Anal. Chem. 2007, 79, 6128-6134
Study of Miscible and Immiscible Flows in a Microchannel Using Magnetic Resonance Imaging Belinda S. Akpa, Sine´ad M. Matthews, Andrew J. Sederman, Kamran Yunus, Adrian C. Fisher, Michael L. Johns, and Lynn F. Gladden*
Department of Chemical Engineering, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA, UK
Magnetic resonance imaging (MRI) is a noninvasive technique that can be used to visualize mixing processes in optically opaque systems in up to three dimensions. Here, MRI has been used for the first time to obtain both cross-sectional velocity and concentration maps of flow through an optically opaque Y-shaped microfluidic sensor. Images of 23 µm × 23 µm resolution were obtained for a channel of rectangular cross section (250 µm × 500 µm) fed by two square inlets (250 µm × 250 µm). Both miscible and immiscible liquid systems have been studied. These include a system in which the coupling of flow and mass transfer has been observed, as the diffusion of the analyte perturbs local hydrodynamics. MRI has been shown to be a versatile tool for the study of mixing processes in a microfluidic system via the multidimensional spatial resolution of flow and mass transfer. Microfluidic devices have attracted much interest in the fields of biology, biotechnology, and analytical and synthetic chemistrys with applications as varied as protein crystallization,1 analyte diagnostics,2 cytometry,3 and combinatorial chemistry.4 These miniaturized fluidic systems have many advantages over their macroscale equivalents. They employ smaller liquid volumes, have lower production costs, and exhibit superior mixing and heattransfer properties. Such systems have also made feasible the integration of multiple processes on one devicesthe so-called lab on a chip or micro total analysis system. Sample preparation, analysis, and detection thus have the potential to be carried out in a single automated step. Many attempts have been made to observe and characterize mixing performance in microfluidic systemsswith a view to optimizing their design and operation. Both flow and concentration mapping have typically been achieved by using optical methods. With regard to solute mapping, these include conventional fluorescence microscopy,5 confocal fluorescence microscopy,6 optical microscopy,7 and optical coherence tomography (OCT).8 These methods typically probe mixing efficiency by tracking a * To whom correspondence should be addressed. E-mail:
[email protected]. ac.uk. Fax: +44 (0)1223 334796. (1) Hansen, C.; Quake, S. R. Curr. Opin. Struct. Biol. 2003, 13, 538-544. (2) Weigl, B. H.; Yager, P. Science 1999, 283, 346. (3) Kruger, J.; Singh, K.; O’Neill, A.; Jackson, C.; Morrison, A.; O’Brien, P. J Micromech. Microeng. 2002, 12, 486-494.. (4) Watts, P.; Haswell, S. J. Curr. Opin. Chem. Biol. 2003, 7, 380.
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tracer or optically active label in solution. Changes in color or degree of fluorescence of the tracer are measured and subsequently correlated with changes in physical or chemical properties that result from the intermixing of streams (e.g., Kamholz et al.9). Techniques that have been used to visualize flow in microfluidic systems include fluorescence correlation spectroscopy (FCS), particle imaging velocimetry (PIV), OCT, and optical Doppler tomography (ODT). FCS is an extension of confocal microscopy that is capable of acquiring high-resolution velocity images in optically transparent media.10 PIV has largely been applied to macroscale systems and provides useful information regarding bulk flow characteristics.11-15 The technique requires that fine particles be injected into the flowing fluid. A pulsed light source then illuminates the particles, allowing a time series of images to be acquiredsfrom which a velocity field is inferred by tracking the position of individual particles as a function of time.16,17 While standard PIV methods struggle to capture the features of flow near interfaces, Shinohara et al.18 have demonstrated the ability of high-speed micro-PIV to map immiscible countercurrent flows in a microscale system. OCT and ODT19 techniques have been used to generate high-resolution velocity images in microfluidic systems.3,20 Both techniques rely on incident laser photons being (5) Sato, Y.; Irisawa, G.; Ishizuka, K.; Hishida, K.; Maeda, M. Meas. Sci. Technol. 2003, 14, 114-121. (6) Ismagilov, R. F.; Stroock, A. D.; Kenis, P. J. A.; Whitesides, G.; Stone, H. A. Appl. Phys. Lett. 2000, 76, 2376-2378. (7) Liu, R. H.; Stremler, M. A.; Sharp, K. V.; Olsen, M. G.; Santiago, J. G.; Adrian, R. J.; Aref, H.; Beebe, D. J. J. Microelectromech. S 2000, 9, 190. (8) Xi, C.; Marks, D. L.; Parikh, D. S.; Raskin, L.; Boppart, S. A. Proc. Natl. Acad. Sci U.S.A. 2004, 101, 7516-7521. (9) Kamholz, A. E.; Weigl, B. H.; Finlayson, B. A.; Yager, P. Anal. Chem. 1999, 71, 5340-5347. (10) Kuricheti, K. K.; Buschmann, V.; Brister, P.; Weston, K. D. Appl. Spectrosc. 