Size-Dependent Inertial Focusing Position Shift and Particle

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Size-dependent inertial focusing position shift and particle separations in triangular microchannels Jeong-ah Kim, Je-Ryung Lee, Tae-Jin Je, Eun-Chae Jeon, and Wonhee Lee Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.7b03851 • Publication Date (Web): 22 Dec 2017 Downloaded from http://pubs.acs.org on December 24, 2017

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Analytical Chemistry

Size-dependent inertial focusing position shift and particle separations in triangular microchannels Jeong-ah Kim,a Je-Ryung Lee,b Tae-Jin Je,b Eun-Chae Jeonb* and Wonhee Leea* a.

Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and

Technology (KAIST), Daejeon 34141, Republic of Korea. E-mail: [email protected] b.

Department of nano manufacturing, Korea Institute of Machinery & Materials (KIMM), Daejeon 34103, Republic of Korea.

Abstract A recent study of inertial microfluidics within non-rectangular cross-section channels showed that the inertial focusing positions changes with cross-sectional shapes, therefore, the crosssectional shape can be a useful control parameter for microfluidic particle manipulations. Here, we conducted detail investigation on unique focusing position shift phenomena, which occurs strongly in channels with the cross-sectional shape of the isosceles right triangle. The top focusing positions shift along the channel walls to the direction away from the apex with increasing Reynolds number and decreasing particle size. A larger particle with its center further away from the side walls experiences shear gradient lift towards the apex, which leads to opposite result with changes of Reynolds and particle size. The focusing position shift and the subsequent stabilization of corner focusing lead to changes in the number of focusing positions, which enables a novel method for microparticle separations with high efficiency (> 95%) and resolution (< 2 μm). The separation method based on equilibrium focusing, therefore, the operation is simple and no complex separation optimization is needed. Moreover, the separation threshold can be easily modulated with flow rate adjustment. Rare cell separation from blood cell was successfully demonstrated with spiked MCF-7 cells in blood by achieving the yield of ~ 95% and the throughput of ~106 cell/min.

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Introduction Inertial microfluidics has drawn much attention with its many applications1,2 including microparticle synthesis,3 flow shaping,4,5 single cell analysis,6,7 and particle manipulations including capture,8 fluid exchange,9,10 and separation.11-14 Especially, inertial separation and enrichment of cells has been extensively studied due to high-throughput and simplicity in device structure, fabrication, and operation.15-19 Except for a few examples,20-22 inertial microfluidic techniques separate particles or cells based on their sizes. Simple inertial microfluidic separation devices take advantages of differences in the equilibrium focusing positions of particles within straight channels with rectangular cross-sections; larger particles tend to focus further away from the channel wall.23 However, the differences in the focusing positions are relatively small and limit separation efficiency. Several channel designs were devised to overcome the limitation by utilizing additional drag forces of secondary flows. In spiral channels, Dean flows alter the focusing positions due to the different scaling of the inertial lift forces and the Dean drag force to the particle sizes.11,24,25 Similar to the spiral channel, expansion-contraction17,26,27, and serpentine structures13,28 were also suggested as separation methods using secondary flow effects. However, the magnitude and directions of the drag force and lift forces in these channels remain difficult to predict and the optimization of the separation requires a large set of experiments covering large parameter space with multiple variables. It is difficult to make a fair comparison of the separation performance of different inertial microfluidic devices because the separation efficiency and the yield of target particles are sensitive to flow speed and concentration which is also related with throughput. Most of the inertial microfluidic devices can have high efficiency (> 90%) after careful optimization. Among them, spiral channels generally show the best performances and, in


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particular, have advantages of highest throughput and capability to handle high concentration samples. Inertial focusing positions are known to change with the cross-sectional shape of the microfluidic channel.25,29-31 Slight changes in the aspect ratio of rectangular channels can lead to the change of the number of focusing positions; there are four focusing positions in square channels, whereas there are two focusing positions in rectangular channels because of the dominance of wall effect lift force near the long channel walls.29 We previously studied inertial focusing in non-rectangular channels.31 In half-circular channels, particles are focused at two focusing positions as in case of low-aspect-ratio rectangular channels. Triangular channels had three focusing positions near each channel face as expected. The unique cross-sectional shape of triangular channels can allow control of complex inertial lift force direction and magnitude distribution. Unlike in case of rectangular channels with two mirror symmetry planes, the broken symmetry of triangular channels results in interesting complexity in lift force balance and subsequent equilibrium positions. In this study, the inertial focusing position shift parallel to channel side wall is investigated in detail using channels with the cross-sectional shape of an isosceles right triangle with varying Reynolds number (Re) and particle size. The unexpectedly large difference in focusing configurations and strong focusing position shift were observed with varying particle size and Re. We analyzed the focusing position shift and proposed mechanism of the shift. The size-dependent focusing position shifts enabled separation of microparticles and cells with high efficiency (> 95%) and resolution (< 2 μm), which is similar or better compared to the best performance of existing inertial microfluidic separation techniques. Furthermore, the threshold for separation could be tuned easily with Re because the onset Re of focusing configuration switching depends on the particle size.



