Microfl uidics

Three Dimensional, Sheathless, and High-Throughput Microparticle Inertial Focusing Through Geometry-Induced Secondary Flows

Aram J. Chung , Daniel R. Gossett , and Dino Di Carlo *

The ability to continuously control microparticle position

tightly in a confi ned microchannel is remarkably useful for a

wide range of biomedical studies. [ 1–3 ] In order to achieve par-

ticle focusing in microchannels various approaches have been

reported. [ 4 ] Important parameters for ideal micro particle

focusers are (1) simplicity in operation, (2) elimination of

extra input fl uid streams, (3) high-throughput processing and

(4) effi cient and narrow focusing; however to date it is still

extremely challenging to create a microfl uidic focuser having

all of these characteristics. Current state-of-the-art sys-

tems can be categorized as either passive or active focusing

approaches depending on the presence of an external force.

Active systems are based on an externally applied force for

example acoustic, [ 5–7 ] optical, [ 8 , 9 ] magnetic, [ 10 , 11 ] and dielec-

trophoretic. [ 12 , 13 ] Although these approaches offer active

and effi cient particle control, they require complicated and

expensive fabrication processes, may contain bulky external

set-ups, and often operate in a low-throughput manner.

On the other hand, passive systems rely only on channel

geometry or topology changes to achieve focusing. Hydro-

dynamic focusing is the representative approach to achieve

continuous particle focusing in many commercial fl ow cyto-

meters. In microfl uidic implementations, typically two sheath

fl uids with high fl ow rates compress the center fl uid yielding

two-dimensional focusing of particles in that fl uid stream.

This technique is easy to implement however it suffers from

logistically burdensome sheath fl uid and poor optical inter-

rogation due to its intrinsic two-dimensional focusing profi le.

While some existing hydrodynamic focusing systems [ 14 , 15 ]

also possess the capability of single-stream focusing, addi-

tional sheath fl uids are still required. In addition, high fl ow-

rate sheath fl ows can cause a distortion in the focusing profi le

due to an uneven pressure gradient caused by fl uid inertia, [ 16 ]

preventing high-throughput particle focusing.

© 2013 Wiley-VCH Verlag Gmb

DOI: 10.1002/smll.201202413

Dr. A. J. Chung, Dr. D. R. Gossett, Prof. D. Di CarloDepartment of BioengineeringCalifornia NanoSystems InstituteUniversity of CaliforniaLos Angeles, CA 90095, USAPhone: (310) 983-3235, Fax: (310) 794-5956 E-mail: dicarlo@seas.ucla.edu

small 2013, 9, No. 5, 685–690

For other passive and sheath-free systems, bifurcating

(hydrodynamic fi ltration [ 17 ] ) or structured (hydrophoretic

focusing [ 18 , 19 ] ) channels have been used to focus micropar-

ticles. Advantages of these approaches are relatively simple

and sheathless operation, however focusing is relatively

broad, and no high-throughput system has been reported

(most operate with a fl ow rate on the order of 0.1–1 μ L/min).

As an alternative sheathless and passive approach, using

the inertia of the fl uid acting on particles in microchannels

has been gaining attention as a powerful particle focusing

technique because it allows precise and predictable par-

ticle ordering in a high-throughput manner. [ 20–24 ] Due to its

intrinsic focusing characteristics inertial microfl uidic focusing

has the potential of being an ideal particle focuser. However

positioning particles (1) into a single focal plane, (2) in a

single position and (3) to the channel center with high effi -

ciency ( > 99%) is still challenging. Recently, Oakey et al. [ 25 ]

and Bhagat et al. [ 26 ] demonstrated microparticle focusing

using curving channels taking advantage of Dean fl ows, how-

ever the focusing profi les (distribution of focusing positions)

were two to three times broader (large full width at half

maximum (FWHM)) than the particle size. It is still diffi cult

to manipulate particle position precisely using Dean fl ow in

a curving channel because this secondary fl ow intrinsically

perturbs the entire fl ow fi eld in the channel, with the drag

force due to this fl ow dependent on the particle size. [ 19 ] In

addition, particles in previous designs were positioned close

to a channel wall which prevents traditional fl ow cytom-

etry scatter measurements and other optical interrogation

methods [ 27 ] due to unavoidable scattering of the excitation

beam at the wall interface.