2004, 58, 1180-1186. (11) Hosoi, J. J. Flow Visualization 1980, 5, 247. (12) Kawahashi, M. J. Flow Visualization 1987, 7, 84. (13) Kobayashi, T.; Saga, T.; Segawa, S. Flow Visualization V; Hemisphere: Washington, DC, 1990. (14) Chen, L. J.; Chen, C. J. San Francisco, CA, August 28-31, 1991; p 407. (15) Kanamori, H.; Lee, Y. H.; Kobayashi, T.; Saga, T., San Francisco, CA, August 28-31, 1991; p 401. (16) Lourenco, L.; Krothapalli, A. Exp. Fluids 1987, 5, 29. (17) Erbeck, R.; Merzkirch, V. Exp. Fluids 1988, 6, 89. (18) Shinohara, K.; Sugii, Y.; Aota, A.; Hibara, A.; Tokeshi, M.; Kitamori, T.; Okamoto, K. Meas. Sci. Technol. 2004, 15, 1965. (19) Koelink, H.; Slot, M.; de Mul, F. F. M.; Greve, J.; Graaff, R.; Dassel, A. C. M.; Aarnoudse, G. Appl. Opt. 1992, 31, 3401-3408. (20) Wang, L.; Xu, W.; Bachman, M.; Li, G. P.; Chen, Z. Appl. Phys. Lett. 2004, 85, 1855-1857. 10.1021/ac070364a CCC: $37.00
© 2007 American Chemical Society Published on Web 07/14/2007
back-scattered by particles suspended in a liquid medium. In an OCT experiment, back-scattered light is detected and lowcoherence interferometry is used to provide depth discrimination. ODT can yield in situ velocity measurements by exploiting the Doppler shift phenomenon that arises when photons are reflected by moving particles. Ahn et al.21 have applied these two techniques in concert to simultaneously yield cross-sectional concentration maps and flow profiles of particles dispersing in water. Despite the achievements of workers using optical techniques, there remain some inherent limitations of these methods. For example, the applicability of optical methods is limited to systems that have been fabricated and sealed with optically transparent materials. Optical methods are also often limited with respect to the type of device geometry that can be studied. In an optical imaging experiment, fluorescence should ideally be collected evenly from all parts of the channel cross section. To this end, the focal plane (typically parallel to the direction of diffusive mixing) is located as close as possible to the middle of the channel depth. Furthermore, the images acquired by conventional microscopy are of the en face type; i.e., they superimpose the concentration fields of flows at different depths. As a consequence of this mode of detection, narrow etch depths are generally used with the aim of reducing errors such as those introduced by the butterfly effect (i.e., the nonuniform concentration profiles that are a direct consequence of a laminar flow profile). Slower velocities near the walls of the microchannel allow longer residence times in these regions. As a result, interdiffusion occurs over a longer length scale here compared with mixing at the center of the channelsscaling as z1/3 rather than z1/2 as predicted by Brownian motion6 (where z denotes position along the length of the channel). The projection yielded by an optical image can thus lead to an overestimation of mixing efficiency.8 As the butterfly effect is less pronounced if the channel width far exceeds its depth, channels of high aspect ratio (typically >100) are frequently used in studies of microfluidic mixing.9,22 Confocal microscopy does have the ability to resolve a third spatial dimension, albeit with imaging depths limited to ∼100 µm, while OCT can be used to image 3D microstructures at penetration depths on the order of several centimeters in optically transparent media.8 The techniques described above have typically been applied to single-phase systems containing an optically active tracer. In the one multiphase study,18 only the aqueous phase was velocitymapped as it alone contained an optically active species. More recently, researchers have begun to explore nuclear magnetic resonance (NMR) as a tool for the study of microscale systems. Hilty et al.23 reported the use of time-of-flight imaging techniques for the study of gaseous flow in a microchannel. Harel et al.24 have extended this technique to the study of liquid flow in a T-mixersacquiring chemically specific spin density images of a nonmixing system with the addition of a time-of-flight dimension. Ahola et al.25 have demonstrated NMR velocity mapping of solute(21) Ahn, Y. C.; Jung, W.; Zhang, J.; Chen, Z. Opt. Express 2005, 13, 81648171. (22) Kamholz, A. E.; Schilling, E. A.; Yager, P. Biophys. J. 2001, 80, 1967-1972. (23) Hilty, C.; McDonnell, E. E.; Granwehr, J.; Pierce, K. L.; Han, S. I.; Pines, A. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 14960-14963. (24) Harel, E.; Hilty, C.; Koen, K.; McDonnell, E. E.; Pines, A. Phys. Rev. Lett. 2007, 98, 017601.
