Lab on a Chip

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PAPER View Article OnlineView Journal

This journal is © The Royal Society of Chemistry 2015

BioMicroSystems Laboratory, Department of Electrical Engineering and

Computing Systems, Ohio Center for Microfluidic Innovation, University of

Cincinnati, Cincinnati, OH 45220, USA. E-mail: ian.papautsky@uc.edu;

Tel: +1 (513) 556 2347

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4lc00803k

Cite this: DOI: 10.1039/c4lc00803k

Received 10th July 2014,Accepted 29th December 2014

DOI: 10.1039/c4lc00803k

www.rsc.org/loc

Size-based microfluidic multimodalmicroparticle sorter†

Xiao Wang and Ian Papautsky*

Microfluidic sorting of synthetic and biological microparticles has attracted much interest in recent years.

Inertial microfluidics uses hydrodynamic forces to manipulate migration of such microparticles in

microfluidic channels to achieve passive sorting based on size with high throughput. However, most

inertial microfluidic devices are only capable of bimodal separation with a single cutoff diameter and a

well-defined size difference. These limitations inhibit efficient separation of real-world samples that often

include heterogeneous mixtures of multiple microparticle components. Our design overcomes these

challenges to achieve continuous multimodal sorting of microparticles with high resolution and high

tunability of separation cutoff diameters. We demonstrate separations with flexible modulation of the

separation bandwidth and the passband location. Our approach offers a number of benefits, including

straightforward system design, easily and precisely tuned cutoff diameters, high separation resolution, and

high throughput. Ultimately, the unique multimodal separation functionality significantly broadens applica-

tions of inertial microfluidics in sorting of complex microparticle samples.

Introduction

Microfluidics has received considerable attention in recentyears for sorting of synthetic (e.g., polymer beads) or biologi-cal (e.g., cells) microparticles. Some of the promising advan-tages of such systems include reduced sample volume, fastersample processing, high efficiency, high throughput and lowcost.1,2 Active microfluidic systems that rely on optical,3 mag-netic,4 dielectrophoretic,5 or acoustic6 principles have beenreported. They often offer limited throughput and requiresophisticated external controls,7 despite high separationefficiency. Contrary to these active approaches, passive micro-fluidic techniques such as deterministic lateral displace-ment,8 hydrodynamic filtration,9 and pinched flow fraction-ation10 only rely on the inherent hydrodynamics to separatemicroparticles which significantly simplifies the design, fabri-cation and operation of devices.

Passive, label-free ordering and sorting of microparticles,which is achieved by manipulating hydrodynamic forces, hasattracted much interest in recent years.11–30 The interactionof these forces on microparticles in flowing fluid leads tolateral migration across streamlines into specific cross-sectional positions depending on their size,12,16–19,21,25–27,29,30

shape,31 and deformability.32 Recent studies demonstratedthese effects in microchannels of various geometries, includ-ing straight,21,33 spiral25,26,30 and serpentine channels,15,29

and termed them “inertial microfluidics”.13 A number ofhighly-promising applications, including sheath-less flowcytometry,14,23,24,34 label-free cell separation12,18,21,26,35,36 andrare cell enrichment17,20 with orders of magnitude higherthroughput and much simpler external instrumentation thanactive microfluidic systems2 were demonstrated. However,most inertial microfluidic devices are only capable ofbimodal separation with a single attenuation diameter and awell-defined size difference.11,16–19,21,25–27,29,30 These limita-tions inhibit efficient separation of complex real-world samples,which often include heterogeneous mixtures of multiple micro-particle components. Further, precise adjustment of the separa-tion cutoff in most devices is challenging,11,16,17,19,21,25,26,29,30

and often requires re-design and re-fabrication of devicegeometry.