Here, we present a novel inertial focusing platform to

create a single-stream microparticle train in a single-focal

plane without sheath fl uids and external forces, all in a high-

throughput manner. The proposed design consists of a low

aspect ratio straight channel interspersed with a series of con-

strictions in height orthogonally arranged, making use of iner-

tial focusing and geometry-induced secondary fl ows. Briefl y,

the combination of inertial focusing upstream and a pair of

local helical secondary fl ows induced by the steps in channel

height allows for migration of cells and particles to a single

position as shown in Figure 1 (see also Movie S1). We suc-

cessfully demonstrate extremely narrow focusing of initially

randomly distributed microparticles into a single-stream with

685wileyonlinelibrary.comH & Co. KGaA, Weinheim

A. J. Chung et al.

68

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Figure 1 . Design and operating mechanisms of a single-stream inertial focuser. A. (1) A schematic view of the platform and particle focusing principles (not to scale). (i) Randomly distributed incoming microparticles focus (ii) mainly into two positions (blue and yellow circles) due to fl uid inertia for a channel aspect ratio ( ≥ 2 or ≤ 0.5). (iii) Then particles (blue circles) laterally migrate in response to helical rotation of the fl uid induced by stepped channels (iv) exiting as a single-stream chain in a single-focal plane. (2) Particle migrations are depicted in the x-z plane. B. A bright fi eld image of a fabricated PDMS stepped microchannel. C. Microparticle focusing of (1) 9.9 μ m polystyrene beads and (2) Jurkat cells. Scale bars represent 50 μ m.

a focusing effi ciency (a ratio of the number of beads in the

fi nal equilibrium position and in the correct plane as a frac-

tion of total beads) as high as 99.77% and a throughput of

approximately 36 000 particles/s. We discuss comprehensive

numerical and experimental studies of the particle focusing

mechanism in these channel types, characterizing the role

of fl ow deformation, determining focusing accuracy in and

out of plane, and demonstrating on-chip fl ow cytometry as a

useful application.

The device is a combination of a straight channel and

a series of stepped channels that yield controlled inertial

focusing and secondary fl ows, respectively (Figure 1 A). In

short, at fi nite Reynolds number ( Re = ρ vD h / μ , a dimension-

less parameter describing the ratio of the inertial forces to

the viscous forces), [ 28 ] particle migration in a straight channel

occurs due to a balance of two inertial lift forces: shear-

gradient ( F SL ) and wall-effect lift forces ( F WL ). [ 20 ] An inter-

action between the particle wake and the wall leads to F WL directed towards the channel centerline, while the parabolic

velocity profi le causes shear-gradient induced F SL acting

towards the channel wall throughout the channel except where

it is zero at the channel centerline. The balance of the two forces

leads to well-defi ned equilibrium positions in channel fl ows.

In square channels, particles focus to four equilibrium posi-

tions at each face of the microchannel, however for rectan-

gular channels with higher aspect ratio, there is a reduction

6 www.small-journal.com © 2013 Wiley-VCH Verlag GmbH & Co. KGaA

in equilibrium positions from four to two

partly due to a blunted velocity profi le

along the long face of the channel and a

corresponding reduction of shear-gradient

lift. [ 22 , 29 ] The upstream straight channel in

this paper has an aspect ratio of 0.5 such

that randomly distributed particles close

to the inlet migrate to mainly two posi-

tions at the long face of the microchannel

(see Figure 1 A(1)(ii)). Then, focused par-

ticles reposition again through a series of

stepped channels. Stepped channels induce

a pair of helical secondary fl ows (net lat-

eral motion of fl uid parcels) that direct par-

ticles into a single equilibrium position on

the channel face opposite to the steps. Var-

ious microparticles were observed to focus,

including 9.9 μ m polystyrene microbeads

(see Movie S2) and Jurkat cells (see Movie

S3 and Figure 1 C). Standard two-step

photolithography and replica molding

protocols were used for microchannel fab-

rication (see Experimental Section below).

Figure 1 B shows a zoom-in view of a

stepped channel. Channel width is 84 μ m

with a height of 41.5 μ m and a total length

of 6 cm. The design consists of 30 stepped

channels spaced out 1 mm apart with a

height of 21 μ m and a length of 40 μ m.

