sheath and sample velocities are nearly identical,
and the inertial effects diminished. The focusing in this
boundary region was similar to the focusing that occurred
in the channel at low flow-rate ratios where the concen-
tration profile was flat and perpendicular to the adjacent
channel walls.
4.2 Effect of Reynolds number
To discriminate clearly the effects of angle of confluence
and the Re on the final shape of the focused stream, sim-
ulations were performed assuming a Stokes flow (Re = 0)
condition imposed on the flow inside a 90� asymmetric
flow-focusing channel. The sheath and sample flow rates
were chosen so that the flow-rate ratio was 25 and the
channel dimensions (described in Sect. 3.1) were kept
constant. The results are shown in Fig. 3. At Re = 0, the
sheath flow entering the junction initially filled the main
channel. Since there were no momentum effects and a large
ratio of sheath fluid to focused fluid, this filling included a
slight backflow toward the inlet of the focused stream.
Subsequently, the streamlines originating in the sheath
stream travelled parallel to the side walls as they proceeded
down the main channel. As a result, the focused stream had
a very flat concentration distribution (Fig. 3a). However,
when Re = 25, inertia carried the sheath stream down into
the sample stream at the junction of the two flows, and the
backflow region was absent. The higher momentum of
the sheath stream in the center of the channel pushed the
sample fluid toward the lower corners. This resulted in
distribution of the focused stream along the walls and the
formation of the cusps in the concentration distribution
(Fig. 3b). Unlike the Re = 0 case, the shapes of the
streamlines varied significantly across the channel. Stokes-
flow simulations performed using designs with different
angles of confluence (results not shown) exhibited only
subtle differences in the small backflow region seen at the
junction.
In order to observe the flow focusing effect at the
junction, particle image velocimetry (PIV) was performed
with the 90� symmetric channel at two different Re’s
(Fig. 4). The sample and sheath flow rates were 1 and 28
ll/min for Re = 1 case and 28 and 707 ll/min for Re = 25
case. The backflow region was present at Re = 1 but not
Re = 25. At low Re, the sheath fluid departed from its
original trajectory upon first entering the junction while at
higher Re, the fast-moving sheath fluid continued on its
original trajectory, in the direction parallel to the sheath
Fig. 2 Channel cross sections from COMSOL simulations (columns
1 and 2) and confocal microscopy (columns 3 and 4) show the
concentration profiles for symmetric channel designs. Three angles of
confluence (45�, 90�, and 180�) and two Re (10, 25) were used for
comparison. COMSOL simulations were performed for half the
channel height. The cross sections were mirrored and stitched for
easier comparison with confocal experiments. The actual channels
were 380 lm 9 600 lm, and the simulated channels were
500 lm 9 500 lm (height 9 width). See Sect. 3 for more details
on the flow-rates used for simulations and confocal studies
124 Microfluid Nanofluid (2011) 11:119–128
123
channel. As the sheath flow velocity (and hence Re)
increased, the fluid behavior switched from predominantly
filling just the volume at the junction to actively pushing
the sample stream. PIV results showed that as the Re
increased, the difference in the velocity distribution across
the channel height became more pronounced, with the
sheath pushing deep into the center of the main channel and
causing the sample stream to be confined along the channel
walls (data not shown). The experimental PIV results
agreed with the simulated velocity fields from our COM-
SOL simulations (ESI Fig. S2).
4.3 Effect of channel symmetry
To investigate the effect of channel symmetry, symmetric
and asymmetric designs with common confluence angles
(45� and 90�) were tested. For the symmetric designs, the
angles between the main channel and the sheath and
sample stream inlets were equal (Fig. 1b, left). For the
asymmetric designs, the sample inlet was aligned with
the main channel while the sheath was introduced from the
side (unless the reverse is specified). The channel dimen-
sions were kept constant in all cases (described in Sect.
3.1). As before the sheath and sample flow rates were
chosen such that the Re in the main channel was 10 or 25.