In this work, we demonstrate a microfluidic chip basedon inertial migration that achieves efficient multimodal sepa-ration of mixture of three components of microparticleswith small differences in size. Our approach uses a straightmicrochannel to pre-focus microparticles, followed down-stream by a channel expansion (microchamber) with siphon-ing outlets as a powerful unit for continuous inertial separa-tion. Through theoretical and experimental investigations,we illustrate the separation principle as well as the high reso-lution and flexible tunability of the separation cutoff.By sequencing two separation units and designing proper

Lab Chip

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system parameters, we demonstrate continuous multimodalseparation of complex microparticle mixtures into threecomponents with high resolution. Further, due to the tun-ability of the cutoff diameter in each stage, separationbandwidth or passband location can be modified in a widerange exhibiting the versatility of the system for sorting ofsamples with different size range.

Our approach offers a number of benefits, in addition tothe unique multimodal separation functionality, which sig-nificantly broaden applications of inertial microfluidics insorting of complex microparticle samples. First, the straight-forward system design permits the attenuation diameters tobe easily and precisely tuned by adjusting input flow orfluidic resistance of outlet channels. Second, the device offersthe highest reported separation resolution which leads tomore precise separation of samples with smaller sizedifferences. Third, the continuous nature of the device

Lab Chip

Fig. 1 Schematic illustration of device principle. (a) Inertial microfluidic mufor particle focusing followed by sequencing of two sets of microchamberdistribution before and after separation, with a and f represent particle size afor multimodal separation. (b) Two-stage inertial focusing in a high-aspect-rawhich driving particles downstream along streamlines. Fs and Fw represent shthese two forces leads to focusing of particles at equilibrium positions (grey ddirecting particles to the center of the wall. (c) Size-selective separation in mrated into main flow, sheath flow and vortices indicated as red, blue and greyforce Fs to migrate far enough to cross the boundary streamline (red dash linparticles (red) is limited due to smaller Fs. As a consequence, they remain in th

operation lends itself to high throughput and high volumeapplications, especially if the microchannels are paralleled.And finally, the device has a single inlet and requires onlyone syringe pump for sample delivery, which largely reducescomplexity of external instrumentation often associated withelectrical, optical or acoustic separators (leading to the “chipin a lab” modality). Ultimately, this straight planar geometryallows easy integration with downstream detection or mea-surement techniques permitting automated on-chip samplepreparation and processing for a broad range of applications.

ResultsInertial focusing and hydrodynamic-vortex separation

Our multimodal separation chip uses microfluidic hydrodynamic-vortices to continuously separate microparticles based on size(Fig. 1a). These vortices form by the sudden expansion of

This journal is © The Royal Society of Chemistry 2015

ltimodal separation. The device consists of a high-aspect-ratio channels for multimodal separation. The inset schematics indicate particle sizend frequency. ahc and alc represent high-pass cutoff and low-pass cutofftio channel in top view and cross-section view. FD represents drag forceear-gradient induced lift force and wall-induced lift force. The balance ofash lines) along the side walls. FΩ represents rotational-induced lift forceicrochambers with three outlets. In this channel geometry, flow is sepa-regions. Large particles (blue) undergo larger shear-gradient induced lift

e), thus are extracted from the side outlets. The lateral migration of smalle main flow exiting through main outlet.

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channel cross-section and act to selectively siphon micropar-ticles from the main channel into side outlets with high reso-lution. With addition of an upstream microchannel thatfocuses particles into equilibrium positions near sidewalls,the system can efficiently sort microparticles from the highly-ordered streams on the basis of their size. Sequencing ofmultiple focusing channels and vortex chambers leads tonovel multimodal multistage separation functionality for pro-cessing of complex samples.

Before describing the integrated system for multimodalseparation, a basic understanding of inertial focusing andhydrodynamic-vortex separation is required. In inertial focus-ing, particles traveling downstream a microfluidic channelmigrate across streamlines and order deterministically atequilibrium positions near channel walls.13,33,37 In straightmicrochannels, inertial migration is believed to be caused bythe balance of lift forces arising from the curvature of thevelocity profile (the shear-induced lift Fs) and the interactionbetween microparticle and the channel wall (the wall-inducedlift Fw).