Experimental Fabrication of triangular channel Triangular channels can be fabricated from a Si mold made with anisotropic KOH etching. However, wet etching technique requires careful control of etching temperature and mass transport during the etching to create an isosceles right triangular channel. Intrinsically, the channels made with wet-etching have limitations in a variety of the angles available. We fabricated triangular channel molds by planing processes that scratch a workpiece (64brass) using diamond cutting tools (Figure S-1). The cutting tools are composed of single crystal diamond of which edge is v-shape with a specific angle. The planing process allows fabrication of various types of triangular channels; it is possible to change the angles of the channel and depth by changing the tip angle of the cutting tool and the total cutting depth of the diamond cutting tools. A PDMS (Sylgard) mold was replicated from the v-groove on the brass mold. Then, this PDMS mold was used to create a PDMS replica of the brass mold for capillary molding of UV-glue. The capillary molding of UV-glue transfers triangle cross-section channel onto a Si wafer. After the UV-glue channel mold was fabricated, PDMS microfluidic channels were made by a conventional soft lithography technique.32 The triangular PDMS channel was plasma bonded onto a glass slide (Harrick plasma cleaner) for the top view channels. The side view device and separation channel were fabricated in the same method described in the previous study.31

Fabrication of the separation channel The separation channel consists of a rectangular channel, a triangular channel and an expansion channel with five outlets. First, a triangular channel mold was formed on Si wafer by filling UV-glue into PDMS mold of the engraved triangular channel. Then, a rectangular channel and


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an expansion channel with outlets were aligned and patterned (MA6, Suss MicroTec) on top of the triangular channel mold using photolithography with SU-8 resist (SU-8 3025, MicroChem).

Experimental setup and measurements Polystyrene particles (Micromer) with a particle density of 1.03 g/cm3 were used. Tween 20 (1%(v/v), Sigma-Aldrich) was added to prevent aggregation of particles and NaCl was used to match the density of solution with particles for creating neutrally buoyant conditions. Addition of NaCl also helps to maintain uniform concentration particles during experiments by preventing particle sedimentation. Density matching with NaCl is not necessary for general separation applications. The particle concentration was 0.2-0.3%(w/v) for 15 μm, 0.050.1%(w/v) for 10 μm and 0.02-0.05%(w/v) for 8 μm. The particle suspension was injected using a syringe pump (Harvard Apparatus, PHD ULTRA CP syringe pump) while controlling the volumetric flow rate. The particle dynamics was observed from top and side views of the channel by using an optical microscope (Nikon Eclipse Ti-U) and the images were captured with a high speed camera (Phantom v7.3). The centers of particle positions from the captured images were detected using a MATLAB code which implemented a Circular Hough Transform algorithm. This code finds the sudden change of color gradient at both sides of a particle and presents the center of the transition position as the center of particles.

Sample preparation for cell separation Fresh human blood cells from healthy donors were dispersed in DPBS with 500-fold dilution and MCF-7 cells were spiked into the diluted blood with the ratio of RBCs to MCF-7 cells as



10000:1. The densities of fluid and cells were not matched with NaCl for cell separation because the influence of density mismatch to inertial focusing is generally negligible while osmotic stress adversely affects cells. MCF-7 cells were labeled for fluorescence imaging (Vybrant® DiO Cell-labelling solution, absorption 484 nm and emission 501 nm). The MCF-7 cells were cultured based on Dulbecco’s Modified Eagle’s Medium (DMEM, WELGENE) including 10 %(v/v) Fetal Bovine Serum (FBS, WELGENE) and 1 %(v/v) PenicillinStreptomycin solutions (WELGENE) in a CO2 incubator (5% CO2 concentration and 37 °C, SANYO).


