Anal. Chem. 2003, 75, 1387-1392
Mapping Fast Flows over Micrometer-Length Scales Using Flow-Tagging Velocimetry and Single-Molecule Detection J. Patrick Shelby and Daniel T. Chiu*
Department of Chemistry, University of Washington, Seattle, Washington 98195-1700
This paper describes a technique of characterizing microfluidic flow profiles from slow laminar flow to fast nearturbulent flow. Using a photo-activated fluorophore, nanosecond-duration photolysis pulses from a Nitrogen laser, and high-sensitivity single-molecule detection with Ar+ laser excitation, we report the measurement of flow speeds up to 47 m/s in a 33-µm-wide straight channel and the mapping of flow profiles in a 55-µm-wide microchamber. Sensitive single-molecule detection is necessary both because of the short time delay (submicrosecond) between laser photolysis and fluorescence detection and the fast transit times (as low as 10 ns) of the fluorescent molecules across the diffraction-limited beam waist of the Ar+ laser focus. This technique permits the high-resolution three-dimensional mapping and analysis of a wide range of velocity profiles in confined spaces that measure a few micrometers in dimension. Microfluidic devices are gaining popularity for a wide range of applications, from the development of microscale chemical analyses1-3 to the study of biological processes.4,5 Although most microfluidic applications, such as capillary electrophoresis,6 employ low-velocity laminar flow, a growing number of chip-based analyses, such as flow cytometry,7 can involve pressure-driven flow that has the potential to reach flow rates in the meter per second range in channels having characteristic length scales from a few to hundreds of micrometers. Because fluid flow in a microchannel can often exhibit unexpected behavior as a result of surface or topographical effects,8-10 a sensitive technique is required to elucidate flow properties under a broad range of flow conditions and channel geometries. Although nonintrusive velocimetry techniques have been utilized previously,11-13 they usually have * To whom correspondence should be addressed. (1) Reyes, D. R.; Lossitidis, D.; Auroux, P.; Manz, A. Anal. Chem. 2002, 74, 2623-2636. (2) Auroux, P.; Lossitidis, D.; Reyes, D. R.; Manz, A. Anal. Chem. 2002, 74, 2637-2652. (3) Thorsen, T.; Maerkl, S. J.; Quake, S. R. Science 2002, 298, 580-584. (4) Whitesides, G. M.; Ostuni, E.; Takayama, S.; Jiang, X.; Ingber, D. E. Annu. Rev. Biomend. Eng. 2001, 3, 335-373. (5) Chiu, D. T. Curr. Opin. Chem. Biol. 2001, 5, 609-612. (6) Paegel, B. M.; Emrich, C. A.; Weyemayer, G. J.; Scherer, J. R.; Mathies, R. A. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 574-579. (7) Fu, A. Y.; Chou, H. P.; Spence, C.; Arnold, F. H.; Quake, S. R. Anal. Chem. 2002, 74, 2451-2457. (8) Stone, H. A.; Kim, S. AIChE J. 2001, 47, 1250-1254. (9) Ho, C.-M.; Tai, Y.-C. Annu. Rev. Fluid Mech. 1998, 30, 579-612. (10) Stroock, A. D.; Dertinger, S. K. W.; Armand, A.; Mezic´, I.; Stone, H. A.; Whitesides, G. M. Science 2002, 295, 647-651. 10.1021/ac026275+ CCC: $25.00 Published on Web 02/13/2003
© 2003 American Chemical Society
limited spatial resolution and are not applicable to very fast flows. In addition, it is usually difficult to use these techniques to obtain a true high-resolution three-dimensional image of the flow profile. A discussion of flow tracking must begin with particle image velocimetry (PIV), because it has been widely used in many applications in fluid mechanics, including microfluidics.14-17 By mapping particle trajectories and by assuming the particles trace out the flow-lines, a detailed picture of the flow field can be constructed. An implicit assumption made in PIV is that because the particle size is small in comparison with the length scale of the flow, the influence of the particle on the fluid flow is negligible. Although this assumption is valid for most macroscale fluidic studies, its validity for microfluidics requires careful examination. We have reported that colloidal particles (e.g., 1-µm beads) in flows inside microchannels can experience a significant hydrodynamic lift, which can lead to the dynamic formation of patterns of these particles within the flow.18 This lift force originates from the deformation by the particles of the steep velocity profiles that are unique to microfluidic systems. Nonetheless, PIV has been utilized to map accurately low velocity microfluidic flows with very good spatial resolution. Nonintrusive flow tagging techniques, such as molecular tagging velocimetry (MTV)13 and flow-tagging velocimetry (FTV),11,12 in which molecules rather than particles are used to trace fluid flow, eliminate particle-induced flow disturbances. For example, phosphorescent dyes have been used to measure velocity