13,33,37 As shown in Fig. 1b, microparticles rapidlyequilibrate along each sidewall into bands where these twodominant lift forces balance each other. Once this initialequilibrium is reached, microparticle motion near channelsidewalls is dominated by the rotation-induced lift force FΩwhich drives them towards the center of channel sidewalls.As a result, particles finally equilibrate at the center of eachsidewall (Fig. 1b). For hydrodynamic-vortex separation inmicrochambers, the upstream focusing microchannel utilizesthe first stage of migration only, focusing microparticlesin two bands along microchannel sidewalls (design detailsare in ESI† S1). Such ordered manner provides consistencyto particle focal positions which is critical for efficienthydrodynamic-vortex sorting downstream.

Next, we discuss the basis of size-selective hydrodynamic-vortex separation. As illustrated in schematics (Fig. 1c) andnumerical simulation (Fig. 2a), flow in a microchamber isseparated into the main and sheath components, exitingthrough the main and side outlets, respectively. Suddenexpansion of the microchannel modulates lateral flow veloc-ity and leads to formation of microscale vortices. Presence ofthese vortices has been confirmed experimentally and numer-ically.17,20 Neutrally-buoyant particles entering the expansionregion experience a sudden absence of the microchannel walland the significantly reduced wall-induced lift force Fw. Thus,the dominating shear-gradient induced lift force Fs drivesparticles to migrate towards the sheath flow (Fig. 1c). It wasshown previously that the magnitude of Fs scales as Fs ∝Uf

2a2, where Uf is flow velocity and a is particle diame-ter.20,22,38,39 Assuming that Fs is balanced by the Stokes drag(FD = 3πμaUL), the lateral migration velocity of these particlesscales with particle size as UL ∝ Uf

2a. Consequently, thelarger particles migrate across the streamlines faster than thesmaller particles (UL ∝ a). Once the larger particles cross theboundary streamline between the main and the sheath flows,they become entrained and exit through side outlets. Mean-while, the smaller particles remain in the main flow due to

This journal is © The Royal Society of Chemistry 2015

insufficient lateral migration (Fig. 1c). It is this vortex-initiated lateral migration that enables continuous separationof different-sized particles at high resolution.

In a sorting system, ability to adjust cutoff diameter isessential for separation of different samples. From the dis-cussion of inertial migration above, the lateral migrationvelocity UL of a particle is strongly related to the flow velocityin the microchannel Uf (UL ∝ Uf

2). Faster input flows lead tofaster lateral migration and longer lateral migration distancesfor all particles (Fig. 2b), resulting in a smaller cutoff diam-eter ac. This offers the possibility of tuning cutoff diameterthrough simply adjusting input flow rate. Another parameterthat influences the separation cutoff diameter is the posi-tion of the boundary streamline db, which determines thelateral migration distance dm needed for a particle to reachthe boundary (Fig. 2c). Our numerical results illustrate the3-dimensional boundary at the entrance of the chamber(Fig. 2d) and show that position of db can be preciselytuned by engineering the channel fluidic resistance ratior/R, where r is the resistance of a side outlet channel and Ris the resistance of the main outlet. As Fig. 2e shows, atr/R < 2 initial equilibrium position of all particles is withinthe sheath flow boundary, leading to non-selective extrac-tion of all particles through side outlets. As the boundarystreamline shifts towards the side wall at higher r/R, theinitial equilibrium position of particles shifts into the mainflow, leading to a possible separation. Since larger r/R leadsto longer migration distance dm, the cutoff diameter acincreases at larger r/R. This offers the possibility of tuningcutoff diameter through resistance modification of outletchannels. Adjustment of resistance can be accomplished bydesigning different lengths or widths for side and mainoutlet channels.40 Alternatively, external outlet tubing can becut into appropriate lengths and used to provide additionalfluidic resistance to further modify resistances of outputchannels. In summary, our theoretical analysis indicates thatthe microfluidic geometry provides size-based, continuousseparation functionality with the capability of tuning attenua-tion diameter.