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Results Inertial focusing in triangular channels depending on particle size and Reynolds number Inertial focusing of microparticles was investigated in isosceles right triangular channels with varying particle size and Reynolds number (Re =

𝜌𝑈𝐻 𝜇

, where 𝜌 and 𝜇 are the density and

dynamic viscosity of fluid, 𝑈 is the average velocity of the fluid, 𝐻 is hydraulic diameter). First, to study size-dependency of focusing positions, dilute suspensions of microparticles with three different sizes (diameter, a = 8, 10, 15 μm) were prepared and flowed through the triangular channel while controlling flow rate with a syringe pump (Harvard Apparatus PHD ULTRA CP syringe pump). The concentration of particle solution was 0.3 %(w/v) for 15 μm, 0.1 %(w/v) for 10 μm, and 0.05 %(w/v) for 8 μm. Triangular channels with various sizes were fabricated and tested to study the size effects. One channel that showed the largest changes in inertial focusing positions with the given particle sizes was chosen among them and studied in detail. The channel height (h) was 38 μm and the channel length (L) was 3.5 cm. The details of the channel fabrication, the experiment and analysis methods are described in the experimental section. Figure 1A shows the normalized statistical distributions (P) of particle positions in the channel, which were measured near the outlet of the channel (Re=60, n = 1000, n is the number of particles). Surprisingly, the focusing positions of the different-sized particles were completely different, even to the extent that the number of focusing positions is different. The largest particles (15 μm) formed 2 focusing positions near the apex and center of bottom channel face while smaller particles (8, 10 μm) formed 3 focusing positions as observed previously (Figure 1A). A velocity profile in an isosceles right triangular channel is similar to a velocity profile in a half-circular channel. The similarity in focusing position may seem natural if the wall-effect lift forces from the side walls are not considered. In general, the larger



particles feel the larger inertial lift forces and it is less likely to form a stable focusing position near a channel corner. Figure 1B shows the similar focusing position configuration at a lower Re (Re=20). At Re=20, 10 μm particles that previously had a three-focusing-position configuration changed to a two-focusing-position configuration. Again, this change was unexpected because the lift force would be reduced by lowering Re and for smaller particles to behave like larger particles larger lift force or higher Re number would be favorable.

Figure 1 Size-dependent inertial focusing in an isosceles right triangular channel. Statistics of particle positions (n = 1000) and corresponding high speed capture images were obtained from the top view and side view. The focusing positions of different size particles were drawn in the cross-section. Changes in Reynolds number also changes focusing configurations. (A) Re=60 and (B) Re=20. The bin size of the histogram corresponds to 1 μm. The particle positions are non-dimensionalized by dividing with the channel width (w) and height (h).

The focusing position changes were studied in detail with varying Re (Figure 2). In case of 15 μm particles, the histogram of particle position shows one peak in the top view and two peaks in the side view over the entire Re range (Figure 2A), which indicates stable focusing


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positions are formed near the apex and the center of the bottom channel wall (Figure 1). The previous study showed only three focusing positions in triangular channels.31 The two focusing position configuration appears with substantially large a/H (a=particle size, H=hydraulic diameter). The values for a/H are 0.48, 0.32, and 0.25 for 15, 10, and 8 μm particles respectively. When the particle size is decreased to 10 μm, the shift of focusing positions becomes apparent with varying Re (Figure 2B). The number of focusing positions is clearly three at Re=60 and the top focusing positions get closer with decreasing Re and merge into one, resulting in two focusing positions at Re=20. The direction of the focusing position shift with the Re change is the same as the previous study.31 With a further decrease in the particle size (8 μm), three focusing positions were observed in the overall Re regime (Figure 2C). We also tested inertial focusing using different size channels (H) and particles (a). The inertial focusing positions are found to be almost identical if a/H is same (supporting information Figure S-2).



Figure 2 Focusing position changes with varying Re. Statistics of particle position for 8 μm particles (A), 10 μm particles (B), 15 μm particles (C) in the top view and the side view (n = 1000). (D) Summary of focusing position shifts.

