1600

INERTIAL MICROFLUIDIC STUDY OF INTERPARTICLE-INDUCED DEFOCUSING AND STEPWISE EXPANSION CHANNELS THAT REDUCE DEFOCUSING 1

W. Lee1, 2, 3 , H. Amini1, 2, and D. Di Carlo1, 2 *

Department of Bioengineering, University of California Los Angeles, USA. 2 California NanoSystems Institute, USA 3 Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, REPUBLIC OF KOREA ABSTRACT We present a method to systematically study particle-particle interactions in microfluidic channels using inertial focusing[1]. Various designs of expansion channel are tested to determine how expansion rate and vortex formation affect particle-particle interactions. We demonstrate how an understanding of particle-particle interactions leads to channel designs that suppress these interactions and allow improved focusing which could assist particle separations when channels are expanded. Although we used inertial effects to create focused particle streams, the origin of the interaction is a viscous disturbance flow such that our results are applicable to general low Reynolds number microfluidic channel flows as well. KEYWORDS: Particle separation, Hydrodynamic interaction, Inertial microfluidics INTRODUCTION Manipulation of microscale particles, such as cells and microspheres, has been an important research area in lab-on-a-chip based automation. Inertial microfluidic systems have demonstrated various ultra-high throughput particle manipulations: focusing, separation, self-assembly and tuning of the self-assembled structures (Fig. 1) [2-5]. For high-throughput particle manipulation, it is necessary to work with high particle concentration, where particle-particle interactions become more significant. Particle-particle interactions usually lead to reduced efficiency of the particle manipulation techniques. However these interactions are considered unpredictable and no quantitative experimental study has been possible due to the complex nature of many-particle systems. We used inertially focused particle systems to study these interactions and extended the results to more general, Stokes flow, microfluidic systems. EXPERIMENTAL It is possible to manipulate microscale particles with inertial effects in microfluidic systems (Fig 1) [ref]. We prepared a narrow inertially focused particle stream in microfluidic channels (Fig 1A). Particles experience inertial lift forces and focus to dynamic equilibrium positions within microchannel flow with finite Reynolds number (Re); the microfluidic channels we used have 25 µm width and 80 µm height and, with a typical ~ 100 µL/min flow rate, Re is 16. To reduce the complexity of particle-particle interactions, we used microfluidic channels with a rectangular cross-section (Fig 1B) and 2inlet co-flow to further restrict particle focusing positions, which leads particles to be focused at a single focusing position. Then the channel width expands as shown in Figure 2. Interparticle spacings become smaller when particles enter an expanding channel, where the local concentration of particles becomes larger and particle-particle interactions become more significant accordingly. This results in defocusing of particles to a broadened particle stream (Fig 1D, 2). By

A

B

C

D

Figure 1: Particle manipulation using inertial effects. A. Randomly distributed particles are focused and self-assembled by the shear gradient lift force (FSL), wall effect lift force (FWL), and particle-particle interactions (FI). B. Equilibrium positions can be controlled with channel cross-section geometry. C. Interparticle spacing can be tuned with an expansion-contraction geometry. Interaction strengths between different focusing positions are different (a’/a>b’/b). D. Particles entering an expanding channel show interesting cross- stream migration due to viscous disturbance flows. Inertial force decreases with decreasing particle Reynolds number while the viscous disturbance increases with decreasing interparticle spacing.

978-0-9798064-4-5/µTAS 2011/$20©11CBMS-0001

1600

15th International Conference on Miniaturized Systems for Chemistry and Life Sciences October 2-6, 2011, Seattle, Washington, USA

measuring extent of defocusing we investigated how the particle-paricle interactions are related to several controllable parameters: particle concentration, flow rate, and

channel design (Fig 3, 4, 5).

