Lab on a Chip PAPER. Size-based microfluidic multimodal microparticle sorter. Introduction. Xiao Wang and Ian Papautsky*

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1 PAPER View Article Online View Journal Cite this: DOI: /c4lc00803k Received 10th July 2014, Accepted 29th December 2014 DOI: /c4lc00803k Introduction Size-based microfluidic multimodal microparticle sorter Xiao Wang and Ian Papautsky* Microfluidics has received considerable attention in recent years for sorting of synthetic (e.g., polymer beads) or biological (e.g., cells) microparticles. Some of the promising advantages of such systems include reduced sample volume, faster sample processing, high efficiency, high throughput and low cost. 1,2 Active microfluidic systems that rely on optical, 3 magnetic, 4 dielectrophoretic, 5 or acoustic 6 principles have been reported. They often offer limited throughput and require sophisticated external controls, 7 despite high separation efficiency. Contrary to these active approaches, passive microfluidic techniques such as deterministic lateral displacement, 8 hydrodynamic filtration, 9 and pinched flow fractionation 10 only rely on the inherent hydrodynamics to separate microparticles which significantly simplifies the design, fabrication and operation of devices. Passive, label-free ordering and sorting of microparticles, which is achieved by manipulating hydrodynamic forces, has attracted much interest in recent years The interaction of these forces on microparticles in flowing fluid leads to lateral migration across streamlines into specific crosssectional positions depending on their size, 12,16 19,21,25 27,29,30 BioMicroSystems Laboratory, Department of Electrical Engineering and Computing Systems, Ohio Center for Microfluidic Innovation, University of Cincinnati, Cincinnati, OH 45220, USA. ian.papautsky@uc.edu; Tel: +1 (513) Electronic supplementary information (ESI) available. See DOI: / c4lc00803k 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 applications of inertial microfluidics in sorting of complex microparticle samples. shape, 31 and deformability. 32 Recent studies demonstrated these effects in microchannels of various geometries, including straight, 21,33 spiral 25,26,30 and serpentine channels, 15,29 and termed them inertial microfluidics. 13 A number of highly-promising applications, including sheath-less flow cytometry, 14,23,24,34 label-free cell separation 12,18,21,26,35,36 and rare cell enrichment 17,20 with orders of magnitude higher throughput and much simpler external instrumentation than active microfluidic systems 2 were demonstrated. However, most inertial microfluidic devices are only capable of bimodal separation with a single attenuation diameter and a well-defined size difference. 11,16 19,21,25 27,29,30 These limitations inhibit efficient separation of complex real-world samples, which often include heterogeneous mixtures of multiple microparticle components. Further, precise adjustment of the separation cutoff in most devices is challenging, 11,16,17,19,21,25,26,29,30 and often requires re-design and re-fabrication of device geometry. In this work, we demonstrate a microfluidic chip based on inertial migration that achieves efficient multimodal separation of mixture of three components of microparticles with small differences in size. Our approach uses a straight microchannel to pre-focus microparticles, followed downstream by a channel expansion (microchamber) with siphoning outlets as a powerful unit for continuous inertial separation. Through theoretical and experimental investigations, we illustrate the separation principle as well as the high resolution and flexible tunability of the separation cutoff. By sequencing two separation units and designing proper

2 system parameters, we demonstrate continuous multimodal separation of complex microparticle mixtures into three components with high resolution. Further, due to the tunability of the cutoff diameter in each stage, separation bandwidth or passband location can be modified in a wide range exhibiting the versatility of the system for sorting of samples with different size range. Our approach offers a number of benefits, in addition to the unique multimodal separation functionality, which significantly broaden applications of inertial microfluidics in sorting of complex microparticle samples. First, the straightforward system design permits the attenuation diameters to be easily and precisely tuned by adjusting input flow or fluidic resistance of outlet channels. Second, the device offers the highest reported separation resolution which leads to more precise separation of samples with smaller size differences. Third, the continuous nature of the device operation lends itself to high throughput and high volume applications, especially if the