Figure 2D summarizes the changes in focusing positions with varying Re and particle size. The locations of the focusing positions are determined by the modes of the graphs in Figure 2A, B, C. Top focusing positions of 8 μm particles and 10 μm particles tend to shift away from the center in the top view and away from the top in the side view as Re is increased. In other words, top focusing positions shift away from the apex with increasing Re. We found the top focusing positions shift with Re in the previous study, where a/H was 0.26 with a = 10 µm.31 The results with 8 μm particles (a/H = 0.25) agree with the observation from the previous study. On the contrary, results with 15 μm particles (a/H = 0.48) is completely unexpected and results


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with 10 μm particles (a/H = 0.32) show transitional trend between two cases. More interestingly, the direction of the focusing position shift with varying a/H was opposite to the theoretical prediction; the increase in a/H and the increase in Re is expected to give similar results because 𝑎

the inertial lift forces generally scale with the particle Reynolds number (Re𝐩 = Re(𝐻)2 = 𝜌𝑈𝑎2 𝜇𝐻

). However, the increase in a/H led to the opposite result, that is, the increasing particle

size resulted in focusing position shift towards the apex. The differences in focusing positions can be used for particle separation applications. Large differences in separation distances (defined as the distances between focusing positions from a reference point) are preferred for high separation efficiency. The particle-size dependent focusing position shift in triangular channels is significantly larger than the focusing position changes in rectangular channels. The separation distances from the channel center were ~0.5a for the 8 μm particles and 0 for 10 and 15 μm particles from the top view at Re=20. They were ~1a for 8 μm particles, ~ 0.7a for 10 μm particles, and 0 for 15 μm particles from the top view at Re=60. The actual distances between focusing positions of two different particles in the cross-section are ~5 μm for 8 and 10 μm particles at Re=20, and ~8 μm for 10 and 15 μm particles at Re=60. In a rectangular channel with similar flow conditions, the actual focusing position difference was ~1 μm for 8 and 10 μm particles.23

Microparticle separations using size-dependent focusing position changes The direction of the focusing shift with the size change is counterintuitive; the larger particle is expected to focus further away from the apex in accordance with the Re-dependency. Luckily, the opposing dependency leads to a large separation distance between particles and can allow highly efficient and tunable particle separation. If the direction of the size-dependent shift was opposite, the focusing positions of the larger particles would be almost stationary near the



center of the side walls and increasing Re would lead to a decrease in separation distance and narrow Re ranges for separation. The size-dependent focusing position shift in a triangular channel can be used for separation of microparticles including cells. We elucidated variation of focusing positions in accordance with particle size and Re in the previous section. Although the top focusing positions shift with particle size, there is a common bottom focusing position, which should be eliminated for particle separation applications. In the previous study31, we demonstrated the manipulation of the accessible focusing positions by assembling channels with different cross-section shapes. We fabricated a similar channel to make the common focusing position inaccessible (Figure 3).

Figure 3 Design of the separation channel and its working principle. Overlapping focusing positions are made inaccessible by matching the basins of attractions and focusing positions. Size-dependent focusing position shift enables the particle separations.

The separation channel consists of a straight channel with varying cross-section, an expansion channel, and five outlets. The cross-section of the straight channel changes from a high-aspect-ratio rectangle (w=21 μm, h=40 μm, L=2 cm) to an isosceles right triangle (w=76


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μm, h=38 μm, L=2 cm). The expanding channel and outlets have rectangular cross-sections consisted of same height with rectangular channel part (Figure 3). Particles introduced in the separation channel are first focused at the two equilibrium positions in the high-aspect-ratio rectangular channel. As the channel cross-section shape changes, focused particles in the rectangular channel migrate to the top focusing positions of the triangular channel. Here, the bottom focusing position becomes inaccessible, which is a common focusing position for different size particles. In the triangular channel, top focusing positions are determined by particle size as shown in Figure 1. The larger particles are aligned along the centerline of the channel and the smaller particles are ordered along the two lines away from the centerline in the top view. These particles flowing along different streamlines can be separated into different outlets after the expanding channel. The fluidic resistance of each outlet was adjusted to increase the separation efficiency. The middle outlet has 1.4 times larger fluidic resistance than the others (see supporting information for more detail. Figure S-3). We divided the triangle cross-section based on the focusing positions according to particle size and Re from Figure 1 and determined the ratio of the flow to be separated into each outlet matching with the divided cross-section area. The movements of three different size particles at the expansion channel were observed with varying Re. Figure 4 shows the standard deviation plots33 that were acquired by stacking high-speed capture images (N = 3000, N is the number of high-speed capture images) of particles in the expansion channel area. The standard deviation plots allow the estimation of the extent of the overlap of the trajectories of many particles. Re of 20 and 60 was chosen for comparison of different particle trajectories because particle focusing positions showed clear distinction depending on particle size (Figure 1). Here the Re of the separation channel was calculated using the dimensions of the triangular channel and the flow speed in the triangular channel. In case of Re=20, 10 and 15 μm particle trajectories stayed in the middle of the channel