free liquid flow in a commercial micromixer. In this work, magnetic resonance imaging (MRI) has been usedsfor the first timesto perform both in situ concentration and velocity mapping of the cross section of a microfluidic device. Both single-phase and multiphase systems have been studied. Velocity mapping has been carried out for both miscible and immiscible streamssand, notably, a system where solute diffusion perturbs local hydrodynamics. MRI provides an entirely noninvasive method of visualizing mixing processes even in optically opaque systems. In addition, cross sections of the microfluidic device can be imaged without geometric restrictions. Spatial resolution can be obtained in three dimensions; consequently, it is not necessary to average measurements over the microchannel depth. Also, different fluid phases need not be matched with respect to their physical properties in the way that refractive index matching is typically a prerequisite of optical techniques. Our motivation for developing MRI tools for the study of microchannels extends beyond experimental visualization of mixing performance. The data thereby obtained can be used in the validation of numerical codes for simulating micromixing processes. Such codes will play a key role in the design and optimization of microfluidic systems. Indeed, images presented in this work have been used by Sullivan et al.26 to validate a lattice-Boltzmann code capable of simulating coupled diffusive mass transfer and hydrodynamics in 3D. EXPERIMENTAL METHODS The device studied in this work has a Y-shaped confluence of the inlet channels. The inlet channels are square with dimensions of 250 µm × 250 µm. These join with a 45° angle to form a rectangular channel of 500-µm width and 250-µm depth. The longitudinal geometry of the device was designed such that the inlet channels converged in the imaging region of the radio frequency (rf) coil. The microchannel was fabricated using standard photolithographic techniques.27-30 The Y-shaped channel was formed in a layer of Microchem SU8-2100 photoresist (Microchem Inc.), which was spin-coated onto a glass substrate (Soham Scientific) to a thickness of ∼250 µm. The photoresist was then exposed to ultraviolet (UV) light (340 nm) through a high-resolution mask of the desired channel network (printed by Circuit Graphics) and was subsequently baked to promote crosslinking of the exposed polymer. The desired channels are protected from UV exposure by the dark portions of the mask and remain soft and vulnerable to a developer solution (EC Solvent, Microchem Inc.) that is used to reveal the desired 3D pattern. The patterned substrate was then diced to a width small enough to fit in a 5-mm rf coil. Holes were subsequently drilled into the top of the device to create an inlet region. A thermal plastic superstrate was used to seal the microchannel, and outlet tubing was attached using a heat-shrink connection and adhesive resin. Pressure-driven flow was provided by a syringe pump (Harvard Apparatus 22). (25) Ahola, S.; Casanova, F.; Perlo, J.; Munnemann, K.; Blumich, B.; Stapf, S. Lab Chip 2006, 6, 90-95. (26) Sullivan, S. P.; Akpa, B. S.; Matthews, S. M.; Fisher, A. C.; Gladden, L. F.; Johns, M. L. Sens. Actuators, B: Chem. 2007, 123, 1142-1152. (27) Okazaki, S. J. Vac. Sci. Technol. 1991, B9, 2829. (28) Jeong, H. J.; Markle, D. A.; Owen, G.; Pease, F.; Grenville, A.; Von, Bunau, R. Solid State Technol. 1994, 37, 39-42. (29) Levenson, M. D. Solid State Technol. 1995, 38, 57. (30) Geppert, L. IEEE Spectrum 1996, 33, 33.