Note that total channel length can be sig-

nifi cantly shortened by simply introducing

curving channels as demonstrated in our

previous works. [ 21 , 30 ]

Stepped channels create localized net secondary fl ows

that compete with inertial lift forces to create fi nal modi-

fi ed equilibrium positions. Figure 2 A shows two dimensional

cross-sections of the fl ow deformation as fl uids fl ow past a

series of stepped channels at fi nite Reynolds number. Based

on the net fl ow in the cross-section seen in 2A(1a)-(8a), cor-

responding lateral particle migrations are depicted in which

particles are drawn away from the channel face containing

the steps (Figure 2 A(1b)-(8b)). Due to inertial focusing

upstream, microparticles are initially positioned at the long

faces of the microchannel (blue and yellow circles), but note

that some unfocused particles were found at the short faces

as well (green circles) for a given upstream channel length. [ 20 ]

Particles positioned at the top and side equilibrium positions

(blue and green circle) are more easily deviated from their

inertial equilibrium positions because the secondary fl ows

moving along the channel perimeter operate against weaker

F WL . These particles can easily follow the stronger sec-

ondary fl ows as depicted. As particles approach the bottom

center position (yellow circle), the secondary fl ow becomes

directed towards the channel centerline against a strong F SL . These particles are captured in the bottom inertial focusing

equilibrium position. This position becomes the most stable

focusing position because the inertial lift force and the sec-

ondary fl ow both point inward towards the center of the

long face aligning microparticles tightly and creating a single

, Weinheim small 2013, 9, No. 5, 685–690

Microparticle Inertial Focusing via Secondary Flows

Figure 2 . Finite element analysis of transport and characterization of net rotational motion at fi nite Reynolds number. A. (1a-8a) Images show cross-section of normalized concentration after 1, 5, 10, 15, 20, 25 and 30 steps in the channel, with the initial condition being concentration of 1 on the top half of the channel and 0 on the bottom half. The corresponding expected particle trajectories are depicted in (1b-8b). B. Vector plots of net streamline displacement following a single stepped channel at (1) Re = 83.33 and (2) Re = 0.2778. (3) Average net displacement plot as a function of Reynolds number (light blue) and the height of the stepped channel (from 0 μ m to 20 μ m) with a fi xed Reynolds number of 83.33.

Figure 3 . Demonstration of continuous microparticle focusing. A. Standard deviation plots from 4,000 image stacks showing qualitative particle position information. B. Schematics of particle focusing as particles fl ow downstream. C. Sequential snapshot images of 9.9 μ m polystyrene beads focusing at Re = 83.33 for every 5 stepped channels (total of 30 stepped channels). High-speed images are recorded at the focal plane of the bottom inertial focusing equilibrium position (dotted line in B). Arrows indicate the particle migration direction. Scale bar represents 50 μ m. D. Focusing effi ciency (a ratio between particles in the fi nal equilibrium position to total particle number) versus number of stepped channels is shown.

equilibrium position in a single focal plane. This mechanism

has similarities to Dean fl ow-modifi ed inertial focusing [ 31–33 ]

in that unstable equilibrium positions are observed where

the secondary fl ow diverges, while locations of convergence

are stable.

The net secondary fl ow induced by a channel step depends

on fl uid inertia. To better understand the helical motion of

the geometry-induced fl ows, a single stepped channel model

(see Supporting Information (SI) text and Figure S1 for more

details) was investigated. Figure 2 B(1-2) plots the amount

each fl uid packet at each point is displaced after passing a

single stepped channel. To compare inertial and Stokes fl ows,

two separate simulations ( Re = 83.33 and Re = 0.2778) are

shown. In the Stokes regime ( Re ≈ 0) there is negligible lat-

eral displacement of fl uid streams to infl uence particle lateral

migration. The magnitude of the net displacement increased

with increasing Reynolds number (Figure 2 B(3)) confi rming

the importance of fl uid inertia. As channel step height

becomes higher, stronger secondary fl ows were also induced

(Figure 2 B(3) and Figure S1). This could be expected as fl ow

© 2013 Wiley-VCH Verlag GmbHsmall 2013, 9, No. 5, 685–690

would be required to turn to a larger extent, creating larger

transverse pressure gradients driving the secondary fl ow.