microchannels are paralleled. And finally, the device has a single inlet and requires only one syringe pump for sample delivery, which largely reduces complexity of external instrumentation often associated with electrical, optical or acoustic separators (leading to the chip in a lab modality). Ultimately, this straight planar geometry allows easy integration with downstream detection or measurement techniques permitting automated on-chip sample preparation and processing for a broad range of applications. Results Inertial focusing and hydrodynamic-vortex separation Our multimodal separation chip uses microfluidic hydrodynamicvortices to continuously separate microparticles based on size (Fig. 1a). These vortices form by the sudden expansion of Fig. 1 Schematic illustration of device principle. (a) Inertial microfluidic multimodal separation. The device consists of a high-aspect-ratio channel for particle focusing followed by sequencing of two sets of microchambers for multimodal separation. The inset schematics indicate particle size distribution before and after separation, with a and f represent particle size and frequency. a hc and a lc represent high-pass cutoff and low-pass cutoff for multimodal separation. (b) Two-stage inertial focusing in a high-aspect-ratio channel in top view and cross-section view. F D represents drag force which driving particles downstream along streamlines. F s and F w represent shear-gradient induced lift force and wall-induced lift force. The balance of these two forces leads to focusing of particles at equilibrium positions (grey dash lines) along the side walls. F Ω represents rotational-induced lift force directing particles to the center of the wall. (c) Size-selective separation in microchambers with three outlets. In this channel geometry, flow is separated into main flow, sheath flow and vortices indicated as red, blue and grey regions. Large particles (blue) undergo larger shear-gradient induced lift force F s to migrate far enough to cross the boundary streamline (red dash line), thus are extracted from the side outlets. The lateral migration of small particles (red) is limited due to smaller F s. As a consequence, they remain in the main flow exiting through main outlet.

3 channel cross-section and act to selectively siphon microparticles from the main channel into side outlets with high resolution. With addition of an upstream microchannel that focuses particles into equilibrium positions near sidewalls, the system can efficiently sort microparticles from the highlyordered streams on the basis of their size. Sequencing of multiple focusing channels and vortex chambers leads to novel multimodal multistage separation functionality for processing of complex samples. Before describing the integrated system for multimodal separation, a basic understanding of inertial focusing and hydrodynamic-vortex separation is required. In inertial focusing, particles traveling downstream a microfluidic channel migrate across streamlines and order deterministically at equilibrium positions near channel walls. 13,33,37 In straight microchannels, inertial migration is believed to be caused by the balance of lift forces arising from the curvature of the velocity profile (the shear-induced lift F s ) and the interaction between microparticle and the channel wall (the wall-induced lift F w ). 13,33,37 As shown in Fig. 1b, microparticles rapidly equilibrate along each sidewall into bands where these two dominant lift forces balance each other. Once this initial equilibrium is reached, microparticle motion near channel sidewalls is dominated by the rotation-induced lift force F Ω which drives them towards the center of channel sidewalls. As a result, particles finally equilibrate at the center of each sidewall (Fig. 1b). For hydrodynamic-vortex separation in microchambers, the upstream focusing microchannel utilizes the first stage of migration only, focusing microparticles in two bands along microchannel sidewalls (design details are in ESI S1). Such ordered manner provides consistency to particle focal positions which is critical for efficient hydrodynamic-vortex sorting downstream. Next, we discuss the basis of size-selective hydrodynamicvortex separation. As illustrated in schematics (Fig. 1c) and numerical simulation (Fig. 2a), flow in a microchamber is separated into the main and sheath components, exiting through the main and side outlets, respectively. Sudden expansion of the microchannel modulates lateral flow velocity and leads to formation of microscale vortices. Presence of these vortices has been confirmed experimentally and numerically. 