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Table 1. Summary of the Y-Channel Experiments expt ID I II III IV a
inlet stream
solvent type
1 2 1 2 1 2 1 2
aqueous aqueous aqueous aqueous aqueous aqueous aqueous organica
solute
solute type
inlet flow rate (mL min-1)
viscosity (cP)
MnSO4 (0.5 mM)
passive
MnSO4 (0.5 mM) glycerol (10 vol %) MnSO4 (0.5 mM) Glycerol (20 vol %) MnSO4 (0.5 mM)
passive active passive active passive
0.006 0.006 0.003 0.003 0.003 0.003 0.07 0.07
0.89 0.89 0.89 1.3 0.89 1.93 0.89 0.82
Octamethyltrisiloxane (Dow Corning 200(R) Fluid).
Figure 1. Multislice T1 saturation-recovery imaging sequence. Saturation of the 1H signal was achieved using a train of rf pulses interspersed with homospoil gradients. After a signal recovery time, τ, a slice-selective imaging sequence was used to acquire 2D images at 8 different positions along the microchannel. This process was repeated for 8 different durations of the recovery delay. Consequently, a total of 64 images was acquired. These were used to generate T1 maps of diffusive mixing.
The work presented here demonstrates the application of MRI to three different fluid systems: (i) miscible, constant velocity flow, (ii) miscible flow with an evolving velocity profile, and (iii) immiscible flow. These three systems can be distinguished both by the type of flow (miscible or immiscible) and the type of solute. The details to follow will refer to two types of solute: passive and active. The term “passive” will be used to describe a solute whose presence has no effect on fluid hydrodynamics. A solute termed “active” perturbs local flow fields by changing the fluid viscosity as a function of the local solute concentration. In the case of miscible fluid streams, concentration and velocity mapping experiments have been carried out using NMR relaxometry and pulsed gradient spin echo (PGSE) imaging methods31 respectively. In the case of immiscible streams, individual fluid phases have been selectively imaged using chemical shift-selective methods. Velocity mapping of the immiscible flow has also been performed. The full array of experiments is summarized in Table 1. MRI Methods. In the experiments to be described, we track the diffusion of a paramagnetic solute whose presence enhances the relaxation rate of 1H nuclei in the solvent, water. A quantitative map of the concentration of the solute is obtained indirectly via probing the spin-lattice relaxation time constant (T1) of the solvent nuclei. T1 maps of the system were obtained by application (31) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Microscopy; Oxford University Press: Oxford, 1991.
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of a multiple-slice T1 saturation-recovery pulse sequence (Figure 1). In experiments I-III, the concentration of a passive solute was mapped using the T1-weighted multislice pulse sequence. This imaging method allows the motion of the paramagnetic solute, MnSO4, to be tracked as it is transferred across the fluid interface by diffusion. MnIISO4 enhances the relaxation rate of 1H nuclei in water such that T1 is significantly reduced even in the presence of small (∼mM) quantities of Mn2+. In the work described here, the inlet concentration of MnSO4 was 0.5 mM. At this concentration, the T1 of water is reduced from ∼3 s to 200 ms. Mn2+ is a well-known contrast agent that is used here in dilute concentrations such that the solute does not affect the viscosity or density of water and hence does not perturb the hydrodynamics of aqueous flow. Thus, it serves as a passive solute. The multislice imaging technique enables the acquisition of a series of T1 parameter maps. A Mn2+ concentration map can be extracted from the T1 map by calibrating the variation of 1H T1 associated with the solvent molecules as a function of Mn2+ concentration. This relationship between NMR relaxation rate, 1/T1, and solute concentration was obtained by performing inversion-recovery measurements of T1 using aqueous Mn2+ solutions of known concentration. The relationship between Mn2+ concentration, C, and spin-lattice relaxation time, T1, was obtained by a linear least-squares fit to the experimental data and is given by eq 1, where T1 is in seconds. Note that the relaxation time, T1,
C ) 1/9414T1 - 6.37 × 10-6 mol L-1
(1)
is frequency dependent and consequently will vary as a function of magnetic field strength. The particular correlation given in eq 1 is thus appropriate only for the 400-MHz NMR system used in this study. The multislice T1 saturation-recovery pulse sequence was used to acquire parameter maps of eight axial slices regularly spaced at 1.6-mm intervals along the length of the microchannel, as indicated by the schematic in Figure 2. Each slice was 1.5 mm thick with a field of view of 1.5 mm square. A 64 × 64 matrix was acquired in each case; the data were zero-filled to 128 × 128 prior to Fourier transformation, giving an in-plane resolution of 11.7 µm × 11.7 µm. In all cases, 32 averages were acquired. Eight recovery delays with values ranging from 10 ms to 8 s were used. Thus, 64 images were acquired. The echo time was 12 ms. With these parameters, the experiment requires ∼11 h irrespective of the number of slices imaged.
