Anal. Chem. 2007, 79, 1947-1953
Stream Spreading in Multilayer Microfluidic Flows of Suspensions Mona Utne Larsen and Nina C. Shapley*
Department of Chemical Engineering, Columbia University, 500 W. 120th Street, MC 4721, New York, New York 10027
The goal of this experimental study is to quantify the spreading of parallel streams with viscosity contrast in multilayer microfluidic flows. Three streams converge into one channel where a test fluid is sheathed between two layers of a Newtonian reference fluid. The test fluids are Newtonian fluids with viscosities ranging from 1.1 to 48.2 cP and suspensions of 10-µm-diameter PMMA particles with particle volume fractions O ) 0.16-0.30. The fluid interface locations are identified through fluorescence microscopy. The steady-state width of the center stream is strongly dependent on the viscosity ratio between the adjacent fluids and exhibits a near power-law relationship. This dependence occurs for both the Newtonian fluids and the suspensions, although the slopes differ. The highconcentration suspension (O ) 0.30) diverges from Newtonian behavior, while the low-concentration suspensions (O ) 0.16, 0.22) closely approximate that of the Newtonian fluids. The observed suspension behavior can be attributed to shear-induced particle migration. Many analytical operations at the microfluidic scale, such as cell sorting, involve flows containing particles.1 Additionally, there are many microfluidic applications that involve networks of converging and diverging channels.2,3 However, only a limited amount of work to date covers the fundamentals of particle behavior during flow in microchannels, especially those with complex geometries. Microfluidic designs often exploit the ability of adjacent fluid layers to flow side by side without mixing, which is seen in a number of applications such as particle size separation using laminar flow around obstacles,1 generation of concentration gradients in a pyramidal microfluidic network,4 and the monitoring and analysis of chemical interactions at the interface between two fluids in a microfluidic T-sensor.5,6 However, a quantitative relationship between layer thicknesses is only rarely found in the literature, for example, in two unusual studies that concern how the interface location depends on the viscosity ratio between two fluids.5-7 * Corresponding author. Fax: 212-854-3054. E-mail:
[email protected]. (1) Huang, L. R.; Cox, E. C.; Austin, R. H.; Sturm, J. C. Science 2004, 304, 987-990. (2) Atencia, J.; Beebe, D. J. Nature 2005, 437, 648-655. (3) Stone, H. A.; Stroock, A. D.; Ajdari, A. Annu. Rev. Fluid Mech. 2004, 36, 381-411. (4) Dertinger, S. K. W.; Chiu, D. T.; Jeon, N. L.; Whitesides, G. M. Anal. Chem. 2001, 73, 1240-1246. (5) Kamholz, A. E.; Weigl, B. H.; Finlayson, B. A.; Yager, P. Anal. Chem. 1999, 71, 5340-5347. (6) Hatch, A.; Garcia, E.; Yager, P. Proc. IEEE 2004, 94, 126-139. 10.1021/ac0612271 CCC: $37.00 Published on Web 01/27/2007
© 2007 American Chemical Society
Microfluidics is used to study the spreading of parallel layers because it provides a low Reynolds number flow regime where the interface between the layers is stable and there is no convective mixing.8 These conditions are difficult to access on the macroscopic scale. In addition, microfluidic systems are attractive as a tool for fundamental particulate flow studies due to the ease of fabrication of multiple complex channel geometries.9 Microfluidic studies can give insight into particle distribution in expansion flows of suspensions10,11 and core-annular flow with a viscosity contrast12 on the macroscopic scale. Previous studies consider the interface between two fluids of varying viscosity; however, those systems do not have symmetry around the more viscous stream as in this study. Hitt and Macken used a T-junction channel with a square cross section to measure the interfacial location in convergent microchannel flow for a range of viscosity and flow rate ratios.7 The data compared reasonably well to 1D calculations for a system of infinitely deep channels, with no-slip conditions at the walls and continuity of velocity and shear stress at the interface. Kamholz et al. used a similar geometry to estimate the viscosity of an unknown fluid.5,6 Two fluids of unequal viscosities were introduced in a T-sensor device, and the interface position was used to estimate the viscosity ratio between the two fluids. In analytical operations that involve particles it is important to understand how the particles affect the behavior of the adjacent fluid layers, and we aim to capture the impact of particles on the spreading of parallel layers. Some previous studies have explored how flow can lead to nonuniform spatial distributions of particles in microfluidic systems. One microfluidic device separates red blood cells from the suspending plasma by exploiting an enhanced cell-free layer near the walls after passage through a constriction.13 Another example of research where particle nonuniformity is exploited is the separation of blood cells from smaller molecules such as urea by diffusion while blood is sheathed between adjacent layers of dialysate.14 Previous research on Brownian suspension flow in microchannels has also revealed greater inhomogeneity (7) Hitt, D. L.; Macken, N. J. Fluid Eng. 2004, 126, 758-767. (8) Pozrikidis, C. J. Fluid Mech. 1997, 351, 139-165. (9) Duffy, D. C.; McDonald, J. C.; Schueller, O. J. A.; Whitesides, G. M. Anal. Chem. 1998, 70, 4974-4984. (10) Moraczewski, T.; Tang, H.; Shapley, N. C. J. Rheol. 2005, 49, 1409-1428. (11) Moraczewski, T.; Shapley, N. C. Phys. Fluids 2006, 18, 123303. (12) Van de Griend, R.; Denn, M. M. J. Non-Newtonian Fluid Mech. 1989, 32, 229-252. (13) Faivre, M.; Abkarian, M.; Bickraj, K.; Stone, H. A. Biorheology 2006, 43, 147-159. (14) Leonard, E. F.; West, A. C.; Shapley, N. C.; Larsen, M. U. Blood Purif. 2004, 22, 92-100.