17,20 Neutrally-buoyant particles entering the expansion region experience a sudden absence of the microchannel wall and the significantly reduced wall-induced lift force F w. Thus, the dominating shear-gradient induced lift force F s drives particles to migrate towards the sheath flow (Fig. 1c). It was shown previously that the magnitude of F s scales as F s U 2 f a 2, where U f is flow velocity and a is particle diameter. 20,22,38,39 Assuming that F s is balanced by the Stokes drag (F D =3πμaU L ), the lateral migration velocity of these particles scales with particle size as U L U 2 f a. Consequently, the larger particles migrate across the streamlines faster than the smaller particles (U L a). Once the larger particles cross the boundary streamline between the main and the sheath flows, they become entrained and exit through side outlets. Meanwhile, the smaller particles remain in the main flow due to insufficient lateral migration (Fig. 1c). It is this vortexinitiated lateral migration that enables continuous separation of different-sized particles at high resolution. In a sorting system, ability to adjust cutoff diameter is essential for separation of different samples. From the discussion of inertial migration above, the lateral migration velocity U L of a particle is strongly related to the flow velocity in the microchannel U f (U L U 2 f ). Faster input flows lead to faster lateral migration and longer lateral migration distances for all particles (Fig. 2b), resulting in a smaller cutoff diameter a c. This offers the possibility of tuning cutoff diameter through simply adjusting input flow rate. Another parameter that influences the separation cutoff diameter is the position of the boundary streamline d b, which determines the lateral migration distance d m needed for a particle to reach the boundary (Fig. 2c). Our numerical results illustrate the 3-dimensional boundary at the entrance of the chamber (Fig. 2d) and show that position of d b can be precisely tuned by engineering the channel fluidic resistance ratio r/r, where r is the resistance of a side outlet channel and R is the resistance of the main outlet. As Fig. 2e shows, at r/r < 2 initial equilibrium position of all particles is within the sheath flow boundary, leading to non-selective extraction of all particles through side outlets. As the boundary streamline shifts towards the side wall at higher r/r, the initial equilibrium position of particles shifts into the main flow, leading to a possible separation. Since larger r/r leads to longer migration distance d m, the cutoff diameter a c increases at larger r/r. This offers the possibility of tuning cutoff diameter through resistance modification of outlet channels. Adjustment of resistance can be accomplished by designing different lengths or widths for side and main outlet channels. 40 Alternatively, external outlet tubing can be cut into appropriate lengths and used to provide additional fluidic resistance to further modify resistances of output channels. In summary, our theoretical analysis indicates that the microfluidic geometry provides size-based, continuous separation functionality with the capability of tuning attenuation diameter. Highly tunable separation Having discussed the basic principles of the hydrodynamicvortex separation, we now experimentally demonstrate resolution and tunability of separation. In the first set of experiments, solution of polymer microspheres ( ml 1 ) with continuous size distribution from 10 μm to 27 μm was pumped into a single microchamber device with r/r = 5.4 at Q = 500 μl min 1 or channel Reynolds number Re = 110 (Re = ρu f D h /μ where ρ is density of the fluid, D h is hydraulic diameter of channel and μ is viscosity of fluid). In Fig. 3a, we show that microparticles with diameter larger than the set cutoff size (a > a c ) migrate into the sheath flow as expected, exiting separation channel through side outlets. Microparticles with a < a c elute from the main outlet. This is the typical operation of a bi-modal separator. Histograms in Fig. 3b

4 View Article Online Fig. 2 Theoretical investigation of size-based separation. (a) CFD-ACE+ model showing streamline distribution in two symmetric microchambers with three outlets. In the chambers, the flow is separated into main flow, sheath flow and vortex. The red solid line indicates the boundary of main flow and sheath flow, with R and r representing the channel resistance of the main and side outlets. (b) Schematic illustrating the relationship between the input flow rate and the separation cutoff diameter, with UL representing lateral migration velocity. (c) The close-up images from the numerical model show the entrance and exit regions of the separation unit. The Fs is the shear-gradient induced lift force which drives a particle to migrate towards sheath flow. The dp, db and dm are the particle focusing position, boundary position and migration distance needed for a particle to enter the sheath flow. The red solid