flow profiles in fused-silica tubes that are 705 µm in diameter.13 Although this technique has been used to measure fast flow (e.g., 3.5 m/s), these measurements were made over large-length scales with low spatial resolution. Because this approach relies on the relatively long (tens of microseconds) lifetime of the triplet state and the “tagging” of molecules with an excitation laser, the range of time delays between excitation and imaging (thus, flow velocities that can be measured) is limited by the excited-state lifetime of the phosphorescent dye. In addition, the phosphorescent dyes used for these studies required deep UV (308 nm) excitation, (11) Paul, P. H.; Garguilo, M. G.; Rakestraw, D. J. Anal. Chem. 1998, 70, 24592467. (12) Lempert, W. R.; Harris, S. R. Meas. Sci. Technol. 2000, 11, 1251-1258. (13) Maynes, D.; Webb, A. R. Exp. Fluids 2002, 32, 3-15. (14) Adrian, R. J. Ann. Rev. Fluid Mech. 1991, 23, 261-304. (15) Santiago, J. G.; Wereley, S. T.; Meinhart, C. D.; Beebe, D. J.; Adrian, R. J. Exp. Fluids 1998, 25, 316-319. (16) Taylor, J. A.; Yeung, E. S. Anal. Chem. 1993, 65, 2928-2932. (17) Kwok, Y. C.; Jeffery, N. T.; Manz, A. Anal. Chem. 2001, 73, 1748-1753. (18) Lim, D. S. W.; Shelby, J. P.; Chiu, D. T., submitted.
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which limits the materials through which these measurements could be made. As an alternative to using phosphorescent dyes, caged dye techniques utilize one laser to uncage a photoactivated fluorophore (PAF) and a second laser to interrogate the resultant fluorescent dye.11,12 In many previous studies, CCD cameras were employed as the method of detection. Although the use of a CCD camera provides directly a two-dimensional image of the flow profile, its use often precludes the measurement of high flow rates (e.g., in the meter per second range). To improve the three-dimensional spatial resolution of FTV and to extend FTV for the measurement of fast flows, we applied single-molecule detection for measuring the arrival and transit times of the uncaged fluorescent dyes. In our approach, a tightly focused N2 laser beam was used to photolyze caged fluorescein, followed by detection using a diffraction-limited focus of an Ar+ laser that was displaced a few micrometers downstream from the N2 laser spot. Single-molecule sensitivity is required for measuring fast flows (meter per second) over short distances (micrometers) both because of the short delay times between uncaging and fluorescence detection and the short signal integration times that result from the rapid transit of the molecules across the submicrometer beam waist of the interrogation laser. Although single-molecule correlation spectroscopy has been applied to microfluidic flow profiling with excellent spatial resolution,19 it has been limited to low-flow conditions (25 mm/s). With our method, flow rates as high as tens of meters per second can be routinely measured. The small submicrometer foci of the lasers permit the characterization of flows over only a few micrometers, whereas the confocal geometry of our single-molecule detection scheme allows for the detailed high-resolution three-dimensional mapping of velocity profile. The distance between the photolyzing N2 laser and the interrogation Ar+ laser can be varied from a few micrometers to tens of micrometers or more, which makes possible velocity measurements both in very small, confined areas as well as over relatively long distances using the identical setup. The spatial dynamic range of this technique thus offers an improvement over existing methods while maintaining the high single-molecule sensitivity required to measure fast flows that are tens of meters per second. EXPERIMENTAL SECTION Fabrication of Test Channels. To demonstrate the potentials and limitations of the technique, we studied flow profiles inside two different channel geometries: (1) a simple rectangular channel, 33 µm (width) × 37 µm (depth) × 2 cm (length) (Figure 1A), in which we measured laminar flows of widely varying velocities, and (2) a straight (2 cm length) channel with an attached 55-µm (diagonal) diamond-shaped microchamber in which we mapped the velocity profiles of a recirculation flow (Figure 1B). The test channels were fabricated in poly(dimethylsiloxane) (PDMS) using rapid prototyping, which has been described in detail elsewhere.20,21 Briefly, a high-resolution trans(19) Go ¨sch, M.; Blom, H.; Holm, J.; Heino, T.; Rigler, R. Anal. Chem. 2000, 72, 3260-3265. (20) McDonald, J. C.; Duffy, D. C.; Anderson, J. R.; Chiu, D. T.; Wu, H.; Whitesides, G. M. Electrophoresis 2000, 21, 27-40. (21) Anderson, J. R.; Chiu, D. T.; McDonald, J. C.; Jackman, R. J.; Cherniavskaya, O.; Wu, H.; Whitesides, S.; Whitesides, G. M. Anal. Chem. 2000, 72, 31583164.
