Anal. Chem. 2005, 77, 4323-4328
Accelerated Particle Electrophoretic Motion and Separation in Converging-Diverging Microchannels Xiangchun Xuan, Bo Xu, and Dongqing Li*
Department of Mechanical & Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, Ontario, Canada M5S 3G8
Accelerated particle electrophoretic motions were visualized in converging-diverging microchannels on poly(dimethylsiloxane) chips. The accelerated particle electrophoretic separation is highly desirable in on-chip flow cytometry and high-speed electrophoresis. The effects of electric field, particle size, particle trajectory, and channel structure on the particle electrophoretic motion are examined. We find that the ratio of the particle velocity in the throat to that in the straight channel is significantly lower than their cross-sectional area ratio. This discrepancy may be attributed to the locally higher electric field around the two poles of a particle, as compared to other regions inside the microchannel. We also find that the particle velocity ratio is increased for smaller particles moving through symmetric converging-diverging channels under lower electric fields. These variations may be attributed to the negative dielectrophoretic force that is generated by the nonuniform electric field in the converging-diverging section. In addition, we find that particle trajectory has insignificant influences on the maximum velocity ratio obtained in the throat. Lab-on-a-chip devices have become a convenient platform to execute liquid-phase analysis for chemical and biochemical assays.1-5 On such microchips, a variety of electrophoretic separation techniques have been implemented, for example, capillary electrophoresis,6 capillary gel electrophoresis,7 free-flow electrophoresis,8 and electrochromatography.9 In all of these techniques, reduction of analysis time is always one of the key objectives. The simplest approach to achieving faster separations * Corresponding author. Phone: 416-978-1282. Fax: 416-978-7753. E-mail:
[email protected]. (1) Reyes, D. R.; Iossifidis, D.; Aurous, P.; Manz, A. Anal. Chem. 2002, 74, 2623-2636. (2) Stone, H. A.; Kim, S. AICHE J. 2001, 47, 1250-1254. (3) Vilkner, T.; Janasek, D.; Manz, A. Anal. Chem. 2004, 76, 2273-2285. (4) Stone, H. A.; Stroock, A. D.; Ajdari, A. Annu. Rev. Fluid Mech. 2004, 36, 381-411. (5) Verpoorte, E. Lab Chip 2003, 3, 60N-68N. (6) Harrison, D. J.; Fluri, K.; Seiler, K.; Fan, Z.; Effenhauser, C. S.; Manz, A. Science 1993, 261, 895-897. (7) Woolley, T.; Mathies, R. A. Anal. Chem. 1995, 67, 3676-3680. (8) Raymond, D. E.; Manz, A.; Widmer, H. M. Anal. Chem. 1994, 66, 28582865. (9) Slentz, B. E.; Penner, N. A.; Lugowska, E.; Regnier, F. Electrophoresis 2001, 22, 3736-3743. 10.1021/ac048216x CCC: $30.25 Published on Web 06/01/2005
© 2005 American Chemical Society
is to speed up the sample transport by applying a higher voltage drop over a given channel length. Ultimately, however, Joule heating (and, hence, the elevated liquid temperature)10,11 and the resultant sample dispersion12,13 place a practical limit on the electric field that can be used. This problem of electric-field limitations can be resolved by using extremely narrow-bore channels. Jacobson et al. first demonstrated an on-chip submillisecond electrophoresis by fabricating narrow channels for the injection valve and separation channel and wide channels for all other sections.14 As a result, the potential drop is reduced in areas not contributing to the separation so that high separation field strengths can be attained with modest applied electric potentials. A similar converging-straight-diverging capillary pulled by a micropipet puller has been successfully used to achieve microsecond electrophoresis.15 This same method has also been used to size and sort various biological entities, such as DNA molecules and Escherichia coli cells on a microfabricated device.16,17 Although narrow-bore channels minimize Joule heating effects, there arises a new problem regarding the electrophoretic motion of cells or particles in a closely fitting microchannel of varying cross section. In such a circumstance, the particle electrophoresis and the liquid electroosmosis are coupled via the electric field that is strongly distorted by the presence of particles in both the narrow straight channel and the transition regions of the converging-straight-diverging channel.18-21 For the case of microchannels of uniform cross section, particle electrophoretic motion has been theoretically studied in the vicinity of a plane wall,22,23 along (10) Xuan, X.; Sinton, D.; Li, D. Int. J. Heat Mass Trans. 2004, 47, 3145-3157. (11) Xuan, X.; Xu, B.; Sinton, D.; Li, D. Lab Chip 2004, 4, 230-236. (12) Xuan, X.; Li, D. J. Micromech. Microeng. 2004, 14, 1171-1180. (13) Xuan, X.; Li, D. J. Chromatogr., A 2005, 1064, 227-237. (14) Jacobson, S. C.; Culberston, C. T.; Daler, J. E.; Ramsey, J. M. Anal. Chem. 1998, 70, 3476-3480. (15) Plenert, M. L.; Shear, J. B. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 38533857. (16) Chou, H.; Spence, C.; Scherer, A.; Quake, S. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 11-13. (17) Fu, Y.; Spence, C.; Scherer, A.; Arnold, F. H.; Quake, S. R. Nat. Biotechnol. 1999, 17, 1109-1111. (18) Lyklemma, J. Fundamentals of Interface and Colloid Science; Academic Press: New York, 1991; Vol. 2. (19) Keh, H. J.; Anderson, J. L. J. Fluid Mech. 1985, 153, 417-439. (20) Ennis, J.; Anderson, J. L. J. Colloid Interface Sci. 1997, 185, 497-514. (21) Shugai; Carnie, S. L. J. Colloid Interface Sci. 1999, 213, 298-315. (22) Keh, H. J.; Chen, S. B. J. Fluid Mech. 1988, 194, 377-390. (23) Yariv, E.; Brenner, H. J. Fluid Mech. 2003, 484, 85-111.