along the channel, no change is expected in the flow field once it is fully developed. For this system, a single velocity map was acquired at z ) 6.4 mm. Phase-selective intensity images were obtained using a chemical shift-selective saturation pulse to selectively suppress signal from one phase. In this way, only one or the other of the two liquid phases is imaged in a given experiment.
Figure 2. Schematic of the location of axial slices. Images of eight cross-sectional (axial) slices were acquired in the concentration mapping experiments.
Intensity maps were obtained by Fourier transforming the NMR data to obtain 64 images (8 images for each of 8 positions along the microchannel). Signal intensity in each pixel was then fitted to the following model as a function of recovery time:
I ) I0(1 - exp(-t/T1))
(2)
where I0 is a fitting parameter representing the theoretical signal intensity that would result from fully recovered magnetization, t is the timesafter saturationsat which the image has been acquired (i.e., the recovery time), and T1 is the relaxation time characteristic of fluid in that pixel. Once T1 maps have been obtained, concentration maps can be calculated using eq 1. A PGSE sequence31 was used to acquire 2D velocity mapss transverse to the direction of superficial flowsfor each of the Y-channel experiments. These were acquired from a 2-mm slice with a square FOV of 1.5 mm × 1.5 mm. A 64 × 64 matrix was again acquired in each case; the data were zero-filled to 128 × 128 prior to Fourier transformation, giving an in-plane resolution of 11.7 µm × 11.7 µm. Two flow encoding steps were used. A total of 32 averages was acquired with a repetition time of 500 ms, giving an overall experiment duration of 35 min. In each experiment, δ, ∆, and the gradient increment were chosen to prevent signal aliasing. In experiment I (aqueous solutions, passive solute only), a velocity map was acquired at position z ) 6.4 mm along the microchannel. To ensure that the flow was fully developed, this position was selected such that it lay well beyond the estimated entry length9 of ∼500 µm. In experiments II and III (aqueous solutions, passive and active solutes), flow maps were acquired at three locationssnamely at z ) 3.2, 6.4, and 11.2 mm (see Figure 2). As the inlet streams are miscible, diffusion of the active solute is expected to cause local viscosity to vary with position along the channel; by mapping velocity at multiple positions, it is possible to study the manner in which mass transfer perturbs the hydrodynamics of the system. The concentration of Mn2+ was mapped at eight different positions along the microchannel for experiments I-III. In experiment IV, the two fluid phases are immiscible; hence, no diffusive mixing is observed. As the composition of the fluid streams does not change with position
RESULTS AND DISCUSSION Experiment I: Diffusive Mixing of a Passive Solute. Concentration maps and a velocity map of the constant viscosity aqueous system are shown in Figure 3. Note that the concentration maps are inherently noisier at high ion concentrations. This is because error in the T1 measurement represents a significant part of the very short (∼10 ms) relaxation times characteristic of the higher ion concentrations (i.e., the C versus T1 function is steep in this region). Due to experimental variation in microfabrication and partial volume effects in the magnetic resonance image, the apparent dimensions of the microfluidic device vary somewhat from the intended design. Experiments II and III: Counterdiffusion of a Passive and an Active Solute. In these experiments, the inlet streams have equal flow rates, but differ in their hydrodynamic properties. The viscosity of the Mn2+-free stream has been increased by the introduction of glycerol. Panels A and B in Figure 4 are MRI velocity maps acquired at three different locations along the length of the channelsnamely at 3.2, 6.4, and 11.2 mm from the Y-piece inlets. The flow fields in this case are not parabolic but instead exhibit almost a teardrop shape. In the case of 10 vol % glycerol, it is clear that the shape of the flow field changes as glycerol diffuses across the fluid interface. At the top of the channel, little mixing has occurred and a difference in velocities of the two streams is clearly observed. As flow continues down the channel, the fluid interdiffusion region becomes increasingly disperse and the flow field becomes increasingly homogeneoussmoving away from a teardrop shape and toward a symmetric profile like that shown in Figure 3. Where 20 vol % glycerol has been used, the difference in flow velocities near the top of the