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Figure 1. Schematic representations of (A) a simple 33-µm-wide by 37-µm-deep straight channel, and (B) a 55-µm diagonal diamondshaped microchamber. The main channel length in each case is ∼2 cm. (A) Flow velocities were measured by displacing the Ar+ probe laser 50 µm downstream from the N2 photolysis laser. A single ∼3 ns pulse was used for uncaging. The insets are successive frames showing the development of a parabolic flow profile inside the channel; the velocity was ∼50 µm/s. (B) Velocity profiles inside the diamondshaped microchamber were obtained using a 5-µm displacement between the laser foci. The inset shows the flow profile traced out using 1-µm fluorescent beads. The main straight channel velocity was ∼5 m/s, which corresponded to a rotational velocity inside the chamber of ∼1 m/s. sp, single pulse; cw, continuous wave. Axes denoting the direction of flow in x, y, and z coordinates are shown adjacent to each representation.
parency mask was generated from a CAD file and printed at a resolution of 3600 dpi. The mask was a negative of the channel design and was used in contact photolithography with SU-8 photoresist (MicroChem, Newton, MA) to create a negative “master”, which consisted of bas-relief features of SU-8 on a silicone wafer. From the master, PDMS channels were molded and then sealed irreversibly to a borosilicate glass coverslip by oxidizing the PDMS surface in oxygen plasma. To reduce backpressure, two-step lithography was sometimes utilized to produce wide, thick entry/exit channels that fed narrow, thin test channels containing different morphological features. Access holes to the channels were formed using a punch made from a 21-gauge needle. Polyethylene tubing (PE20) was then inserted into the access holes, which were slightly smaller than the outer diameter of the tubing, to form a pressure seal between the tubing and the hole. The tubing was attached to a 3-mL syringe held in a syringe pump (kd Scientific, New Hope, PA) for driving the fluid flow. Photo-Activated Fluorophore. The caged dye used to test the flow velocity was CMNB-caged fluorescein (Molecular Probes, Eugene, OR). Solutions of caged fluorescein were prepared in 100mM sodium borate (pH 9.3). A dilute solution (0.3- mg/mL) was
Figure 2. Schematic representation illustrating the configuration of our optical setup. The inset shows an example of a single-molecule trace obtained with this setup. The incident power of the Ar+ laser was 5 mW prior to the objective, and the pulse energy of the N2 laser was 45 µJ prior to the objective. ND, neutral density; BP, band-pass; SPCM, single-photon-counting module; MCS, multichannel scalar.
used for profiling relatively slow flows (on the order of cm/s). This concentration of caged dye was further diluted to ∼ 0.1-mg/ mL for measuring fast flows (on the order of meters per second). This decrease in concentration lowered background and increased the signal-to-noise ratio. Arrangement of Optical Setup. Figure 2 shows the arrangement of the lasers and detectors with respect to the sample. A CCD camera was used to image and to measure the distance between the laser foci. The signal obtained from the uncaged fluorescent dyes upon laser excitation was collected by a 100× objective, directed through a 75-µm pinhole to reject out-of-plane light, and passed through a band-pass filter (500-580-nm) onto an avalanche photodiode. The inset in Figure 2 shows an example of a single-molecule trace of 10 pM carboxyrhodamine in phosphatebuffered saline solution obtained with this optical configuration. Photolysis with Nitrogen Laser. A single pulse from a N2 laser (Laser Science Inc., Franklin, MA) was triggered by and synchronized with single-molecule detection using a multichannel scalar (MCS) card (PerkinElmer Instruments, Oak Ridge, TN). The N2 laser pulse was focused into a narrow line that was ∼2 µm wide and ∼10 µm long by passing it through an adjustable slit placed in the N2 beam path prior to entering the microscope (Figure 2). The profile of the N2 focus was imaged by recording the fluorescence from a 25 mM solution of fluorescein (Molecular Probes, Eugene, OR) after the solution was irradiated by the N2 laser pulses. We have imaged the fluorescence both from fluorescein freely diffusing in solution and from surface immobilized fluorescein at varying laser powers. Pixel analysis of the resultant fluorescence image of the laser line yielded a Gaussian distribution of light intensity. Thus, all data recorded for velocity testing were fitted to a Gaussian function. A measurable dead time of 700 ( 50 ns exists between the MCS trigger of the N2 laser pulse and the detection and collection of fluorescence signal by the avalanche photodiode and MCS. To account for this time delay, we subtracted it from all velocity measurements.