Analytical Chemistry, Vol. 79, No. 5, March 1, 2007 1947
Table 1. Weight Percent of Glycerin (the rest being water) in the Test Fluids and Corresponding Viscosities, Viscosity Ratios with the Reference Fluid, and the Ranges of Reynolds Numbers Tested
Figure 1. Channel design.
in the spatial distribution of particles due to shear-induced particle migration with increasing particle concentration and Peclet number.15 In this study, we quantify the effect of viscosity contrast on the spreading of parallel layers in multilayer microfluidic flow. Three streams converge into one channel where a Newtonian fluid or suspension is sheathed between two layers of a Newtonian fluid. The viscosity ratio between these two fluids and the total flow rate are varied. We find that the spreading of the center stream depends on the viscosity ratio between the adjacent fluids in a near power-law relationship. The low-concentration suspensions (particle volume fraction φ ) 0.16, 0.22) exhibit behavior like that of the Newtonian fluids, while the more concentrated suspension (φ ) 0.30) diverges from this behavior. The observed suspension behavior can be attributed to shear-induced particle migration in the entrance channel. EXPERIMENTAL SECTION Design and Fabrication of a Microfluidic Flow Cell. A schematic view of the microchannel design including dimensions used in this study is shown in Figure 1. Three equally sized, 100µm-wide inlet channels (width w) converge into a 300-µm-wide channel (width W). Each inlet channel is 70-channel-widths long. The outlet is identical to the inlet. The height (H) of the channels is approximately 100 µm, so the inlets have a square cross section while the wide channel has a rectangular cross section. Several test fluids were injected into the central inlet channel, while a single reference fluid was pumped into the two side channels. The microfluidic device was fabricated using soft-lithography techniques, specifically, rapid prototyping and replica molding.9,16 A high-resolution transparency mask was generated from a design drawn in Adobe Illustrator CS2 and printed with a resolution of 5080 dpi (PageWorks, Cambridge, MA). The mask was used in contact photolithography to create a master consisting of a silicon wafer (University Wafer, South Boston, MA) with positive relief patterns made from UV-exposure of SU-8 50 photoresist (Micro(15) Frank, M.; Anderson, D.; Weeks, E. R.; Morris, J. F. J. Fluid Mech. 2003, 493, 363-378. (16) McDonald, J. C.; Duffy, D. C.; Anderson, J. R.; Chiu, D. T.; Wu, H.; Schueller, O. J. A.; Whitesides, G. M. Electrophoresis 2000, 21, 27-40.