line represents boundary streamlines. (d) CFD-ACE+ model illustrating the cross-sectional view of the 3-D boundary 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 to reach the boundary streamline. confirm the cutoff size of ac = 14 μm, given the experimental conditions. More importantly, the results show that particles with size difference of ~1 μm can be separated with >70% efficiency (green arrows). The data further show that differences of ~2 μm can be separated with higher, >80% efficiency (blue arrows), while differences of ~3 μm can be separated with even higher, >90% efficiency (orange arrows). The separation resolution Rs (see methods for detailed definition) of this hydrodynamic-vortex platform is Rs > 10, which is at least 2 higher than in previous inertial microfluidic designs.11,12,16 19,21,25,29,30,35 The high resolution stems from the size-dependent inertial migration at the vortex region, which permits differentiation of lateral positions of different sized microparticles across the boundary. This high resolution feature is extremely beneficial for separating particulate mixture with small size difference. Next, tuning of the separation cutoff diameter was explored in order to demonstrate flexibility of the microfluidic platform. As was suggested in the theoretical discussion above, ac can be precisely tuned by modulating the input flow and channel resistance ratio r/r. Two sets of experiments were conducted to measure the change in ac as a 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 linear decrease in the attenuation diameter from 25 μm to 14 μm. This suggests that ac scales with the first order of input flow velocity as ac Uf. Second, as shown in Fig. 3d, increasing r/r from 5.4 to 10 at Re = 110 leads to a parabolic increase in the cutoff diameter from 14 μm to 19 μm. This suggests that ac scales with the resistance ratio as ac IJr/R)1/2. The experimental results confirm that a combination of these two system parameters permit control of the cutoff diameter with

5 Fig. 3 Experimental investigation of the separation resolution and tunability of the cutoff diameter. (a) Particles with continuous size distribution are induced in a device with r/r = 5.4 and Re = 110 to find out the separation resolution. Particles with diameter a > a c migrate inside sheath flow exiting through the side outlets (blue dash lines), while particle with diameter a < a c elute from the main outlet (red dash lines). A few large particles (a > 25 μm) are recirculating in the vortices (orange dash lines) due to the large F s that can push them across the sheath flow into the microvortices. (b) Normalized histogram of main and side outlet samples indicate separation cutoff size (grey arrow) and separation resolution using a device with r/r = 5.4 and Re = 110. (c) Tuning separation cutoff size by changing Re IJr/R = 5.4). (d) Tuning separation cutoff size by changing r/r (Re = 110). broad tunable range. Surprisingly, an input flow condition exhibits a stronger influence on the cutoff diameter and offers a more convenient way of tuning separation. In summary, these experimental results illustrate that size-based separations with high resolution and easily-tunable cutoff size are possible. By cascading multiple hydrodynamic-vortex units and matching cutoff-related parameters, versatile multimodal separation can be achieved as demonstrated in the following section. Multimodal separation of complex microparticle mixture At first glance, one might expect the cascading of hydrodynamicvortex separators to be straightforward, a simple matter of fabricating multiple units in sequence. However, the microchannel resistance network has to be carefully designed to provide proper cutoff size for each microchamber under certain input Re. In Fig. 4a, we show how an analogue electrical circuit model 40 can be used to aid design of fluidic resistances of the cascaded system. In our model, two red knots represent the two microchambers where the current (flow) is siphoned into three branches. The input flow rate Q c (I c )of the second chamber is determined by the resistance ratio of R 1 and R c which further consists of paralleling of R 2, R 3 and R 4. To achieve multimodal separation, Q in has to match R 1 /R c to provide the higher cut-off diameter for high-pass separation in the upstream chamber. Meanwhile, Q c has to coordinate with R 3 /R 4 to offer the lower cut-off diameter for lowpass separation in the downstream chamber. The multimodal separation was validated through separation of a mixture of 21 μm, 18.5 μm and 15 μm diameter polymer microspheres using the device shown in Fig. 4b. At flow rate Q in = 525 μl min 1 (Re = 116), the upstream microchamber provides high-pass separation with a hc ~20μm with resistance ratio R 1 /R c = 4. As the flow is separated