Single-Molecule Detection with Ar+ Laser and Avalanche Photodiode. The 488-nm line of a continuous-wave Ar+ laser (Spectra-Physics, Mountain View, CA) was used to excite the photolyzed dye. The diffraction-limited focus spot was positioned a calibrated distance from the focused N2 laser line, which was 5 µm in the diamond-shaped microchamber and 50 µm in the straight channel. As the uncaged dye passed through the Ar+ laser focus, the dyes were repeatedly excited, and the resultant fluorescence photons were collected, then detected, by an avalanche photodiode (Perkin-Elmer, Fremont, CA). The N2induced fluorescence emission and the back-reflected Ar+ laser light were also relayed onto a CCD camera for monitoring their precise locations on a dimensionally calibrated video screen. The maximum distance between the photolysis N2 laser line and the Ar+ laser focus was limited by the range of the video screen, which was ∼100 µm for our experimental setup. The minimum distance was limited by the measurable spacing between the laser foci, which was ∼1 µm. The signal integration time was varied between 1 µs and 100 µs, depending on the flow velocity. The raw signal from the MCS card was plotted and processed using Kaleidagraph, including fitting the signal to a Gaussian function. The time it takes the photolyzed plug of fluorescent dyes to travel from the N2 laser line to the Ar+ focus was obtained from this Gaussian fit. To corroborate experimental results, we used MATLAB (The Mathworks Inc., Natick, MA) and FEMLAB software (COSMOL Inc., Burlington, MA) to obtain simulated results based upon conditions identical to those used experimentally. RESULTS AND DISCUSSION Photolysis of Caged Fluorescein in Microchannels. Figure 1A shows both schematic and fluorescence images (inset) of a developing parabolic pressure-driven flow inside the straight channel; a 50-µm spacing between the N2 and Ar+ laser foci was used for measuring the flow velocities. Figure 1B shows a slightly more complex recirculation flow pattern, which was visualized by tracing the flow with 1-µm-diameter fluorescent polystyrene beads (inset). This fluid recirculation was caused by detachment of main channel flow at the opening of the microchamber. We used a displacement of 5 µm between the N2 and Ar+ foci to probe the velocity distributions inside this recirculation flow. We have observed a number of surprising and interesting fluidic phenomena within the diamond-shaped microstructure shown in Figure 1B, such as the spontaneous formation of patterns of recirculating colloidal particles and the presence of high centrifugal accelerations. The main disadvantage of using caged dyes, as noted by a number of researchers,12,13,22 is the time delay imposed by the photochemical activation of the dye molecule, because it takes a finite amount of time for the uncaging event to occur. The reported photolysis time of caged glycine using a 337-nm laser pulse, for example, is 3 µs.23 For caged fluorescein, however, the uncaging time is on the order of a few milliseconds.12,22 The reported minimum time delay used between photolysis and detection for caged fluorescein was ∼200 µs.12 The delay times between photolysis and detection for our velocity measurements, however, can be often as short as a few microseconds, since the foci of the (22) Lempert, W. R.; Magee, K.; Ronney, K.; Gee, R. R.; Haughland, R. P. Exp. Fluids 1995, 18, 249-257. (23) Ramesh, D.; Wieboldt, R.; Niu, L.; Carpenter, B. K.; Hess, G. P. Proc. Natl. Acad. Sci. 1993, 90, 11074-11078.