Highly tunable separation

Having discussed the basic principles of the hydrodynamic-vortex separation, we now experimentally demonstrate resolu-tion and tunability of separation. In the first set of experi-ments, solution of polymer microspheres (4 × 104 mL−1) withcontinuous size distribution from 10 μm to 27 μm waspumped into a single microchamber device with r/R = 5.4 atQ = 500 μL min−1 or channel Reynolds number Re = 110(Re = ρUfDh/μ where ρ is density of the fluid, Dh is hydraulicdiameter of channel and μ is viscosity of fluid). In Fig. 3a, weshow that microparticles with diameter larger than the setcutoff size (a > ac) migrate into the sheath flow as expected,exiting separation channel through side outlets. Microparti-cles with a < ac elute from the main outlet. This is the typicaloperation of a bi-modal separator. Histograms in Fig. 3b

Lab Chip

Fig. 2 Theoretical investigation of size-based separation. (a) CFD-ACE+ model showing streamline distribution in two symmetric microchamberswith three outlets. In the chambers, the flow is separated into main flow, sheath flow and vortex. The red solid line indicates the boundary of mainflow and sheath flow, with R and r representing the channel resistance of the main and side outlets. (b) Schematic illustrating the relationshipbetween the input flow rate and the separation cutoff diameter, with UL representing lateral migration velocity. (c) The close-up images from thenumerical model show the entrance and exit regions of the separation unit. The Fs is the shear-gradient induced lift force which drives a particleto migrate towards sheath flow. The dp, db and dm are the particle focusing position, boundary position and migration distance needed for a particleto enter the sheath flow. The red solid line represents boundary streamlines. (d) CFD-ACE+ model illustrating the cross-sectional view of the 3-Dboundary streamlines. The red area represents main flow, while the blue area indicates sheath flow. (e) Close-up of the upper left channel quadrant(indicated as black dashed lines in panel (d)). Channel resistance ratio r/R influences the boundary position and migration distance for particles toreach the boundary streamline.

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confirm the cutoff size of ac = 14 μm, given the experimentalconditions. More importantly, the results show that particleswith size difference of ~1 μm can be separated with >70%efficiency (green arrows). The data further show that differ-ences of ~2 μm can be separated with higher, >80% effi-ciency (blue arrows), while differences of ~3 μm can be sepa-rated with even higher, >90% efficiency (orange arrows). Theseparation resolution Rs (see methods for detailed definition)of this hydrodynamic-vortex platform is Rs > 10, which is atleast 2× higher than in previous inertial microfluidicdesigns.11,12,16–19,21,25,29,30,35 The high resolution stems fromthe size-dependent inertial migration at the vortex region,which permits differentiation of lateral positions of differentsized microparticles across the boundary. This high resolu-tion feature is extremely beneficial for separating particulatemixture with small size difference.

Lab Chip

Next, tuning of the separation cutoff diameter wasexplored in order to demonstrate flexibility of the micro-fluidic platform. As was suggested in the theoretical discus-sion above, ac can be precisely tuned by modulating theinput flow and channel resistance ratio r/R. Two sets ofexperiments were conducted to measure the change in ac asa function of these two parameters. First, as shown in Fig. 3c,increasing Re from 44 to 110 at r/R = 5.4 leads to a lineardecrease in the attenuation diameter from 25 μm to 14 μm.This suggests that ac scales with the first order of input flowvelocity as ac ∝ Uf. Second, as shown in Fig. 3d, increasingr/R from 5.4 to 10 at Re = 110 leads to a parabolic increase inthe cutoff diameter from 14 μm to 19 μm. This suggests thatac scales with the resistance ratio as ac ∝ IJr/R)1/2. The experi-mental results confirm that a combination of these twosystem parameters permit control of the cutoff diameter with