at the upstream microchamber, the downstream flow rate Q c is decreased to ~350 μl min 1 (Re = 77). Thus, resistance ratio R 3 /R 4 = 5.6 is designed for the downstream microchamber enabling low-pass separation with a lc ~17μm. Using these system parameters, the cascaded device successfully separates the particle mixture into its components into O1, O2 and O3 correspondingly (Fig. 4c). The histograms and sample images before and after separation indicate dramatic enhancement of purity of each sized particles (Fig. 4d). Furthermore, the concentration of 21 μm, 18 μm and 15 μm diameter microparticles are enriched by 2.4, 3.8 and 1.7 after separation, as Fig. 4e shows. The separation efficiencies for these particles were measured to be 78%, 87% and 99% respectively, which confirms the device can perform high-resolution multimodal separation of complex particle mixtures without compromising efficiency (Fig. 4f). Size distributions of microparticle or cellular mixtures vary from sample to sample. Size range of interest may also vary. Thus, tunability of separation at each stage becomes significant in sample preparations. Here, we demonstrate the versatility of this microfluidic multimodal sorter through tuning of the separation bandwidth and passband location. Such capabilities lead to successful separation of mixtures into components with different size range. First, we are able to precisely tune separation bandwidth by using proper combination of input flow and resistance network (Fig. 5a). To widen the bandwidth, we fixed the resistance ratio of the upstream chamber R 1 /R c to maintain the high-pass separation with a hc ~20μm, while use a smaller ratio R 3 /R 4 = 4.9 to enable low-pass separation with a smaller a lc ~12μm. Under this modification, 21 μm diameter particles still exit through O1, while both 18.5 μm and 15 μm diameter particles are extracted from O2. 11 μm diameter particles instead elute to O3 as shown in experimental images of microchambers (Fig. 5b) and outlets (Fig. 5c). Such changes in separation

6 View Article Online Fig. 4 Inertial microfluidic multimodal separation. (a) The microfluidic resistance network and its analogous electrical circuit model. (b) Dry-film mold for PDMS casting exhibiting actual device for multimodal separation. The scale bar is 10 mm. (c) Stacked bright field images illustrating separation 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 after multimodal separation, the purities of 21 μm, 18.5 μm and 15 μm diameter particles are dramatically elevated from 38%, 29.3%, 32.7% (inlet) to 89.4% (O1), 80.7% (O2), 95.9% (O3) respectively (e) The concentration plot shows enrichment of concentration of 21 μm, 18.5 μm and 15 μm diameter 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 count shows that the separation efficiencies for 21 μm, 18.5 μm and 15 μm diameter particles are 78%, 87% and 99% respectively indicating efficient multimodal separation of particles with only 3 μm difference in size (n = 3). indicate clear broadening of the separation bandwidth from 3 μm to 8 μm (quantitative measurements of concentration and efficiency are demonstrated in ESI Fig. S2a b). We should also note that narrowing of the bandwidth is also possible by using larger ratio R3/R4. Second, we are able to adjust the passband location while maintaining the bandwidth (Fig. 5d). We used larger resistance ratio R1/Rc ~ 5.5 to provide high-pass separation with larger ahc ~ 22 μm in the upstream chamber. Similarly, we applied a larger resistance ratio R3/R4 ~ 11 to upshift the alc of downstream microchamber. Consequently, 23 μm diameter particles instead of 21 μm diameter particles are found in O1, while 21 μm and 18.5 μm diameter particles are separated in the downstream microchambers as demonstrated in experimental images of both microchambers (Fig. 5e) and outlet channels (Fig. 5f). This result indicates successful offsetting of passband location of the device by 3 μm (quantitative measurements of concentration and efficiency are demonstrated in ESI Fig. S2c d). In summary, we have demonstrated two important abilities for tuning multimodal separations in the device including the modulation of bandwidth and passband location. Such versatility can greatly benefit sample preparations of different complex mixtures according to size distribution or help precisely selecting cells or particles with size of interest. To demonstrate capability of separating a heterogeneous sample, we used a microparticle mixture with continuous diameter distribution from 10 μm to 27 μm. The sample was introduced into the device at Qin = 0.5 ml min 1 (Re = 110). With resistance ratio R1/Rc = 5.5, the upstream microchamber permits a high-pass separation with attenuation at ahc ~ 24 μm. As the flow bifurcates in the upstream microchamber, the downstream flow rate decreases to Qc ~ 370 μl min 1 (Re = 81). With resistance ratio R3/R4 = 11, the downstream