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two lasers are only a few micrometers apart. Because the uncaging event follows a probabilistic distribution, a very small population of caged dye molecules can be photolyzed within this short time period. The need to detect this small population of uncaged dyes is one reason a high sensitivity single-molecule approach is required. The maximum measurable velocity can be increased easily, therefore, by increasing the distance between the laser foci and, thereby, the delay time between photolysis and detection. The drawback to this strategy for accessing fast flows is the resultant sacrifice in spatial resolution and the inability to probe velocity profiles in micrometer-sized confined spaces. Using a 5-µm separation between the photolysis and detection laser, we could measure rotational velocities up to meters per second within the diamond-shaped microchamber (Figure 1B). Performance of Optical Setup. Two factors limit our ability to measure very fast flows over small distances at a given concentration of dye: (1) the extremely small populations of uncaged dyes, owing to the short time delay between photolysis and detection, and (2) the short signal integration times caused by the fast transit times of the molecules across the diffractionlimited beam waist of the laser focus. Using caged fluorescein, we reached our limit of detection when the time delay between photolysis and detection was ∼0.3 µs. For a 50-µm separation distance between the two lasers, a 1-µs time delay would correspond to a flow rate of 50 m/s and to a transit time of ∼10 ns across the ∼500 nm width of the single-molecule probe volume. Figure 3A shows the raw signal and the corresponding Gaussian fit obtained by measuring the flow in a 33-µm × 37-µm straight channel using a separation distance of 5 µm between the N2 and Ar+ lasers. The inset shows a CCD image of the focused N2 line (∼2 µm wide) and Ar+ spot (∼0.5 µm in diameter). By calibrating the system and by measuring the time it takes the plug of fluorescent dyes to travel the 5-µm separation distance as well as the 0.5-µm beam waist of the Ar+ focus, we calculated the flow rate to be 11 ( 1 cm/s (U ) d/t, where U is the maximum parabolic velocity, d is the laser displacement, and t is the time delay between photolysis and detection). Our system was calibrated to use the time it takes the fluorescence signal to reach half of its maximum intensity as the delay time for the fluorescent dyes to travel the 5-µm separation distance. The presence of the large slope at half-height in comparison with the slope at maximum intensity makes locating the half-height more facile and accurate. Figure 3B shows the measurement of a fast flow, which is approaching our limit of detection, under identical conditions as in Figure 3A. The fluorescence intensity reached its maximum intensity at 3 µs and its half-maximum value, at 1 µs. Because of the 700-ns dead time between the MCS trigger, which defines the start time, and the actual output of the N2 laser pulse, the travel time between the photolysis and detection laser is only 300 ns, which corresponds to a flow velocity of 16 ( 3 m/s. The uncertainty in this case came mostly from the dead time in triggering the N2 laser, which can be significantly reduced by using a more precise scheme for triggering the photolysis laser or by increasing the delay time between photolysis and detection. In general, the two significant contributors to error are (1) the measurement of distance, where the calibration of distance was accomplished using polystyrene beads (10 ( 0.1 µm); and (2) 1390 Analytical Chemistry, Vol. 75, No. 6, March 15, 2003
Figure 3. (A) A representative raw signal and the corresponding Gaussian fit are shown for a single measurement at a flow rate of 11 cm/s. The vertical arrow indicates the point at which the time interval was taken. The inset is a CCD image showing the position of the pulsed N2 laser line with respect to the Ar+ laser focus; d denotes the displacement between the two lasers. The N2 laser was triggered by the multichannel scalar (MCS) data acquisition card, which simultaneously started to record the arrival of fluorescent photons on the detector as a function of time. (B) Raw data and the corresponding Gaussian fit obtained for a fast flow (16 m/s) near the limit of our detection. The laser spacing was 5 µm, with a corresponding time delay between photolysis and detection of 300 ns and a transit time across the probe volume of 30 ns.
the measurement of time, where error is influenced by uncertainty in dead time (700 ( 50 ns) and error associated with curve fit (in general, data points varied from the plotted curve by an average of 5% or less). The cumulative effect of both of the components is the stated error (cumulative error e(U) ) [(e(d)/d)2 + (e(t)/ t)2]1/2U, where e(d) is the error in laser displacement and e(t) is error in the determination of time). Velocity Profiles inside Microchannels. Using the same test channel as in Figure 3, but with a spacing of 50 µm between the two lasers, we measured the peak velocities of the parabolic flow profile as a function of volumetric flow rate (Figure 4). The lower inset shows a color map of the velocity distribution inside the microchannel obtained from solving the Navier-Stokes equations numerically using FEMLAB. As expected, the fluid velocity in the small channel (red) is considerably faster than the larger main channel velocities (dark blue). The resulting plots are linear from low (millimeters per second) through high (meters per second)
Figure 4. Plot of measured maximum velocities (tip of the parabolic flow profile) as a function of volumetric flow rates delivered via the syringe pump for a 33-µm × 37-µm channel. (O) denotes experimental measurements, and (b) are simulated velocities. The lower inset shows the simulated velocity profile. P marks the position of photolysis, and D, the position of detection. The upper inset shows a loglog plot of the velocity as a function of volumetric flow rate.