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Fig. 3 Experimental investigation of the separation resolution andtunability of the cutoff diameter. (a) Particles with continuous sizedistribution are induced in a device with r/R = 5.4 and Re = 110 to findout the separation resolution. Particles with diameter a > ac migrateinside sheath flow exiting through the side outlets (blue dash lines),while particle with diameter a < ac elute from the main outlet (reddash lines). A few large particles (a > 25 μm) are recirculating in thevortices (orange dash lines) due to the large Fs that can push themacross the sheath flow into the microvortices. (b) Normalizedhistogram of main and side outlet samples indicate separation cutoffsize (grey arrow) and separation resolution using a device with r/R =5.4 and Re = 110. (c) Tuning separation cutoff size by changing ReIJr/R = 5.4). (d) Tuning separation cutoff size by changing r/R (Re = 110).

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broad tunable range. Surprisingly, an input flow conditionexhibits a stronger influence on the cutoff diameter andoffers a more convenient way of tuning separation. In sum-mary, these experimental results illustrate that size-basedseparations with high resolution and easily-tunable cutoffsize are possible. By cascading multiple hydrodynamic-vortexunits and matching cutoff-related parameters, versatile multi-modal separation can be achieved as demonstrated in the fol-lowing section.

Multimodal separation of complex microparticle mixture

At first glance, one might expect the cascading of hydrodynamic-vortex separators to be straightforward, a simple matter of

This journal is © The Royal Society of Chemistry 2015

fabricating multiple units in sequence. However, the micro-channel resistance network has to be carefully designed toprovide proper cutoff size for each microchamber under cer-tain input Re. In Fig. 4a, we show how an analogue electricalcircuit model40 can be used to aid design of fluidic resis-tances of the cascaded system. In our model, two red knotsrepresent the two microchambers where the current (flow) issiphoned into three branches. The input flow rate Qc (Ic) ofthe second chamber is determined by the resistance ratio ofR1 and Rc which further consists of paralleling of R2, R3 andR4. To achieve multimodal separation, Qin has to match R1/Rc

to provide the higher cut-off diameter for high-pass separa-tion in the upstream chamber. Meanwhile, Qc has to coordi-nate with R3/R4 to offer the lower cut-off diameter for low-pass separation in the downstream chamber.

The multimodal separation was validated through separa-tion of a mixture of 21 μm, 18.5 μm and 15 μm diameterpolymer microspheres using the device shown in Fig. 4b. Atflow rate Qin = 525 μL min−1 (Re = 116), the upstream micro-chamber provides high-pass separation with ahc ~ 20 μm withresistance ratio R1/Rc = 4. As the flow is separated at theupstream microchamber, the downstream flow rate Qc isdecreased to ~350 μL min−1 (Re = 77). Thus, resistance ratioR3/R4 = 5.6 is designed for the downstream microchamberenabling low-pass separation with alc ~ 17 μm. Using thesesystem parameters, the cascaded device successfully sepa-rates the particle mixture into its components into O1, O2and O3 correspondingly (Fig. 4c). The histograms and sampleimages before and after separation indicate dramaticenhancement of purity of each sized particles (Fig. 4d).Furthermore, the concentration of 21 μm, 18 μm and 15 μmdiameter microparticles are enriched by 2.4×, 3.8× and1.7× after separation, as Fig. 4e shows. The separation effi-ciencies for these particles were measured to be 78%, 87%and 99% respectively, which confirms the device can performhigh-resolution multimodal separation of complex particlemixtures without compromising efficiency (Fig. 4f).