1948 Analytical Chemistry, Vol. 79, No. 5, March 1, 2007
weight percent of glycerin
average viscosity (µtest) (cP)
viscosity ratio (µtest/µref)
range of Reynolds numbers
0 25 50 60 65 70 75 80
1.1 1.9 5.5 9.7 13.1 19.3 27.7 48.2
1.0 1.8 5.1 8.9 12.1 17.7 24.4 44.2
0.13-25.5 0.077-15.4 0.028-5.7 0.017-3.3 0.012-2.5 0.0085-1.7 0.0060-1.2 0.0035-0.35
Chem, Newton, MA). The patterns had a height of approximately 100 µm, measured by an Alpha-Step IQ Surface Profiler. This durable master was used to replicate microchannels in poly(dimethylsiloxane) (PDMS; Sylgard 184, Corning, Midland, MI) by replica molding. Silicone elastomer tubing was embedded in the PDMS before the replica was cured in the oven. The PDMS mold was then peeled off the master, and holes were made to connect the tubing with the replicated channels and for the outlet reservoirs. The flow cell was then assembled by reversibly sealing the mold to a glass slide and clamping them together. Test and Reference Fluids. Eight mixtures of water and glycerin were prepared to obtain Newtonian test fluids with various viscosities (µtest ) 1.1 cP-48.2 cP). The fluids were dyed with 25 ppm of calcein, a green-yellow fluorescent dye (Sigma-Aldrich, St. Louis, MO). One of the Newtonian fluids (µtest ) 5.5 cP) was used as a base fluid to suspend 10-µm-diameter poly(methyl methacrylate) (PMMA) spherical particles (Bangs Laboratories, Inc., Fishers, IN) at three different volume fractions (0.16, 0.22, and 0.30). In the suspension, 0.53-0.56 wt % each of MBI-40 (Maxi-Blast, South Bend, IN) and Triton X-100 (J. T. Baker, Phillipsburg, NJ) surfactants were added to keep the particles from clustering. In addition, a reference fluid of water (µref ) 1.1 cP) dyed with 100 or 200 ppm of calcein was prepared. The test and reference fluids were dyed with different concentrations of fluorescent dye for identification purposes under a fluorescence microscope. Furthermore, the fluid viscosities were characterized in a TA Instruments AR 2000 rheometer. Table 1 shows the weight percent of glycerin used in the Newtonian fluids with corresponding viscosities (µtest), viscosity ratios of test fluids to the reference fluid (µtest/µref), and the ranges of tested Reynolds numbers. Similarly, Table 2 shows the particle volume fractions (φ), viscosities (µtest), and viscosity ratios (µtest/ µref) for the suspensions and the corresponding ranges of flow Reynolds numbers that were tested. Three of the Newtonian fluids have viscosities that approximately match the viscosities of the suspensions. Fluorescence Microscopy and Multilayer Flow Procedure. A Zeiss Universal Microscope was used to image the fluorescent flow using a mercury arc lamp to excite the fluorescent dye. Images were acquired with a CCD camera (Sensys 0401E, Roper Scientific) and recorded and stored on a computer using IPLab v.3.70 software. Blood collection tubing with a 23 3/4 gauge needle was inserted into the tubing embedded in the PDMS. The tubing was
Table 2. Volume Fraction of Particles in the Base Fluid, and Corresponding Viscosities, Viscosity Ratios with the Reference Fluid, and the Ranges of Flow Reynolds Numbers Tested particle volume fraction (φ)
average viscosity (µtest) (cP)
viscosity ratio (µtest/µref)
range of Reynolds numbers
0 0.16 0.22 0.30
5.5 9.2 13.7 29.7
5.1 8.5 12.6 27.3
0.0098-2.0 0.0080-1.6 0.0042-0.83
attached to 1-mL syringes held in syringe pumps (New Era Pump Systems Inc., Farmingdale, NY) to control the fluid flow. The syringes connected to the two side inlets were loaded with the reference fluid, and the syringe connected to the center inlet was loaded with either the Newtonian or suspension test fluids. The flow rates of the fluids in the three inlet streams were controlled with the syringe pumps and were always kept equal to each other. Flow rates ranging from 0.05 to 10 mL/h for each of the three streams, corresponding to Reynolds numbers from 0.0035 to 25.5 for the center stream and from 0.13 to 25.5 for each of the side streams, were tested (see Tables 1 and 2). The Reynolds numbers were calculated from Re ) FUw/µ, where F is the density of the fluids, U is the average velocity in the inlet channels, w is the width of the inlet channels, and µ is the viscosity of the fluids. Furthermore, the tested range of flow rates corresponds to water Peclet numbers from 69 to 13 889 for each of the three inlet streams, calculated from Pe ) Uw/D. U and w are defined above, and D is the diffusivity of water, equal to 2 × 10-5 cm2/s. Images were acquired at the inlet, where the channels converge, during stable, steady-state flow. The images had an exposure time of 1000 ms to achieve the best obtainable contrast at the interface between the test fluid and reference fluid. The typical image size was 768 × 512 pixels with a field of view of approximately 698 × 1047 µm2 or 840 × 1260 µm2. The images were analyzed with Image J 1.36b, a public domain Java image processing and analysis program, by measuring the spreading of the center stream in pixel units at several points along the length of the channel. The widths of the center stream were normalized as a fraction of the total channel width. RESULTS AND DISCUSSION Newtonian Fluids. Fluorescence images were obtained at a range of flow rates for eight different viscosity ratios between the center (test) and sheathing (reference) streams in the multilayer flow system. Figure 2 shows representative images of the inlet region for two viscosity ratios, 5.1 (a) and 44.2 (b), both recorded at a flow rate of 1.0 mL/h for each of the inlet streams. The volumetric flow rates were always kept equal for each of the three inlet streams so that the effect of the viscosity ratio between the center stream and the side streams could be observed. The impact of the viscosity ratio is illustrated in these images, and it can be seen that the center stream spreads significantly farther at the higher viscosity ratio. After this initial immediate spreading, the width of the center stream stays constant throughout the rest of the channel. Figure 3 shows the normalized width of the center