Channel cross sections showing concentration distributions
from COMSOL simulations (ESI Fig. S3) were imported in
MATLAB and plotted using a suitable concentration range.
A comparison of simulation results from symmetric and
asymmetric design showed that cusps were greater for the
asymmetric designs for either Re (Fig. 5). The cusp height
was greatest for Re = 25 with the 90� asymmetric design
than any other geometry/parameter combination. For this
case, the flow entering from the faster flowing sheath fluid
was perpendicular to both the sample input and outflow
directions, and thus the perpendicular component of the
Fig. 3 Focusing with a flow-
rate ratio of 25 was simulated
with HYTIDE solver for a
channel with square cross
sectional geometry
(500 lm 9 500 lm) under
a Stokes flow (Re = 0) and
b Re = 25. The streamlines
show the direction of flow of the
sheath stream through the
channel. An X–Y section along
the center of channel height was
used for velocity field plots and
showed the highest velocity in
the center of the channel. A
Y–Z cross section at the outlet is
used for comparison of the
concentration distributions
Fig. 4 Vector field plots with normalized velocity field and contour
plots showing the velocity magnitude are overlayed for an X–Y cross
section at the middle-depth of the channel using PIV for a Re = 1,
b Re = 25. Channels used for PIV are the same as used previously for
confocal experiments. The channel dimensions were 380 lm 9
600 lm with the angle of confluence a = 90�. The flow-rate ratio
was 25 in each case with the sheath flow entering from left and the
sample from right. The outflow channel is at the bottom
Microfluid Nanofluid (2011) 11:119–128 125
123
sheath velocity was maximized. When flowing at such high
relative velocity, the fluid momentum caused the sheath
stream to penetrate almost all the way to the opposite wall
and nearly caused the sample stream to be split into two.
In the symmetric design, although the flow-rates and
channel dimensions were identical, the sheath velocity
component perpendicular to the main flow was smaller and
the sheath fluid did not have to turn as sharply to be flowing
directly toward the outlet of the main channel. Slight
changes in the flow direction reduced the effect of the
momentum of the sheath fluid. With the velocity constant,
the sharper the turn, the more likely was the sheath fluid to
approach the opposite wall at the junction. Since the sheath
flow did not penetrate as far into the main channel as it did
for the asymmetric design, the cusps in the concentration
distribution were also smaller. Results from the confocal
experiments confirmed the simulations (ESI Fig. S3).
In all cases tested, the Re was well within laminar flow
regime, but increasing the Re from 10 to 25 resulted in a
pronounced impact of the inertial forces on the flow-
focusing behavior. The channel design varied the degree to
which the inertial forces played a part in shaping the
focused stream. The role of fluid momentum was investi-
gated further by comparing two cases where sheath and
sample stream inlets were switched in the 90� asymmetric
design (Fig. 6). Where the faster flowing sheath fluid was
aligned with the main channel, the focused stream was very
flat even at higher Re. The sample stream was flowing
much slower than the sheath stream, and therefore the
momentum carried by the sample stream was not signifi-
cant enough to cause it to penetrate the sheath flow before
turning the 90� corner at the junction. Consequently, the
focused stream had a flat concentration profile. In order to
minimize the effects of sheath fluid momentum on the
focused stream, the channel should be designed in such a
way that the sample stream changes direction rather than
the sheath stream.