Size distributions of microparticle or cellular mixtures varyfrom sample to sample. Size range of interest may also vary.Thus, tunability of separation at each stage becomes signifi-cant in sample preparations. Here, we demonstrate the versa-tility of this microfluidic multimodal sorter through tuningof the separation bandwidth and passband location. Suchcapabilities lead to successful separation of mixtures intocomponents with different size range. First, we are able toprecisely tune separation bandwidth by using proper combi-nation of input flow and resistance network (Fig. 5a). Towiden the bandwidth, we fixed the resistance ratio of theupstream chamber R1/Rc to maintain the high-pass separa-tion with ahc ~ 20 μm, while use a smaller ratio R3/R4 = 4.9 toenable low-pass separation with a smaller alc ~ 12 μm. Underthis modification, 21 μm diameter particles still exit throughO1, while both 18.5 μm and 15 μm diameter particles areextracted from O2. 11 μm diameter particles instead elute toO3 as shown in experimental images of microchambers(Fig. 5b) and outlets (Fig. 5c). Such changes in separation

Lab Chip

Fig. 4 Inertial microfluidic multimodal separation. (a) The microfluidic resistance network and its analogous electrical circuit model. (b) Dry-filmmold for PDMS casting exhibiting actual device for multimodal separation. The scale bar is 10 mm. (c) Stacked bright field images illustrating sepa-ration of 21 μm, 18.5 μm and 15 μm diameter particles into O1, O2 and O3. (d) The histograms of the samples from inlet and outlets indicate aftermultimodal separation, the purities of 21 μm, 18.5 μm and 15 μm diameter particles are dramatically elevated from 38%, 29.3%, 32.7% (inlet) to89.4% (O1), 80.7% (O2), 95.9% (O3) respectively (e) The concentration plot shows enrichment of concentration of 21 μm, 18.5 μm and 15 μmdiameter particles by 2.4×, 3.8× and 1.7× which is due to separation of input sample volume into different outlets (n = 3). (f) The normalized countshows that the separation efficiencies for 21 μm, 18.5 μm and 15 μm diameter particles are 78%, 87% and 99% respectively indicating efficientmultimodal separation of particles with only 3 μm difference in size (n = 3).

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indicate clear broadening of the separation bandwidth from3 μm to 8 μm (quantitative measurements of concentrationand efficiency are demonstrated in ESI† Fig. S2a–b). Weshould also note that narrowing of the bandwidth is alsopossible by using larger ratio R3/R4.

Second, we are able to adjust the passband location whilemaintaining the bandwidth (Fig. 5d). We used larger resis-tance ratio R1/Rc ~ 5.5 to provide high-pass separation withlarger ahc ~ 22 μm in the upstream chamber. Similarly, weapplied a larger resistance ratio R3/R4 ~ 11 to upshift the alcof downstream microchamber. Consequently, 23 μm diame-ter particles instead of 21 μm diameter particles are found inO1, while 21 μm and 18.5 μm diameter particles are sepa-rated in the downstream microchambers as demonstrated inexperimental images of both microchambers (Fig. 5e) andoutlet channels (Fig. 5f). This result indicates successful off-setting of passband location of the device by 3 μm

Lab Chip

(quantitative measurements of concentration and efficiencyare demonstrated in ESI† Fig. S2c–d). In summary, we havedemonstrated two important abilities for tuning multimodalseparations in the device including the modulation of band-width and passband location. Such versatility can greatly ben-efit sample preparations of different complex mixturesaccording to size distribution or help precisely selecting cellsor particles with size of interest.