Figure 2. Multilayer flow images taken at a flow rate of 1.0 mL/h for each inlet stream. The sheath in both images is the reference fluid, water dyed with 100 ppm of calcein. (a) The test fluid in the center stream contains 50 wt % glycerin dyed with 25 ppm of calcein. µtest/µref ) 5.1. (b) The test fluid has the same dye, but 80 wt % glycerin. µtest/µref ) 44.2.
Figure 3. The effect of viscosity ratio (4 1.0, 2 1.8, O 5.1, b 8.9, 0 13.1, 9 17.7, ] 27.7, [ 44.2) between the two inlet fluids on the spreading of the center stream along the length of the channel. The flow rates are constant for all the cases at 1.0 mL/h for each inlet stream.
stream as a function of position along the channel length for the tested viscosity ratios. It can be seen from the graph that the spreading of the center stream occurs immediately and is almost complete within an axial distance of half the large channel width. In addition, the final width of the center stream increases significantly with increasing viscosity ratio between the test and reference streams. The effect of Reynolds number on the spreading of the center stream is shown in Figure 4 for the case where µtest/µref ) 44.2. From the data it appears that the flow rate has little or no impact on the spreading of the center stream when the flow rates are equal for the three inlets. However, for the lowest Reynolds number of 0.0035 and water Peclet number of 69, which correspond to an inlet flow rate of 0.05 mL/h for each inlet stream, the width decreases along the length of the channel due to diffusion. This decrease happens after a maximum value at half the large channel width downstream of the convergence of the channels. For Peclet numbers greater than 100, the spreading of the center stream is not observed to decrease due to diffusion along the length of the channel. In addition, at other viscosity ratios, for the highest flow rate of 10 mL/h for each inlet stream, necking of the center stream is observed near the inlet where the three streams converge. Therefore, the stable maximum width is not reached until farther downstream as compared to the lower flow rates. Previous work described in the literature discusses the error that is involved with the readings of the interface location, when Analytical Chemistry, Vol. 79, No. 5, March 1, 2007
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Figure 4. Effect of Reynolds number (0 (grey) 0.0035, 9 0.007, 4 (grey) 0.035, 2 0.07, O 0.35 (grey)) on the spreading of the center stream along the length of the channel for µtest/µref ) 44.2.
the converging liquids are of differing viscosities and as the Reynolds number increases, due to curving of the surface (i.e., the interface position varies over the height of the channel). According to Hitt and Macken,7 the surface cannot be assumed to be planar when Re g 10 for the case where the fluids have equal viscosity and the junction angle is 90°. However, our system has a reduced junction angle of 45° and only has a few experiments with Reynolds numbers above 10, resulting in less significant curving.7 The curvature of the interface is known to be more significant when the viscosity ratio is increased, as was shown in an experimental and theoretical tube flow study of a T-junction where two tubes of different diameters converge, reported by Ong et al.17 They found that the surface bulged farther away from the side branch as the viscosity ratio was increased. However, the curvature of the surface is also expected due to the difference in diameters of the inlet branch and main tube, according to previous experimental18 and theoretical19 studies. In our images, there is a visible layer at the interface between the two fluids that is likely due to the surface curvature described in the literature (see Figure 2b). We have estimated the uncertainty in the reading of the interface location on the basis of this surface curvature, along with uncertainties arising from diffusion observed at low flow rates and small imperfections at the inlet junction that also can cause deviation from a planar interface as the Reynolds number is increased.7 In each experiment, the minimum interface width was always measured. Therefore, the data presented here indicate a lower bound on the spreading of the center stream. At 1.2 large channel widths downstream of the converging channels, the average error for the interface reading is estimated to be 8.3%, ranging from 3.2% for the viscosity ratio of 1.0 to 11.8% for the viscosity ratio of 25.4. These errors are estimated at a flow rate of 1.0 mL/h for each of the streams, but are also representative for the higher flow rates. The errors decrease with decreasing flow rate. Another phenomenon that was noticed for certain conditions is that the flow was no longer a stable multilayer flow in that the interface became unstable.8 This instability of the flow was (17) Ong, J.; Enden, G.; Popel, A. S. J. Fluid Mech. 1994, 270, 51-71. (18) Rong, F. W.; Carr, R. T. Microvasc. Res. 1990, 39, 186-202. (19) Enden, G.; Popel, A. S. Trans. ASME 1992, 114, 398-405.