RESULTS AND DISCUSSION Without particle-particle interactions, individual particle trajectories should be almost identical, therefore very pure particle separation should be achievable. However, with decreasing interparticle spacing, particle motion is disturbed by nearby particles and thus defocusing becomes more significant with increasing particle concentration (Fig 2, Figure 2: Defocusing of particle streams at an expansion channel. Higher Fig 3A). The particle-particle interaction that particle concentration leads to increased defocusing due to increased parleads to defocusing originates from the visc- ticle-particle interactions, which can reduce the efficiency of particle sepaous disturbance flow a particle creates that is ration applications and limit throughput. The viscous disturbance flow efreflected by a nearby channel wall [2]. Pair fect is the major interaction (zoom-in at 0.2% v/w ratio, 10 µm particle). interactions between particles result in staggered positions: the leading particle is pushed away from the channel wall and the lagging particle A pushed toward the wall (Fig 1D). Therefore, smaller average interparticle spacing due to larger particle concentration leads to more particles at staggered positions, which in turn leads to larger standard deviation of particle center positions as show in Figure 2. With increasing flow rate, inertial lift force increases and particles are found to be focused better. Counterintuitively, a less focused stream at lower flow rates results in less defocusing at expansions (Fig 3B). We believe this is because there is a larger z-height variance which allows particles to pass each other out of plane. As shown in the microscope images of Figure 3B, particles at the expansion overlap at a 40 µL/min flow rate while particles align in a long chain at 120 µL/min. Within a rectangular channel, inertial lift forces focus particles near longer faces of the channel. For a tall channel (height>width) particles focus in the width direction B first, then move in the height direction [ref]. At low flow rate (40-60 µL/min) , particles look very well focused but, in fact, their z-height differences are fairly large. Above 100 µL/min, there is little increase in defocusing because most of particles are well focused and increasing flow rate does not make a large difference. To reduce defocusing, it is desirable to have a focused particle stream farther from channel walls. Because the inertial focusing position cannot be changed significantly, we designed expansion channels that moved the particle stream away from the wall quickly (Fig 4). ParticleD particle interactions decrease rapidly with increasing interparticle distances (in this case, particle-wall distances). In a stepwise expanding channel, the distance between the particle stream and channel wall is larger than a linear expansion even though the trajectories in both cases is almost Figure 3: Particle defocusing with concentraidentical. The key design feature is the sudden expansion that leads to vor- tion and flow rate in a linear expansion. A. tex formation. The vortex keeps particles away from channel wall and Standard deviation of y-position of particles thus reduces the strength of wall reflected viscous disturbance flows. (σ) vs. particle concentration (C). B. Standard The stepwise expansion channel gives less defocusing (Fig 5). Similardeviation of y-position of particles (σ) vs. flow ly, a convex shaped expansion also shows less defocusing because the rate (Q). At high flow rate, particles are fosudden expansion provides detached vortices at lower flow rate. Results in cused better and form long chains while parFigure 5 are measured at the same expansion width with a flow rate of 100 ticles can move in different z-height at lower µL/min. These results can be expanded to Stokes flow conditions, because particles move away from walls quickly and streamlines are less dense at flow rate (z-overlap gives small σ).

1601

the corner of a step expansion although there is no vortex formation. We observed similar defocusing suppression when using stepwise expansion with very low flow rate (1 µL/min, data not shown). At this flow rate the Reynolds number in straight channels is very small thus the inertial focusing effect is very small (Re=0.16, compared to Re=16 for 100 µL/min). We used pinch flow to accumulate particles towards one side of a channel. CONCLUSION Expansion channels are widely used to increase the separation distance in microfluidic particle-separation applications. We studied particleparticle interactions in expansion channels and found that channel design can be used to control particle-particle interactions. Because a defocusing particle-particle interaction is mediated by nearby channel walls, designs that can move particles quickly away from channel wall, such as stepwise expansions, show less defocusing of particle streams. The importance of particle-particle interactions in microfluidic systems has been relatively underestimated. We have demonstrated that understanding the origins of particle-particle interactions can help provide practical solutions to minimize or enhance the influence of neighboring particles for separations or focusing. ACKNOWLEDGEMENTS ?

Figure 4: Stream lines and detached vortices in expansion channels. A. Stepwise expansion channels develop vortices at lower flow rates (100 µL/min). Both designs show large vortex formation at 160 µL/min. Due to small vortices at the steps particles can move away from the side wall more quickly – reducing the wall-reflected viscous wake that leads to defocusing.

REFERENCES CONTACT * D. Di Carlo, [email protected]

Figure 5: Channel design and defocusing suppression. Sudden expansion channel designs lead to less defocusing than a linear expansion.

1602