To demonstrate capability of separating a heterogeneoussample, we used a microparticle mixture with continuousdiameter distribution from 10 μm to 27 μm. The sample wasintroduced into the device at Qin = 0.5 mL min−1 (Re = 110).With resistance ratio R1/Rc = 5.5, the upstream microchamberpermits a high-pass separation with attenuation at ahc ~ 24 μm.As the flow bifurcates in the upstream microchamber, thedownstream flow rate decreases to Qc ~ 370 μL min−1 (Re = 81).With resistance ratio R3/R4 = 11, the downstream

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Fig. 5 Tuning of bandwidth and passband location. (a) By tuning flow rate and resistance network, the separation bandwidth is increased from3 μm to 8 μm. (b) As shown in the stacked bright field images, the 21 μm diameter particles are extracted from O1, while both 18.5 μm and 15 μmdiameter particles elute from O2. The 11 μm diameter particles exit through O3. (c) Bright field images at each outlet channel illustrate thesuccessful separation. (d) By tuning input flow rate and resistance network, the passband location can shift towards a higher cut-off diameter,while maintaining the separation bandwidth. Bright field images taken at two sequenced microchambers (e), and outputs O1, O2 O3 (f) demon-strate a successful separation of the 23 μm, 21 μm and 18.5 μm diameter particles. In all images, the scale bar is 50 μm.

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microchamber enables a low-pass separation with attenua-tion at alc ~ 21 μm. Bright field images of both chambersillustrating this separation are shown in Fig. 6a. With thesedesign parameters, the device successfully sorts a heteroge-neous sample (Fig. 6b) into three distinct distributions, asexpected. As Fig. 6c shows, the majority of particles withdiameter a > 24 μm are sorted into the high-pass outlet O1.Particles 21–24 μm in diameter (our passband range) eluted

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from the passband outlet O2, while particles with diametersa < 21 μm eluted primarily through the low-pass outlet O3.

Discussion

In summary, we demonstrated a microfluidic device capableof versatile multimodal separation of microparticle samplesbased on sizes, with high resolution and high tunability of

Lab Chip

Fig. 6 Multimodal sorting of heterogeneous mixture. (a) Heterogeneous mixture of microparticles was sorted into three different size distributionafter passing the device. (b) Size distribution of inlet particle mixture. The distribution was normalized to the highest count at a specific particlediameter. (c) Size distributions of samples from O1, O2 and O3. The size distribution in each outlet was normalized to the highest count within thatoutlet.

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separation cutoff diameter. Unlike the conventional bimodalmicrofluidic separators, the presented device provides a novelmultimodal separation functionality. This feature signifi-cantly expands the capability of the microfluidic separator forsample preparation of complex mixtures of microscale partic-ulate components such as cell mixtures. Additionally, thedevice exhibits higher resolution than previous bimodal iner-tial microfluidic separators, which permits more precise sep-aration of samples with small size-difference or heteroge-neous size distribution. Moreover, the cutoff diameter ofseparation can be easily tuned by input flow rate and fluidicresistance network. This high tunability offers versatile func-tions such as tuning bandwidth and passband location whichare beneficial for precise modulation of separation parametersto achieve separation in high efficiency. Ultimately, thisdevice is easy-to-use, because it has a single inlet and offerscontinuous separation, thus only requires a single syringepump and allows non-stop separation of high-volume samplewith high throughput (~0.5 mL min−1). We envision this versa-tile microfluidic multimodal separator will open new oppor-tunities in the microfluidic separation field for size-basedseparation of complex particulate materials from biological,environmental to synthetic microparticles for a wide range ofapplications including industrial microparticle purification,cellular sample preparation, biomedical research and clinicaldiagnostics.

MethodsSeparation resolution

Separation resolution Rs was defined based on the spectralresolution. In our case, resolution measures the ability of

Lab Chip

separating two different sized particles and is defined as Rs =a/Δa where Δa is the smallest difference in diameter that canbe separated in a microfluidic device, and a is the averagediameter of the separable particles. For example, if a devicecan separate 20 μm diameter particles from 10 μm diameterparticles, the average diameter is a = 15 μm, with a diameterdifference Δa = 10 μm. In this case, the separation resolutionis calculated to be Rs = 1.5.