and the particles exited to the center outlet, while 8 μm particle trajectories shifted away from the center with expansion and the particles exited to the side outlets. In case of Re=60, 15 μm particle trajectory alone stayed in the middle, while 8 μm and 10 μm particle trajectories led to the side outlets. The standard deviation plots of the particles moving along the middle of the channel (15 μm particle at Re=20 and 60, and 10 μm particle at Re=20) were shown as single bright lines. These lines had almost the same width as the particle diameters, which indicated that the particles were tightly focused to the single top focusing position. The width of the particle trajectories leading to the side outlets was relatively broader. The data from the Figure 1 supports this observation. The peaks for the separated top focusing positions on two side walls were broader than the single top focusing position near the apex from both of the top and the side views. The distance of the focusing position shift from the apex becomes larger and the widths of the particle trajectories become narrower with increasing Re. The width of the trajectory is also expected be narrower with longer channel length by allowing enough time for the migration while the shift distance will not change with the longer channel.

Figure 4 The standard deviation plots showing trajectories of three different size particles at two Re conditions in the expansion channel and the outlets (N = 3000).


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Interestingly, some portion of the 8 μm particle was found in the middle of the expansion channel, forming a narrow line as if they were focused in the middle of the triangular channel. This unexpected result was due to the particle focusing at the bottom focusing position in the triangular channel. In a high-aspect-ratio rectangular channel, particles first migrate in the width direction quickly then focus into the focusing positions. Particles that did not fully focus in the height direction in the rectangular channel can lie in the basin of attraction of the bottom focusing position in the triangular channel. This problem can be solved with a longer rectangular channel and higher Re. However, the middle trajectory of 8 μm particles became more intense with large Re. We tracked down the source of the bottom focusing with the higher Re and found some of the particles were focused in the middle of the rectangular channel (from the top view). It is known, for a high-aspect-ratio rectangular channel, that the unstable focusing positions near the short faces can be stabilized for small a/H at high Re.1,34 Note, the value of Re in the rectangular channel corresponds to 90 when it is 60 in the triangular channel. It was found that a little portion of the particles focused at the short faces in the rectangular channel with Re=90 (Figure S-4), and these particles would migrate to the bottom focusing positions in the triangular channel (Re=60) and contribute to the particle trajectory found in the middle of the expansion channel.

Particle and cell separation results and control of separation threshold As expected from the size-dependent focusing position shift (Figure 2), the particle trajectories at the expansion channel changed dramatically depending on the particle size and Re (Figure 4). This property allows microparticle separations and the control of the threshold by changing Re. The concentration of particle solution for separation was 0.2 %(w/v) for 15 μm, 0.05 %(w/v) for 10 μm, and 0.02 %(w/v) for 8 μm. Particles are injected into the inlet with flow rate 50~160



μl/min. At low Re (Re=20), 8 μm particles were collected at the side outlets and 10 μm particles were collected at the center outlet. As Re was increased (Re>30), focusing positions of 10 μm particles changed and they were collected at the side outlets, whereas 15 μm particles were still collected at the center outlet. We could successfully demonstrate separations of microparticle with high efficiency and high resolution with up to 2 μm difference in diameter (Figure 5).


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Figure 5 Stacked high-speed capture images (N = 75) showing separation of particles and separation purities for (A), (B) 8 μm and 10 μm particle mixture (Re=20) and (C), (D) 10 μm and 15 μm particle mixture (Re=60). Separation if three different sized particle (Re=45). (E) Stacked high-speed capture images. (F) Separation purities of particles at each outlet.

The statistics in Figure 5 show the purity of the separations of an 8 and 10 μm particle mixture (Figure 5B) and 10 and 15 μm particle mixture (Figure 5D). The ratio of the 8 and 10 μm particles in the mixture was ~1:1. The purity was calculated by the ratio of the number of collected target particles from the target outlet(s) to the number of total particles from the target outlet(s) and particles were counted from high-speed capture images. High purity indicates the absence of unwanted particles in the collected particles from the specific outlets. For the 8 and 10 μm particle separation (Figure 5A and B), a particle mixture was prepared by mixing an approximately equal number of two types of particles (51.7% for 8 μm and 48.3% for 10 μm particles). After the separation, purity of the 10 μm particles at the center outlet was 96.8 ± 1.7% and the purity of the 8 μm particles at the side outlets was 99.6 ± 0.9%. Three independent experiments were performed and particle count was 300 for each experiment. The purity of the 10 μm particles at the center outlet was lower than that of the 8 μm particles at the side outlets as expected from the results in Figure 4. As discussed in the previous section, a small portion of the 8 μm particles was collected at the center outlet due to the incomplete removal of 8 μm particles from the bottom focusing position of the triangular channel. Results are similar for the 10 and 15 μm particle separation (Figure 5C and D). The purity of particle mixture of 10 and 15 μm particle was 52.5% and 47.5% before separation. After the separation, the purity of the 15 μm particles at the center outlet was 95.4 ± 0.8% indicating that the smaller particles were not perfectly separated to the side outlets, while the purity of the 10 μm particles at the side outlets was 99.4 ± 0.2%. Overall, the particles with 2 and 5 μm difference in diameter