1950 Analytical Chemistry, Vol. 79, No. 5, March 1, 2007
Figure 5. Axial cross-section views of the flow for the (a) 1D model, and (b) 2D model.
observed for certain combinations of high viscosity ratios and high flow rates, particularly for the case of the highest flow rate of 10 mL/h and highest viscosity ratio of 44.2 where the viscous center stream completely dominated the flow. Therefore, no data could be recorded for that case. Three other combinations of flow rates and viscosity ratios showed the same tendencies, but the flow was stable long enough that data could be recorded. This behavior happened for the cases where the viscosity ratios were 17.7 and 24.4 with a flow rate of 10 mL/h, and where the viscosity ratio was 44.2 at a flow rate of 5.0 mL/h. Newtonian Fluid Calculations. The Navier-Stokes equation can be used to predict the relative Newtonian stream widths near an axial position of one large channel width, z ) W, where the interface position is slowly varying along the axial direction, but blurring of the interface by diffusion is not yet detectable. It is assumed that the flow is steady, fully developed, and unidirectional. Hence, momentum conservation reduces to 3Pi ) µi32vi, solved in each fluid domain (where index i indicates the reference or the test fluid). Here, vi is the velocity, µi is the viscosity, and Pi is the modified pressure of each fluid. Also, it is assumed that the flow is symmetrical over the center line in both of the lateral (x- and y-) directions, is described by no-slip boundary conditions applied at the walls of the channel, and is characterized by velocities, shear stresses, and normal stresses that are continuous at the interface between the two fluids. Finally, we assume that the interface between the two fluids is planar, with negligible interfacial tension,7 so that Ptest ) Pref at each axial position (z). Following the work of Hitt and Macken,7 we solve a onedimensional version of the problem, where the unidirectional and fully developed channel flow is assumed to have a very large height in the y-direction relative to the width W in the x-direction (see Figure 5a). The following expression relates the viscosity
Figure 7. Multilayer flow images taken at a flow rate of 1.0 mL/h for each inlet stream. The sheath in both images is the reference fluid, water dyed with 200 ppm of calcein. (a) The test fluid in the center stream is a suspension with φ ) 0.16 PMMA particles suspended in a fluid that contains 50 wt % glycerin and is dyed with 25 ppm of calcein. µtest/µref ) 8.5. (b) The base fluid is the same as in (a) but has φ ) 0.30 PMMA particles. µtest/µref ) 27.3.
Figure 6. Comparison of Newtonian fluid calculations to experimental data for the dependence of the normalized center stream width x0/W on the viscosity ratio µtest/µref. Proceeding from the bottom to the top of the graph, the curves indicate: s ‚ s, 1D channel flow; s s, velocity continuous at interface; 0 data, 1 mL/h; ), shear stress continuous at interface; ) (grey), movable wall between two duct flows; ) ) ), movable wall between two channel flows.
ratio µtest/µref and the normalized width of the center stream x0/W:
(
)( )
2 µref x0 3 x0 1Qtest 3 µtest W W ) 3 Qref x0 1 x0 2 W 3 W 3
()
(1)
The ratio of volumetric flow rates Qtest/Qref ) 0.5 matches the experimental system. A numerical solution for the normalized center stream width x0/W as a function of viscosity ratio µtest/µref is shown in Figure 6. In another simple case, streams of differing viscosities are considered isolated flows separated by a movable wall that adjusts until the pressure drops are equal in the three streams. This solution (identical for duct flows and for channel flows with H , W) gives
x0 ) W
1 Qref µref 1+ Qtest µtest
( )( )
(2)
Several previous studies of contrasting viscosity fluids in high aspect ratio channels (H