4.4 Effect of channel cross section
Although not thoroughly investigated here, the similarity of
results for simulated (square) and experimental (rectangu-
lar) channels also demonstrated that the inertial effects
significantly affect the shape of the focused stream for a
wide range of channel cross sections. The behavior only
deviated for channels with extreme aspect ratios where
shallow channel approximations were applicable (i.e., 2D
flow dynamics can be used for 3D geometry). Even though
the experimental study was conducted on 500 lm square
channels, the results apply to flow in smaller channels with
matching Reynolds and Peclet numbers (ESI Fig. 4). The
curved interface shape for Re = 25 in the 500 lm square
Fig. 5 Concentration distribution profiles for symmetric and asym-
metric designs at 45� and 90� and two Re conditions. a Re = 10, b Re= 25 are shown. The simulated channel dimensions were 500 lm 9
500 lm (height 9 width). The sample and sheath flow rates were 11
and 283 ll/min for Re = 10 and 28 and 707 ll/min for Re = 25. The
profiles were extracted from COMSOL simulations by importing
Y–Z cross sections in MATLAB and then parsing through the data
using a suitable concentration range (0.45–0.55). This essentially
plots the narrow diffusion region band between the sheath and the
focused streams and allows the visualization of cusps in each case
Fig. 6 Channel cross sections from confocal microscopy show the
concentration profiles for asymmetric channel design (a = 90�). The
sheath and the sample streams were switched for each case of the Re(10, 25). The first row shows the results when sheath stream was
aligned with the outflow channel and the second when sample stream
is aligned with the outflow channel. The channel dimensions were 380
lm 9 600 lm (height 9 width). The sample and the sheath flow
rates, respectively, were 11 and 283 ll/min for Re = 10 and 28 and
707 ll/min for Re = 25
126 Microfluid Nanofluid (2011) 11:119–128
123
channel matched the interface generated in a 100 lm
square channel. At a fixed velocity, the smaller channel
amplified the effects of the diffusion and the viscous forces
relative to the advective transport and the inertia. Increas-
ing the flow velocity by the same factor, however, can
mitigate this effect by reducing the residence time over
which diffusion occurs and by making the inertial terms
more significant. Thus, keeping the LV product (Eq. 1) and
the fluid properties constant can produce the same relative
strengths of the competing effects in the differently sized
channel.
5 Conclusion
Recent studies have highlighted the effects of inertia in
microchannels (Di Carlo 2009). Operating at Re in the
range of 5 to 120, Dean forces and secondary flows have
been used in micromixers (Howell et al. 2004) as well as
for separation of particles based on their size (Choi et al.
2011). The findings of this theoretical and experimental
investigation reinforce the importance of inertial forces in
flow focusing channels and can serve as a benchmark for
choosing the optimal design of many microfluidic devices.
The confluence angle of the merging streams has a strong
impact on the shape of the focused stream. While most
microfluidic channels operate within the laminar flow
regime, the design of the channel can have unintended
consequences by exaggerating the effects of the inertial
component of the faster flowing stream. For a flat interface
between the sheath and the focused stream, the angle of
confluence should be as small as possible within fabrica-
tion constraints. Even for 2D flow focusing channels, the
side channels should merge at shallow angles as opposed to
entering the channel at right angles. Decreasing the Re also
helps to produce a focused fluid layer that is very flat across
the height of the channel. If the flow focusing channel is to
be used in conjunction with a sensing technique where an
angled inlet is not possible due to machining and fabrica-
tion constraints (Nasir et al. 2009), then the best way to
achieve a uniform height is to operate at lower Re. Of
course this must be weighed against the longer time needed
to reach steady state flow as well as the increase in diffu-
sive mixing between the streams due to longer resident
times. Whenever possible, the faster flowing sheath fluid
should be aligned with the focusing channel since this
reduces the inertial effects and produces a focused stream
with a flat concentration profile. The results described here
are applicable to microfluidic devices with a wide range of
channel cross sections. Control over the shape of the
focused stream is critical in many biosensors and lab-on-a-
chip devices. A flat focused stream is desirable for
both detection sensitivity and efficiency of target
immobilization. By controlling the shape of the focused
stream, the interaction between the target analyte in the
sample stream and the functionalized sensor surface can be
enhanced.
Acknowledgments This project is funded by the Defense Threat
Reduction Agency (DTRA #AA07CBT015). The authors would like
to thank Dr. James W Fleming at NRL for use of the PIV instrument.
Dr. Matthew Kennedy is a National Research Council (NRC) Post-
doctoral Fellow. The views are those of the authors and do not rep-
resent opinion or policy of the US Navy or Department of Defense.
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