Note that the direction and shape of the secondary fl ow is

not predictable from prior knowledge and appears to follow

a complex dependence on system parameters. [ 34 ]

Suffi cient lateral motion induced by the step-induced

secondary fl ows is required to yield single-stream focusing.

Figure 3 shows the focusing results of 9.9 μ m polystyrene

microspheres with a coeffi cient of variation (CV) of 5%, and

concentration of 0.1% w/w (see Movie S4) after increasing

numbers of steps. The device was operated at Re = 83.33.

Standard deviation plots (weighted and normalized streak

lines, see Figure S2 for details) show increasing accuracy of

focusing with increasing number of steps (Figure 3 A). High-

speed images (Figure 3 C) taken at the focal plane of the

bottom inertial equilibrium position (dotted line in Figure 3 B)

show lateral microsphere migration (outward and inward)

and vertical migration (from out of focus to in focus) towards

the fi nal focusing position (yellow circle). Particles follow the

secondary fl ow pattern predicted by numerical analysis.

Focusing to a single-stream saturated after the action of

approximately 25 steps. The focusing effi ciency was calculated

and plotted in Figure 3 D. We defi ne the focusing effi ciency

as the ratio of the number of beads in the fi nal equilibrium

position (defi ned in Figure S3) and in the correct plane as

a fraction of total beads. As microbeads passed the stepped

channels, the number of microspheres in the fi nal equilibrium

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A. J. Chung et al.

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Figure 4 . 9.9 μ m polystyrene bead focusing improves with Reynolds number. A. Focusing histograms of the cross-sectional location of all beads (N = 1,000 for each run) regardless of their focal plane from Re = 0.28 to 83.33. B. Focusing effi ciency and focusing purity versus Reynolds number. Focusing effi ciency and purity above 99% is achievable. A control channel without steps shows approximately 50% of particles in the center focusing stream.

position increased and the focusing effi ciency reached 99.77%

(N = 4296). The throughput of the system at Re = 83.33 was

approximately 6,400 particles/s and in order to evaluate the

potential for high-throughput operation we also tested higher

concentration samples.

Higher throughputs are achieved by increasing the par-

ticle concentration without signifi cantly effecting focusing

effi ciency. Because of the fi nite volume of inertial focusing

regions, it is practical to introduce a length fraction ( λ ) taking

account of the focusing volume. [ 20 , 29 ] Theoretically the length

fraction, λ , can be as high as 1 however with high concentra-

tion samples, interparticle interactions and particle crowding

of equilibrium positions cause defocusing. [ 23 ] The results in

Figure 3 are achieved when λ = 0.072. When λ = 0.36 (0.5%

w/w) the focusing effi ciency decreased slightly to 98.01%

8 www.small-journal.com © 2013 Wiley-VCH Verlag GmbH & Co. KGaA,

Figure 5 . Focusing of various particles and cells. A. High-speed images of microparticle focusing results for three different polystyrene bead sizes and two types of mammalian cells at Re = 83.33. Imaging planes were varied depending on particle type to gain better contrast for higher quality image analysis (see Figure S5). Scale bar represents 50 μ m. B. Focusing effi ciency and focusing purity for tested microparticles.

(N = 24 278) though a higher throughput

of 36,000 particles/s is also achieved.

Another key feature enabled by the

secondary fl ows in increased focusing

accuracy at the channel centerline. Parti-

cles are focused in the center extremely

tightly. Figure S4 plots the focusing tight-

ness by fi tting a Gaussian distribution.

The calculated FWHM is 10.995 μ m indi-

cating a very narrow particle focusing dis-

tribution that would allow high sensitivity

optical interrogation in the channel region

away from scattering structures like walls.