channel is more pronounced. The flow images indicate a velocity gradient across the microchannel; the more viscous phase flows more slowly than the phase containing a passive solute. Conservation of mass requires that these fluid phases must then occupy different portions of the channel cross section. As the two inlet streams are of equal flow rate, the aqueous solution of glycerol must occupy a greater fraction of the channel.9,32 As a result, the nominal diffusion path for Mn2+ in the second liquid phase (which occupies a smaller part of the channel) is increased. In the absence of other variations, the solute would be expected to take a longer time to reach the opposite channel wall. Thus, one might expect the presence of glycerol to decrease the efficiency of mixing in this systemswith the retarding effect becoming increasingly evident with higher concentrations of the viscous solute. However, the opposite effect is observed. The MRI concentrations maps for experiments II (10 vol % glycerol) and III (20 vol % glycerol) are shown in Figure 5A and B, respectively. In experiment III, the concentration of glycerol in the inlet stream is twice that in (32) Stiles, P. J.; Fletcher, D. F. Lab Chip 2004, 4, 121-124.
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Figure 3. (A) Concentration maps for the diffusive mixing of aqueous MnSO4 and deionized water in a microchannel. Maps show Mn2+ concentration as a function of position in the direction of flow. Inlet streams 1 and 2 are on the right and left, respectively. (B) Velocity map of flow through the microchannel. (C) Axial velocity as a function of position in x, vz(x), at position y ) 125 µm (z ) 6.4 mm). A second-order polynomial fit to the data has been provided as a visual guide.
Figure 4. Velocity maps for flow of miscible streams of differing viscosities. Inlet streams 1 and 2 are on the right and left, respectively. (A) 10 and (B) 20 vol % glycerol.
experiment II; yet the progress in Mn2+ across the channel is more rapid. This occurs as a direct consequence of residence time effects. The presence of glycerol increases local viscosity and causes fluid to flow more slowly (while occupying a greater part of the channel cross section as demanded by continuity). This slower-moving fluid experiences a longer residence time in the channel. Consequently, there is a longer time frame in which diffusion can occur. Thus, the presence of glycerol enhances the extent of diffusive mixing that occurs in the microchannel. The enhancement of mixing increases with higher concentrations of glycerol. 6132
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Experiment IV: Immiscible Flow. Panels A and B in Figure 6 are phase-selective spin echo images of immiscible fluids in the microchannel. The difference in signal intensities associated with the two phases is related to their different nuclear spin densities and differences in their NMR properties. In image A, the water resonance has been selectively saturated such that NMR signal originates only from the oil. The reverse applies to (B), with only the aqueous phase being imaged. Using such an approach, it would be possible to visualize flow in systems where twisting and trapping occur (i.e., one phase enveloping another either partially or completely). In this work, no deliberate effort has been made to manipulate the wetting characteristics of the microchannel surfaces. The channel has two SU-8 walls in its narrower dimension and one wall each of laminate and glass in the diffusion dimension. Glass tends to be inherently hydrophilic, while SU-8 is intrinsically hydrophobic.33 However, the behaviors of both glass and the photoresist can be altered by chemical treatment. The glass, photoresist, and laminate surfaces yielded by the fabrication process employed here were observed to exhibit a neutral wettability. Hence, the wetting behavior in this system is not expected to introduce an obvious asymmetry in the flow geometry. Indeed, the oil/water interface appears flat. The images of Figure 6 show clearly that the less viscous organic phase occupies a smaller part of the channel cross section than the more viscous aqueous phase. The flow rates of the two phases are equal, so the fluid velocities differ as shown in Figure 6C and D. The water velocity peaks at just below 40 mm s-1 at the fluid interface, while the PDMS exhibits a maximum velocity of 43 mm s-1 at a point central to the organic stream. These data are consistent with the velocity distributions predicted by analysis based on momentum (33) Zhang, J.; Zhou, W. X.; Chan-Park, M. B.; Conner, S. R. J. Electrochem. Soc. 2005, 152, C716-C721.