7 View Article Online Fig. 5 Tuning of bandwidth and passband location. (a) By tuning flow rate and resistance network, the separation bandwidth is increased from 3 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 μm diameter particles elute from O2. The 11 μm diameter particles exit through O3. (c) Bright field images at each outlet channel illustrate the successful 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) demonstrate a successful separation of the 23 μm, 21 μm and 18.5 μm diameter particles. In all images, the scale bar is 50 μm. microchamber enables a low-pass separation with attenuation at alc ~ 21 μm. Bright field images of both chambers illustrating this separation are shown in Fig. 6a. With these design parameters, the device successfully sorts a heterogeneous sample (Fig. 6b) into three distinct distributions, as expected. As Fig. 6c shows, the majority of particles with diameter a > 24 μm are sorted into the high-pass outlet O1. Particles μm in diameter (our passband range) eluted from the passband outlet O2, while particles with diameters a < 21 μm eluted primarily through the low-pass outlet O3. Discussion In summary, we demonstrated a microfluidic device capable of versatile multimodal separation of microparticle samples based on sizes, with high resolution and high tunability of

8 Fig. 6 Multimodal sorting of heterogeneous mixture. (a) Heterogeneous mixture of microparticles was sorted into three different size distribution after passing the device. (b) Size distribution of inlet particle mixture. The distribution was normalized to the highest count at a specific particle diameter. (c) Size distributions of samples from O1, O2 and O3. The size distribution in each outlet was normalized to the highest count within that outlet. separation cutoff diameter. Unlike the conventional bimodal microfluidic separators, the presented device provides a novel multimodal separation functionality. This feature significantly expands the capability of the microfluidic separator for sample preparation of complex mixtures of microscale particulate components such as cell mixtures. Additionally, the device exhibits higher resolution than previous bimodal inertial microfluidic separators, which permits more precise separation of samples with small size-difference or heterogeneous size distribution. Moreover, the cutoff diameter of separation can be easily tuned by input flow rate and fluidic resistance network. This high tunability offers versatile functions such as tuning bandwidth and passband location which are beneficial for precise modulation of separation parameters to achieve separation in high efficiency. Ultimately, this device is easy-to-use, because it has a single inlet and offers continuous separation, thus only requires a single syringe pump and allows non-stop separation of high-volume sample with high throughput (~0.5 ml min 1 ). We envision this versatile microfluidic multimodal separator will open new opportunities in the microfluidic separation field for size-based separation of complex particulate materials from biological, environmental to synthetic microparticles for a wide range of applications including industrial microparticle purification, cellular sample preparation, biomedical research and clinical diagnostics. Methods Separation resolution Separation resolution R s was defined based on the spectral resolution. In our case, resolution measures the ability of separating two different sized particles and is defined as R s = a/δa where Δa is the smallest difference in diameter that can be separated in a microfluidic device, and a is the average diameter of the separable particles. For example, if a device can separate 20 μm diameter particles from 10 μm diameter particles, the average diameter is a = 15 μm, with a diameter difference Δa = 10 μm. In this case, the separation resolution is calculated to be R s = 1.5. Microfabrication We used standard soft lithography process to fabricate microchannels in polydimethysiloxane (PDMS, Sylgard 184, Dow Corning). We used a 100 μm high master formed in MX5050 dry film photoresist (Microchem Corp.). A mixture of PDMS base and curing agent (10 : 1 ratio) were poured on the master; after degassing PDMS was cured for 4 h on a 60 C hotplate. 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-hold plasma surface treater (BD-20AC, Electro-Technic Products, Inc.). Microparticle suspensions To study separation cut-off diameter of devices, we dispensed non-fluorescence PMMA microparticles with continuous size distribution from 10 μm to27μm diameter (Cospheric Inc.) to form a solution of particle mixture with concentration of ml 1. In the experiment of multimodal separations, we mixed 23 μm, 21 μm, 18.5 μm (Polyscience, Inc.), 15 μm (Invitrogen, Inc.) and 11 μm (Bangs Laboratoreis, Inc.) diameter microparticles to obtain a concentration of ~ ml 1 for each of the species. We added Tween-20 at 0.1% v/v