Focusing improves with increasing

Reynolds number. Figure 4 A plots a his-

togram of particle focusing position in

the channel cross-section regardless of

the particle focal plane after passing all

stepped channels (N = 1000 for each Rey-

nolds number). At Re = 83.33, all particles

were focused in the center of the micro-

channel and no beads were found on

either channel sides. Detailed image anal-

ysis was performed to determine particle focusing effi ciency

defi ned above and focusing purity (Figure 4 B). Focusing

purity is defi ned here as the number of beads in focus at the

fi nal single-stream equilibrium position over the total beads

(in focus and out of focus) that were aligned at the channel

centerline. High focusing purity is essential for a small

optical focal spot ( e.g. optical interrogation for a fl ow cytom-

etry system) since higher numerical aperture lenses lead to

a smaller depth of focus and potentially two distinct peaks

from two focused streams. [ 25 ] As can be seen, higher fl ow rate

operation induces stronger secondary fl ows leading to higher

focusing effi ciencies and purities. As a control, a straight

channel with no structures was also tested and its focusing

effi ciency was approximately 50% as expected for a channel

aspect ratio of 0.5 at higher Reynolds number. [ 20 , 35 ]

The single-stream focusing device

accurately focuses multiple types of micro-

particles including three different sizes of

polystyrene microspheres (diameter of

7.9 μ m/CV20%, 9.9 μ m/ CV5% and 13 μ m/

CV15%) and two different cell types

(Jurkat: diameter of 13.03 μ m/CV15.39%

and MCF7 16.28 μ m/CV26.81%). All

experiments were conducted at a Reynolds

number of 83.33 and results are plotted in

Figure 5 .

Smaller microspheres show relatively

reduced focusing effi ciency due to reduced

inertial lift forces. This is expected given

that the aspect ratio of the channel leads

to a balance between F SL and drag due to

the secondary fl ow, and F SL is proportional

to the 3 rd power of particle size ( F L =

f LS ρ U m 2 a 3 / H , where f LS is the lift coeffi -

cient, a is particle diameter, U m is the max-

imum fl uid velocity and H is the channel

Weinheim small 2013, 9, No. 5, 685–690

Microparticle Inertial Focusing via Secondary Flows

Figure 6 . Single-stream inertial focuser integrated with fl ow cytometry. A. Signal layouts (no signal fi ltering) of fl uorescent peaks with a sampling rate of 500 KS/s using 9.9 μ m Envy Green polystyrene microspheres at (1) Re = 83.33 and (2) 0.2778. (3) A comparison plot of two signals from channels operating at different Reynolds numbers. B. For each fl uorescent peak from A, a Gaussian curve was fi tted and its normalized peak value distributions are shown in B and FHWM distributions are also plotted in C for N = 300.

height) as suggested from previous studies. [ 22 , 36 ] Therefore,

smaller beads experience a reduced inertial lift force such

that lift may not be suffi cient to position smaller particles for

the given channel length or these particles can more easily

be perturbed from the bottom inertial focusing equilibrium

position. On the other hand, the focusing effi ciency slightly

decreased for both larger microbeads and cells, and this can

be explained through increased inertial lift forces keeping

these particles at other unwanted equilibrium positions.

Larger beads and cells are less affected by the secondary fl ow

because the balance shifts towards inertial lift forces. Fur-

thermore, inertial focusing equilibrium positions shift closer

to the channel centerline for larger particles [ 20 ] such that the

secondary fl ow can act more strongly to destabilize the pre-

ferred bottom focusing position. The current design showed

excellent focusing effi ciency and purity results over a wide

range of particle and cell sizes though for specifi c particle

sizes, higher focusing effi ciency and purity can be obtained

by tuning the channel dimensions, and therefore the balance

between lift and secondary fl ow-induced drag.

Continuously positioning microparticles in a single optical

focal point is extremely useful particularly for fl ow cytom-

etry, and the single-stream inertial focuser can be applied to

this application. Flow cytometry traditionally employs two

dimensional hydrodynamic focusing with the accompanying

practical limitations as mentioned above, however the iner-

tial focuser platform developed here offers passive, narrow,

sheath-free and high-throughput particle focusing ideal for

fl ow cytometry. Fluorescence signals corresponding to uni-

form beads focused with the single-stream inertial focuser

and the same channel operating outside of the focusing

operational range are collected by our custom fl ow cytometer

excitation and detection system ( Figure 6 ). Signals were

acquired, digitized and analyzed as reported previously. [ 29 ]

A detailed setup also can be found in Figure S6. Acquired

signals are shown in Figure 6 A using 9.9 μ m Envy Green

particle (0.005% w/w, Bangs Laboratories, Inc., IN, USA) at

Re = 83.33 and 0.2778. Each signal represents the fl uorescence

emission while passing a beam spot with a diameter of 21.6 μ m.