Microfabrication

We used standard soft lithography process to fabricate micro-channels in polydimethysiloxane (PDMS, Sylgard 184, DowCorning). We used a 100 μm high master formed in MX5050dry film photoresist (Microchem Corp.). A mixture of PDMSbase and curing agent (10 : 1 ratio) were poured on the mas-ter; after degassing PDMS was cured for 4 h on a 60 °Chotplate. The cured PDMS devices were peeled off, and inlet/outlet ports were punched with a 14 gauge syringe needle.PDMS was bonded to standard glass slide using a hand-holdplasma surface treater (BD-20AC, Electro-Technic Products, Inc.).

Microparticle suspensions

To study separation cut-off diameter of devices, we dispensednon-fluorescence PMMA microparticles with continuous sizedistribution from 10 μm to 27 μm diameter (Cospheric Inc.) toform a solution of particle mixture with concentration of 4 ×104 mL−1. In the experiment of multimodal separations, wemixed 23 μm, 21 μm, 18.5 μm (Polyscience, Inc.), 15 μm(Invitrogen, Inc.) and 11 μm (Bangs Laboratoreis, Inc.) diametermicroparticles to obtain a concentration of ~2 × 104 mL−1

for each of the species. We added Tween-20 at 0.1% v/v

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(Fisher Scientific, Inc.) to the particle solution to avoid issueof particle clogging.

Device operation and imaging

We first loaded a syringe with particle solution andconnected it to the device by using a 1/16" peek tubing(Upchurch Scientific) with proper fittings (UpchurchScientific). We pumped particle solution into devices withdesigned flow rate using a syringe pump (Legota 180, KDscientific). To visualize trajectory of particle in bright-field,we used an inverted epi-fluorescence microscope (IX71, OlympusInc.) equipped with a 12-bit high-speed CCD camera (Retiga EXi,QImaging). We set the exposure time to minimum value (10 μs)and sequentially took 300 images with minimum time interval.By stacking images in ImageJ, we established a complete viewof particle motion.

Measurement of flow resistance ratio

We determined flow resistance ratio of side and main outletIJr/R) by measuring ratio of sample volume from these outlets.For example, after inducing certain volume of DI water intothe device, the sample volume from side and main outlet wasmeasured to be Vside and Vmain correspondingly. The flowresistance ratio was calculated to: r/R = Vmain/Vside.

Characterization of separation

To measure size distribution of particle suspensions, we firstinjected sample into a hemocytometer (Hausser Scientific) toform monolayer of particles and then took bright fieldimages and used Image Pro Plus to automatically measureparticle size distribution. We used the same tool to directlymeasure particle concentration of inlet and outlet samples.To calculate separation efficiency, we combined concentra-tion and corresponding sample volume to estimate the countof each sized particles from each outlet and normalized thecounts as separation efficiency.

Numerical models

We modeled the device using a commercial computationalfluid dynamics software CFD-ACE+ (ESI-CFD Inc., Huntsville,AL). The module we used to solve for fluid motion in thegeometry is FLOW. The physical properties of water wasapplied to the fluid in the simulation (density ρ = 1000 kg m−3

and dynamic viscosity μ = 10−3 kg m−1 s−1). The velocityof x-direction (m s−1) calculated from the flow rate wasapplied to initial inlet velocity. We set convergence limit formass fraction to 10−6 and run simulation for 3000 time stepsto ensure the convergence of the simulation. We analyzedsimulation results in CFD-VIEW. We added multiple stream-lines at multiple x or y locations to form the complete view offlow in separation unit. The boundary-streamline was pre-cisely located and measured by slowly moving y-position of astreamline from the center-line of a channel towards thesidewall until the streamline started to stretch to the side

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outlet. The complete view of 3D boundary streamlines wasbuilt by combining multiple boundary-streamlines at z =50–90 μm.

Acknowledgements

We gratefully acknowledge partial support by the OhioCenter of Microfluidic Innovation (OCMI) at the Universityof Cincinnati.

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