9 (Fisher Scientific, Inc.) to the particle solution to avoid issue of particle clogging. Device operation and imaging We first loaded a syringe with particle solution and connected it to the device by using a 1/16" peek tubing (Upchurch Scientific) with proper fittings (Upchurch Scientific). We pumped particle solution into devices with designed flow rate using a syringe pump (Legota 180, KD scientific). To visualize trajectory of particle in bright-field, we used an inverted epi-fluorescence microscope (IX71, Olympus Inc.) 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 view of particle motion. Measurement of flow resistance ratio We determined flow resistance ratio of side and main outlet IJr/R) by measuring ratio of sample volume from these outlets. For example, after inducing certain volume of DI water into the device, the sample volume from side and main outlet was measured to be V side and V main correspondingly. The flow resistance ratio was calculated to: r/r = V main /V side. Characterization of separation To measure size distribution of particle suspensions, we first injected sample into a hemocytometer (Hausser Scientific) to form monolayer of particles and then took bright field images and used Image Pro Plus to automatically measure particle size distribution. We used the same tool to directly measure particle concentration of inlet and outlet samples. To calculate separation efficiency, we combined concentration and corresponding sample volume to estimate the count of each sized particles from each outlet and normalized the counts as separation efficiency. Numerical models We modeled the device using a commercial computational fluid dynamics software CFD-ACE+ (ESI-CFD Inc., Huntsville, AL). The module we used to solve for fluid motion in the geometry is FLOW. The physical properties of water was applied to the fluid in the simulation (density ρ =1000kgm 3 and dynamic viscosity μ = 10 3 kg m 1 s 1 ). The velocity of x-direction (m s 1 ) calculated from the flow rate was applied to initial inlet velocity. We set convergence limit for mass fraction to 10 6 and run simulation for 3000 time steps to ensure the convergence of the simulation. We analyzed simulation results in CFD-VIEW. We added multiple streamlines at multiple x or y locations to form the complete view of flow in separation unit. The boundary-streamline was precisely located and measured by slowly moving y-position of a streamline from the center-line of a channel towards the sidewall until the streamline started to stretch to the side outlet. The complete view of 3D boundary streamlines was built by combining multiple boundary-streamlines at z = μm. Acknowledgements We gratefully acknowledge partial support by the Ohio Center of Microfluidic Innovation (OCMI) at the University of Cincinnati. References 1 G. M. Whitesides, Nature, 2006, 442, A. A. S. Bhagat, H. Bow, H. W. Hou, S. J. Tan, J. Han and C. T. Lim, Med. Biol. Eng. Comput., 2010, 48, M. P. MacDonald, G. C. Spalding and K. Dholakia, Nature, 2003, 426, N. Xia, T. P. Hunt, B. T. Mayers, E. Alsberg, G. M. Whitesides, R. M. Westervelt and D. E. Ingber, Biomed. Microdevices, 2006, 8, X. Hu, P. H. Bessette, J. Qian, C. D. Meinhart, P. S. Daugherty and H. T. Soh, Proc. Natl. Acad. Sci. U. S. A., 2005, 102, F. Petersson, L. Åberg, A.-M. Swärd-Nilsson and T. Laurell, Anal. Chem., 2007, 79, D. R. Gossett, W. M. Weaver, A. J. MacH, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini and D. Di Carlo, Anal. Bioanal. Chem., 2010, 397, J. A. Davis, D. W. Inglis, K. J. Morton, D. A. Lawrence, L. R. Huang, S. Y. Chou, J. C. Sturm and R. H. Austin, Proc. Natl. Acad. Sci. U. S. A., 2006, 103, M. Yamada and M. Seki,, 2005, 5, J. Takagi, M. Yamada, M. Yasuda and M. Seki,, 2005, 5, A. A. S. Bhagat, S. S. Kuntaegowdanahalli and I. Papautsky, Phys. Fluids, 2008, S. S. Kuntaegowdanahalli, A. A. S. Bhagat, G. Kumar and I. Papautsky,, 2009, 9, D. Di Carlo,, 2009, 9, S. C. Hur, H. T. K. Tse and D. Di Carlo,, 2010, 10, D. Di Carlo, D. Irimia, R. G. Tompkins and M. Toner, Proc. Natl. Acad. Sci. U. S. A., 2007, 104, M. G. Lee, S. Choi and J.-K. Park, J. Chromatogr. A, 2011, 1218, A. J. Mach, J. H. Kim, A. Arshi, S. C. Hur and D. Di Carlo,, 2011, 11, J. Sun, M. Li, C. Liu, Y. Zhang, D. Liu, W. Liu, G. Hu and X. Jiang,, 2012, 12, T. Tanaka, T. Ishikawa, K. Numayama-Tsuruta, Y. Imai, H. Ueno, N. Matsuki and T. Yamaguchi,, 2012, 12, J. Zhou, S. Kasper and I. Papautsky, Microfluid. Nanofluid., 2013, 15, J. Zhou, P. V. Giridhar, S. Kasper and I. Papautsky,, 2013, 13,

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