were successfully separated with outstanding purity of >95%. The results can be summarized as follows. The top focusing positions shift away from the apex with increasing Re. There exists the onset Re that the single top focusing position splits and starts shifting away from the apex. This onset Re becomes larger with larger a/H, which allows easy tuning of the size threshold for separation. The size-dependent focusing position shift also allows simultaneous separations of multiple particle sizes with careful adjustment of flow rate and outlet resistance. In the range of Re=30 to Re=45, focusing positions of the 8, 10 and 15 μm particles are clearly distinguishable (Figure 2D). The Re was adjusted to 45 and the fluidic resistances of the outlet channels were adjusted to R : 5R : 4R : 5R : R for optimal efficiency. The separation devices for two size separation did not utilize all 5 outlets for the collection of separated particles. The extra outlets were designed for easier fluidic resistance adjustment. Here, all 5 outlets were used for collection outlets for each particle size (Figure 5E and F). Different size particles were efficiently separated to designated outlets. The 8, 10 and 15 μm particles had the ratio of 70.3%, 17.5%, and 12.2% respectively in the particle mixture. The separation purity was 97.2 ± 0.2% for 8 μm particles at the side-2 outlets, 93.0 ± 1.4% for 10 μm particles at the side-1 outlets and 92.0 ± 1.0% for 15 μm particles at the center outlet. We also showed the feasibility of CTC(circulating tumor cell) separation from blood using spiked MCF-7 cells in the diluted blood (500×) with a ratio of RBC: MCF-7 = 10000:1. The length of the rectangular channel was increased from 2 cm to 2.5 cm for better focusing of blood cells. Deformable particles tend to migrate slower than rigid particles of the same size and require a longer channel for inertial focusing.1 In addition, we changed the dimension of triangular channel height from 38 μm to 43 μm to increase the difference of focusing positions between blood cells and MCF-7 cells. Blood cells that are smaller than MCF-7 cells focus off-


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center of the triangular channel and exits through the side outlets while MCF-7 cells focus at the center and exit through the center outlet (Figure 6A). Four independent experiments were performed and cells that pass through the channel within a fixed time were counted. The yield of MCF-7 and blood cell rejection ratio was calculated by the number of cells exited through the center (or side) outlet / the number of cells exited through total outlets. The yield of MCF7 was 95.2 ± 4.8% and the blood cell rejection ratio was 94.8 ± 0.6%. The throughput of separation was 1.1x106 cells/min. A high-throughput separation of MCF-7 cells is successfully demonstrated with high yield despite the scarcity of MCF-7 cells in the blood sample (1: 10000). Figure 6B shows the cells before separation and the collected cells from each outlet. All the sample was enriched 4 times by removing top liquid component after cell sedimentation to show the relative population of blood cells and MCF-7 cells. The size variation of MCF-7 was ~13 – 24 μm.



Figure 6 Separation of MCF-7 from blood. MCF-7 cells were spiked with ratio of RBC: MCF7 = 10000: 1. (A) A stacked high-speed capture image (N = 20) of the cell separation at the expansion channel. (B) Bright field and fluorescence microscopy images of the cells before separation and the cells collected from outlets.