velocities. The measured velocities generally match the simulated values to within ∼(5%. The fast flows (tens of meters per second) measured by this method greatly exceed that of current techniques, and the dynamic range demonstrated in this approach is especially pertinent for applications in microfluidics in which flow velocities can vary widely, from micrometers per second (e.g., near solid boundary) to many meters per second over only a few micrometers. The confocal nature of the single-molecule detection scheme permits the three-dimensional mapping of the velocity profile within small, confined volumes. Although mapping the velocity along the direction of flow was straightforward using this method, there were minimal velocity changes in this direction under the steady state, laminar flows that were present in the microchannels we have used. In our experiments, we have therefore focused on the mapping of velocity variations in the plane orthogonal to the flow. Figure 5 profiles the velocity distribution inside a diamond chamber with a 55-µm diagonal length, whereas Figure 6 shows a z-direction velocity profile of a 33-µm by 37-µm straight channel. We used a displacement of 5 µm between the two lasers for the measurements presented in both of these figures. Figure 5A shows the velocity profile along the x direction, and Figure 5B, along the y direction. The no-slip condition imposed at the boundary of the chamber forces the velocity to approach 0 at the wall. The velocity increases from near 0 to a maximum value ∼10 micrometers into the chamber along the x plane and ∼5 micrometers into the chamber along the y plane. The velocity profile then decreases and reaches a minimum near the center of rotation before rising again to peak at ∼40 micrometers into the chamber along the x direction and at ∼25 micrometers in the y direction. Mapping the velocity along each plane was accomplished by translating the microscope stage and, thus, the positions of the N2 and Ar+ laser spots to a new location in the chamber without perturbing the relative distance between the laser spots. Figure 5C,D is two-dimensional simulation results
Figure 5. Velocity profiles inside a diamond-shaped microcavity. (A) and (B) are experimentally measured velocity profiles along two orthogonal directions (x and y) in the plane of the microcavity. The solid arrow in the main channel indicates flow direction, and the open arrow in the chamber indicates direction of measurement. (C) and (D) are two-dimensional simulation results obtained using conditions identical to the experiments for (A) and (B). (E) The recirculation flow of the microvortex causes the repeated crossing of the uncaged dye through the Ar+ probe volume, thereby giving rise to multiple detected peaks. The main channel velocity for each measurement was 3 m/s.
(with FEMLAB) for the x and y directions under identical conditions as Figure 5A,B. The overall velocity profiles obtained in our simulation matches well the experimentally measured profiles. Figure 5E shows the repeated detection of the plug of uncaged fluorescein, which arises from the rotational nature of the recirculation flow inside the microcavity. The peak intensity (or the integrated peak area) initially increases with each additional rotation, owing to the increased delay time between photolysis and detection. The rotational frequency, which is ∼1400 Hz or ∼0.7 ms per rotation, is on the same time scale (ms) as the reported photolysis times for caged fluorescein. Consistent with the reported uncaging times, the integrated peak area reaches a maximum value at around 1.5-2.5 ms. The peaks get progressively broader because of molecular diffusion, the value (diffusion coefficient) of which can be extracted from the series of peaks. Analytical Chemistry, Vol. 75, No. 6, March 15, 2003
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Figure 6. z direction flow profile measured for a straight channel. The data points along z were obtained by adjusting the microscopefocusing knob. The simulated profile is represented by the solid line.
