parameters affecting the shape of a hydrodynamically focused stream

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: [email protected]

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

http://dx.doi.org/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


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


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


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


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


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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