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Discussion In this study, inertial focusing position shift is studied in isosceles right triangle channels with varying Re and particle size. In square channels, unstable equilibrium points are located near the vertices.35,36 Similarly, the symmetry of the triangular channel leads to an unstable equilibrium point near the apex. In fact, the triangular cross-section represents one half of a square channel with a diagonal cutting line and the stabilization of the unstable corner equilibrium point is an interesting phenomenon found only with a large particle size within triangular channels. Inertial focusing positions are located, in general, at the regions of the maximum shear rate in the channel cross-section (Figure S-5). In case of triangular channels, there are three regions of the maximum shear rate associated with each channel wall and the particles are normally focused to these three focusing positions. As the apex angle becomes wider, the regions of maximum shear rate, or focusing positions, at the side walls move closer to the apex. Larger particles can be affected by both attractors when the top two focusing positions are close, which can contribute to a stabilization for the top focusing position with large a/H. Inertial focusing dynamics is generally described as two steps: 1) fast migration towards the channel walls by shear gradient lift force and 2) slow migration along the channel wall by wall-effect lift force,1 which is also true for triangular channels.31 Near the points of maximum shear rate close to the apex, the shear gradient lift force direction can change significantly depending on the particle size because of the difference in the velocity profile experienced by the particles (Figure S-6). An 8 μm particle experiences strong shear in the direction nearly orthogonal to the side wall, which leads to fast migration towards the channel wall. Then the slow migration is determined by the wall-effect lift forces from the other side wall and the bottom wall. The shear gradient lift in the direction parallel to the side wall contributes little in



this step. On the contrary, the shear around a 15 μm particle has a fairly large difference in the direction parallel to the side wall and the direction of the shear gradient lift force can be tilted towards the apex. With a larger particle, larger shear gradient lift force towards the apex is expected, which explains the focusing position shift depending on the particle size (i.e., a/H). In rectangular channels, focusing positions move closer to the channel walls with increasing Re, which originate from the different scaling of the wall effect lift and the shear gradient lift to Re.23 If this scaling is applied to the triangular channel system, the direction of the focusing position shift should be towards the apex with increasing Re, because the increasing Re leads to a relatively larger increase in shear gradient lift force (towards the apex) than wall-effect lift force (away from the apex). This analysis obviously contradicts with the observation; the direction of the focusing position shift is away from the apex with increasing Re. The experimental results imply that the inertial lift coefficient, which is known to be a weak function of Re but varies with position in the channel, varies with Re in such a way that the equilibrium points shift away from the apex. Unlike a rectangular channel that always has equilibrium positions located near the center of the channel faces due to the mirror symmetry, triangular channels allow adjustment of vertex angles and the directions of each wall-effect lift forces. The equilibrium positions are determined by the complex balance between lift forces. In the channel under study, the focusing position shift with Re should be mainly determined by the balance between the wall-effect lift forces from the two adjacent channel walls (the other side wall and the bottom wall). The focusing position shift found in triangular channels implies that the wall-effect lift force scaling with Re is dependent on the distance from the channel wall. The direction of the shift can be an evidence that the wall-effect lift force increases faster in the region near the channel wall than the region far away from the wall with increasing Re. We used the large differences of focusing positions depending on particle sizes for particle and cell separation applications. Inertial microfluidic separation techniques have many


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advantages, including high-throughput, simple operation, and precise particle manipulation,1,2 over other microfluidic separation techniques. Diverse device designs have been developed for separation applications and they can be categorized as 1) straight channel, 2) serpentine channel, 3) spiral channel, and 4) expansion-contraction channels. The summary of performances of these devices can be found from several well-written review papers.37-39 The performance separation devices typically can be evaluated with metrics including separation efficiency (or purity), yield, throughput, and separation resolution. A fair comparison of separation devices with many performance metrics is a difficult task, especially when the metrics are inter-related. For example, the increase in particle concentration increases the throughput while decreases efficiency and yield. In addition, all these performances are strongly dependent on separation target sizes, concentrations, and their relative portions. Generally, most inertial separation designs can achieve high separation efficiency above 95% with careful optimization if target separation sizes are 10 μm and 15 μm.37 Most designs, except spiral channels, have difficulty for separation of particles with small size differences, for example, 8 μm and 10 μm. We have achieved over 95% efficiency for both 8 μm and 10 μm particles due to large equilibrium position difference or separation distance. Moreover, most inertial particle separation techniques focus on maximizing separation efficiency of one target particle, not both. To our knowledge, there was no device reported separation of the particles having only 2 μm size difference with efficiency better than 95% for both particles. The spiral channels are considered to show best performances among inertial separation techniques, which utilize the Dean drag force to enlarge the separation distance. However, the scaling of the Dean-drag and the inertial lift is difficult to predict and there is still no simple guideline for the design of separation devices. The optimization of separation efficiency is highly empirical and should be determined after investigation of many different designs with