The beam spot was calculated from high-speed images and

fl ow cytometry data. It took 12 μ s to pass the beam spot with

a particle traveling velocity of 1.8 m/s yielding a diameter of

21.6 μ m. Higher concentration samples (0.125% w/w) were

also tested and presented in Figure S7. Note that the higher

concentration yielded a throughput of 8900 particles/s, which

is higher than other reported on-chip fl ow cytometry tech-

niques. [ 7 , 25 , 26 , 37 ] The distribution of the signal features were

also obtained by fi tting a Gaussian curve to obtain peak

value (intensity) and FWHM (time) presented in Figure 6 B

and C respectively. At Re = 0.2778, two main peaks are seen

in Figure 6 B with particles passing close to the center of the

beam spot corresponding to the larger peak. The smaller peak

may be partly explained through the particle distribution

shown in Figure 4 A (dark blue). As can be seen, there are

two side bands which are slightly offset from the centerline

location of the beam spot which can result in an extra small

peak. In order to compare the fl uorescence signal variation

(voltage), a coeffi cient of variation (CV) representing the

repeatability and precision of the fl ow cytometry system were

© 2013 Wiley-VCH Verlag Gmbsmall 2013, 9, No. 5, 685–690

calculated. The CVs are 6.69% at Re = 83.33 and 67.12% at

Re = 0.2778 showing signifi cant improvements when micro-

particles are induced to form a single-stream chain. As

another control experiment, an inertial focusing channel of

the same length with no structures at Re = 83.33 was also

investigated and plotted in Figure S6B and C. The CV for a

straight channel was 7.78% which is still larger than that of

the structured channel and the difference is expected to be

even larger when further optimizing the current optical setup

( e.g. smaller beam spot and tighter positioning of the beam

waist at the particle focusing plane).

In summary, we present a continuous single-stream particle

focusing method requiring neither external forces/actuation

nor sheath fl uid providing extremely narrow focusing distri-

butions in a high-throughput manner. The method employs

a combination of inertial focusing and local geometry-

induced secondary fl ows in a fi nite Reynolds number regime

to create single-stream focusing in a single focal plane. We

demonstrate focusing effi ciency as high as 99.77% with

throughput as high as 36 000 particles/s for a variety of dif-

ferent sized particles and cells. As a powerful application, we

also demonstrate an integration of the focusing system with

fl ow cytometry. This approach can be applied to position

cells and particles for not only fl ow cytometry but imaging

cytometry, [ 27 ] deformability cytometry [ 24 ] or to better control

interparticle spacing which relies on a single aligned particle

stream. [ 23 ] The unique characteristics suggest this approach

may serve as a key component for next-generation fl ow

cytometry.

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A. J. Chung et al.

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Experimental Section

Microfabrication : Standard double-step photolithography and SU-8 and polydimethylsiloxane (PDMS) replica molding proto-cols [ 38 ] were used for microchannel fabrication.

Measuring Microparticle Lateral Migration : The microfl uidic device was operated by a single syringe pump (Harvard Appa-ratus, MA, USA). The lateral migration of the microparticles was recorded at 6000 frames per second (167 μ s interval) with a 1 μ s shutter speed using a high-speed camera (Vision Research, NJ, USA) mounted on a Nikon Ti Inverted Microscope (Nikon, Japan). Recorded images were processed using ImageJ ( http://rsb.info.nih.gov/ij/ ) and a custom MATLAB routine (MathWorks, MA, USA).

Cell and Microparticle Preparation : The MCF7 and Jurkat cell lines were cultured using standard protocols and were re-suspended in Dulbecco’s Phosphate Buffered Saline (Thermo Fisher Scientifi c, MA, USA). Dust in the solutions containing micro-particles was fi ltered using cell strainers (Thermo Fisher Scientifi c, MA, USA) to prevent potential clogging.

Supporting Information

Supporting Information is available from the Wiley Onliny Library or from the author.

Acknowledgements

The authors would like to thank Dr. Henry Tse at UCLA and Leo K. Hwang at Comsol for their helpful discussion and technical sup-port. This work was supported by EMD Millipore.

0 www.small-journal.com © 2013 Wiley-VCH V

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Received: October 2, 2012Published online: November 12, 2012

erlag GmbH & Co. KGaA, Weinheim small 2013, 9, No. 5, 685–690