In addition to diffusion, there also exists exchange between the solution contained in the microcavity and the main channel, which causes the eventual disappearance of the uncaged dye molecules. Figure 6 shows a parabolic flow profile taken in the z direction of the channel. The profile along the z axis was taken by parking the lasers in a fixed x-y location while adjusting the microscope focusing knob, which has submicrometer resolution. The solid line represents the simulated profile. Because the width of the 33-µm channel is near the resolution limit of our mask-making procedure using transparency films, there are some localized irregularities in the cross section of the microchannel. The z direction velocity profile obtained experimentally, however, was not significantly altered as a result of these irregularities. Overall, we found varying the dimensions and regularities of the cross section of the microchannel in our simulation does not significantly alter or shift the shape of the resultant simulated velocity profile, which also agrees well with our experimental observations. Spatial and Temporal Resolutions. The spatial resolution of this technique is in principle defined by the width of the diffraction-limited N2 laser line and the Ar+ focus spot, both of which can be as small as a few hundred nanometers. In practice, however, we are constrained by our ability to measure accurately the spacing between the two lasers on our video screen (∼1-µm). Although a number of nonvisual methods may be devised to calibrate this distance, it may be difficult to measure submicrometer distances precisely. The spatial resolution in the z direction is limited by the height of the confocal probe volume, which is also ∼1 µm. At a spacing of 5 µm between the lasers, we were able to accurately measure flows that vary from micrometers per second (by using a high-molecular-weight dextran conjugate of caged fluorescein) to many meters per second. The time required to determine a certain flow rate is determined by the delay time between photolysis and detection, which ranges from ∼300 ns to ∼1 ms, depending on the flow rate and the spacing between photolysis and detection. Because of our ability to vary this spacing down to ∼1 µm, uncertainties associated with molecular diffusion are usually negligible at moderate flow rates (e.g., cm/s) that are common for applications in microfluidics. (24) Nie, S.; Chiu, D. T.; Zare, R. N. Anal. Chem. 1995, 67, 2849-2857.
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The temporal resolution of this technique, which defines the measurable flow velocities, is determined by the sensitivity of the system. The limiting factor in sensitivity is the time delay between photolysis and detection, which must be greater than ∼0.3 µs under our experimental conditions with caged fluorescein. At a separation distance of 5 µm, a 0.3-µs time delay corresponds to a flow velocity of ∼16 m/s. To illustrate the necessity for singlemolecule detection in measuring fast flows, we estimate the percentage of caged fluorescein that was uncaged during a ∼0.3 µs time delay between photolysis and detection (Figure 3B). For a 0.1 mg/mL solution (∼0.1 mM) of caged fluorescein used in our experiments, the number of caged fluorescein molecules estimated to transit the detection probe volume is ∼120 × 103, with a transit time for each molecule of ∼30 ns. If we assume a 2% detection efficiency24 and a ∼4-ns excited-state lifetime, the number of uncaged fluorescein molecules, estimated from our integrated counts of ∼25 photons, is ∼180. The estimated percentage of uncaged fluorescein is thus ∼0.15% at 0.3 µs after photolysis. To measure faster flows, therefore, we must either sacrifice spatial resolution by increasing the separation distance between the lasers or use a caged dye with a faster uncaging time than caged fluorescein. CONCLUSIONS This paper describes a method of characterizing fluid flow within the tiny confines of microfluidic channels on the basis of the principles of flow tagging velocimetry and single-molecule detection. The advantages of this method are (1) the ability to measure flows over a wide dynamic range, from µm/s to tens of m/s, and (2) the capability for obtaining three-dimensional velocity maps with micrometer-scale spatial resolution, which is made possible by both the tight laser foci and the confocal nature of the detection scheme. This spatial resolution is especially pertinent for understanding microfluidic applications that involve complex flows within small micrometer-sized regions, such as the formation of recirculation flows inside a microchamber. The main drawback of this approach is the serial nature by which a velocity map must be created because only one velocity value is measured at a time. In principle, however, this serial mapping can be automated using motorized microscope stages and focusing mechanisms. With intense interest in micro- and nanofluidics and with the rapid development and integration of diverse functionalities onto these chip-based devices, a versatile and accurate flow mapping technique is anticipated to play a critical role in understanding the fluidic phenomena that may arise during these developments. ACKNOWLEDGMENT We thank David Lim and Jason Kuo for assistance with the microfluidic simulations. J.P.S. acknowledges support from the University of Washington Center for Nanotechnology for an IGERT graduate fellowship. This research was funded by NIH (GM 65293-01 and DA 16249-01), NSF (0135109), and a starter grant from the Dreyfus Foundation (NF-00-077).
Received for review October 31, 2002. Accepted January 14, 2003. AC026275+