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multiple parameter changes including channel width, height, curvature with varying flow rate. This is also true for serpentine and expansion contraction designs, which also involve secondary flows. The separation using straight channels including our triangular channel device relies only on inertial lift forces and optimization of separation conditions is straightforward. In addition, the focusing position dependence on viscosity is negligible in the straight channel while the drag force from the secondary flow is strongly dependent on the fluid viscosity, which leads to separation performance changes with biological samples. Moreover, straight channels use equilibrium separation that allows tighter focusing with the longer channel. The increase of the channel length of the spiral channel is limited due to changing channel curvature. The current design of triangular channel device is limited by the bonding strength. We expect further enhancement of the device performance if we use longer channel using a device fabrication method allowing the higher bonding strength.40,41 In addition, straight channels have advantages in multiplexing compared to spiral channels. Spiral channels take up a large area and it is difficult to make common inlets and outlets, while straight channel can be easily connected in parallel and throughput can be multiplied. The dimension of the channel in this research is relatively small (H ~ 30-40 μm) compared to spiral channels (hundreds of micrometers). For a straight channel, a larger channel requires a larger flow rate for complete inertial focusing than a smaller channel. In general, the length 𝐻2

required for inertial focusing in straight channel can be expressed as 𝐿𝑚 ∝ 𝑈𝑎2 .1 When the bonding strength, or the maximum pressure, is the limiting factor, Hagen-Poiseuille equation can provide maximum length of the channel with given flow rate and hydraulic diameter: 𝐿𝑄

𝑈

𝐻2

∆𝑃 ∝ 𝐻 4 = 𝐿 𝐻 2 . If we put 𝐿𝑚 ∝ 𝑈𝑎2 in the equation, U and H cancel out and maximum pressure depends only on particle size, which implies that small channel dimension do not give a disadvantage. The channel cross-sectional area also affects the throughput. If we assume the


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particles are tightly focused for high efficiency, the number of particles per same volume become smaller for larger channel because the length fraction for the focused particles is limited for inertial focusing.42 Therefore, smaller channel may have small throughput in terms of volume of liquid, but it can have similar throughput in terms of number of particles. In case of spiral channel, the smaller particles (typically blood cells) are allowed to circulate within Dean vortices and only larger particles (typically CTSs) are tightly focused, which gives a large throughput of ~106 – 107 cells/min and ~several mL/min. There was also a report of throughput as high as ~1.8×108 cells/min but with smaller flow rate of 800 μl/min using a spiral channel.43 Our cell separation results showed comparable throughput in terms of number of particles (1.1x106 cells/min) but smaller flow rate (~140 μl/min). The fabrication of the triangular channel is not as simple as the conventional rectangular channels. However, the level of the difficulty can be considered easy compared to many other lab-on-a-chip devices. Moreover, the fabricated mold can be reused many times and a few more steps in the mold fabrication would not be a huge concern. The focusing position shift shown in Figure 2D can provide a general guideline for particle separation and the threshold size of particle separation can be determined with a/H and Re. The comparison of the focusing position shift of different size particles with same a/H conditions shows that the focusing positions and shift tendency collapse into the same lines if a/H is same (Figure S-2). Therefore, the focusing position shift trend in Figure 2D can be used for practically any microparticle separation with desired target size if channel dimension (H) is adjusted appropriately.



Conclusions Inertial focusing position shift was investigated using isosceles right triangular channels. The number and the locations of focusing positions were found to be controllable with particle size and Re. The top focusing positions shifts towards the apex with decreasing Re number. These top two focusing positions can be merged into a single focusing position near the apex in case of large a/H. At the same Re condition, the top focusing positions also strongly depend on particle size. With increasing particle size, the location of the focusing positions shifting towards the apex. The size-dependent focusing position shift enables highly efficient microparticle separations. The focusing position shift depends on Re and particle size and the adjustment of Re allows easy control of separation threshold. Separation channels were designed to control accessible focusing position by mapping basins of attraction and focusing positions in varying cross-sections. Separation of particles and cells were successfully demonstrated with high resolution (~2 μm) and high efficiency (>95%). The capability of simple, active tuning of separation parameter without replacing device is expected to allow broad applications requiring separation of complex suspension of particles or cells with a wide range of sizes.

Acknowledgements This work was supported by Radiation Technology R&D program through the National Research Foundation of Korea funded by the Ministry of Science, ICT & Future Planning (NRF-2015M2A2A4A02044826) and the Technology Innova tion Program (10054488,) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea)


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Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: Fabrication of triangular channel; Verification of a/H as a parameter determining focusing position shift; Streamline connections from triangular channel to outlets; Stabilization of short face focusing positions in a rectangular channel; Shear rate distribution in triangular channels; Flow velocity profile over different size particles (PDF)



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For TOC only


Size-Dependent Inertial Focusing Position Shift and Particle

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