Figure 5. Concentration maps for the diffusive mixing of aqueous MnSO4 and aqueous solutions of glycerol. Inlet streams 1 and 2 are on the right and left, respectively. (A) 10 and (B) 20 vol % glycerol.
inlet streams used in the present experiments (i.e., 0.89 and 0.82 cP, or µ1 ) 1.1µ2), these features are not predicted; instead, a nearly parabolic profile is obtained. This discrepancy between prediction and experimental data may lie in the need for wetting and surface tension effects to be included in the analysis. A more detailed comparison of the velocity fields obtained using MRI with the results of theoretical analysis and numerical simulations is ongoing.
Figure 6. Images of multiphase, immiscible flow through the microchannel. Inlet streams 1 and 2 are on the right and left, respectively. (A) Selective saturation of the water resonance has been used in order to image the PDMS independently. (B) Selective saturation of the PDMS resonance was used to image the aqueous stream independently. (C) Velocity map of PDMS flow. (D) Velocity map of aqueous flow.
conservation for adjacent flow of immiscible fluids.34 Solving the momentum balance for two inlet streams of equal flow rate and differing viscosity of µ1 ) 4µ2 (where µ1 and µ2 are the viscosities of the two adjacently flowing liquids), all the essential features observed in the MRI data are predicted. In particular, the analysis predicts the following: (i) the shift of the interface away from x ) 250 µm (i.e., the middle of the channel), (ii) the more viscous fluid has maximum velocity at the interface, and (iii) the less viscous fluid exhibits a well-defined maximum in velocity in its flow profile. However, when considering the viscosities of the two (34) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; John Wiley & Sons, Inc.: NewYork, 2002.
CONCLUSIONS In this work, a single technology has been used to perform both concentration and flow mapping of a microfluidic device. The device studied had a low aspect ratio that would represent an unfavorable geometry when applying visualization techniques that produce en face images. Magnetic resonance imaging was used to map the cross section of the device. Concentration maps were obtained for a dilute solute that did not perturb local flow fields as it moved by diffusive processes into an adjacently flowing stream. Corresponding velocity images showed clearly the symmetric nature of laminar flow of a single fluid phase through a rectangular channel. The butterfly effect resulting from laminar flow was captured in the NMR concentration maps of diffusive mixing of miscible streams. Furthermore, MRI was used to study the coupling of mass transfer and hydrodynamics by imaging the evolving concentration and flow fields in a system where fluid viscosity was a function of local solute concentration. In this system, the flow field was asymmetric and evolved in three dimensions. MRI captures the features of this evolution in a way that many optical techniques cannot. Finally, two-phase immiscible flows have been imaged in cross sections showing the shape of Analytical Chemistry, Vol. 79, No. 16, August 15, 2007
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an oil/water interface and the differential velocities of the two phases. The phenomenon of unequal phase distribution in the channel cross section is clearly demonstrated. Note that the properties of the fluids need not be perturbed in any way to achieve these measurements. No tracers were used, and the system need not be optically transparent. Although MRI has its weaknesses (e.g., possibly lengthy acquisition times and lower spatial resolution compared to some optical methods), it is a versatile tool that has been shown to have relevant applications in the field of microfluidics.
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ACKNOWLEDGMENT We acknowledge EPSRC (grants GR/S20789/01 and GR/ P02776/01) and Syngenta Ltd. (CASE award 03301173) for financial support for aspects of the work.
Received for review February 21, 2007. Accepted May 31, 2007. AC070364A