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a cylindrical capillary,24-29 or in a rectangular microchannel.30 Some experiments have also been conducted to study the wall effects on particle electrophoretic motion in a cylindrical capillary. It was found that the capillary wall could either retard31 or enhance32 the particle electrophoretic motion, depending on the particle position. This phenomenon has been successfully predicted by the available theory.22,23,26,33 As to particle electrophoretic motion in channels of varying cross section, however, very little work has been reported so far. Lettieri et al. demonstrated the trapping of freely moving beads in recirculating flows generated by opposing pressure-driven and electroosmotic flows in etched diverging-converging microchannels.34 This bead-handling approach has potential uses in bioanalysis. In the absence of particles, liquid electroosmotic flow in channels of varying cross sections has been analyzed with lubrication theory.35 In addition, sample dispersion has been numerically calculated in electrically driven flows through converging-diverging tubules formed by adjacent chromatographic pillars (i.e., band broadening in electrochromatography).36 In this paper, we studied experimentally the particle electrophoretic motion in converging-diverging microchannels by visualizing the whole process of acceleration and deceleration of particle motion. Materials and experimental methods are first described. The accelerated particle electrophoretic separation is then demonstrated. After that, the effects of electric field, particle size, particle trajectory, and channel structure on accelerated particle electrophoretic motion are analyzed individually. Some explanations are also presented about the phenomena observed in the experiments. MATERIALS AND METHODS Chemicals and Materials. Fluorescent carboxylate-modified microspheres with 5.7- and 10.35-µm diameters were purchased from Bangs Laboratory (Fisher, IN) in the form of 1% solid suspensions in pure water. Polysciences Inc. (Warrington, PA) supplied 20-µm polystyrene particles packaged as 2.5% aqueous suspension. The standard size deviation of 20-µm particles is (3.2 µm as per the product instruction. These particle solutions were further diluted with pure water before use. This dilution enables both the approximation of negligible particle interactions and the tracking of single-particle motion in converging-diverging microchannels. Because all particles are slightly heavier than water (nominal density is 1.05 g/mL), their solutions required gentle vibrations prior to use. SU-8-25 photoresist (MicroChem Corp., Newton, Massachusetts) and Diacetone-alcohol developer solution (Sigma-Aldrich, St. Louis, Missouri) were used to make (24) Keh, H. J.; Chiou, J. Y. AICHE J. 1996, 42, 1397-1406. (25) Yariv, E.; Brenner, H. Phys. Fluids 2002, 14, 3354-3357. (26) Yariv, E.; Brenner, H. SIAM J. Appl. Math. 2003, 64, 423-441. (27) Ye, C.; Li, D. Langmuir 2002, 18, 9095-9101. (28) Hsu, J.; Kao, C. J. Phys. Chem. B 2002, 106, 10605-10609. (29) Liu, H.; Bau, H. H.; Hu, H. H. Langmuir 2004, 20, 2628-2639. (30) Ye, C.; Li, D. J. Colloid Interface Sci. 2004, 272, 480-488. (31) Ennis, J.; Zhang, H.; Stevens, G.; Perera, J.; Scales, P.; Carnie, S. J. Membr. Sci. 1996, 119, 47-58. (32) Xuan, X.; Ye, C.; Li, D. J. Colloid Interface Sci. 2005, in press. (33) Ye, C.; Xuan, X.; Li, D. Microfluid. Nanofluid. 2005, 1, in press. (34) Lettieri, G.; Dodge, A.; Boer, G.; de Rooij, N. F.; Verpoorte, E. Lab Chip 2003, 3, 34-39. (35) Ghosal, S. J. Fluid Mech. 2002, 459, 103-128. (36) Theemsche, V.; Gzil, P.; Dan, C.; Deconinck, J.; Smet, J. D.; Vervoort, N.; Desmet, G. Anal. Chem. 2004, 76, 4030-4037.
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Figure 1. Photograph of a converging-diverging microchannel fabricated on a PDMS chip. The inset is a magnified view of the converging-diverging section under a microscope. The channel was filled with Rhodamine B dye for a clear demonstration.
channel masters. Liquid poly(dimethylsiloxane) (PDMS) were prepared by thoroughly mixing Sylgard 184 and the curing agent (Dow Corning, Midland, Michigan) at a 15:1 ratio in weight. Microchannel Fabrication. The converging-diverging microchannels were fabricated in PDMS using the soft lithography technique.37 Briefly, masters containing the microchannel patterns were made by spin-coating SU-8 photoresist onto a clean glass slide. After a two-step soft bake (65 °C for 5 min and 95 °C for 15 min), the photoresist film was exposed to UV light for 7 s through a 3500 dpi transparent mask on which the desired channel structure had been printed. Following another two-step hard bake (65 °C for 1 min and 95 °C for 4 min), the slide was gently vibrated in the developer solution for 5 min to dissolve the unexposed photoresist, leaving a positive relief containing the microchannel pattern. Liquid PDMS was then poured over the master and cured in a vacuum at 75 °C for 3-4 h. The negative PDMS cast of the microchannel pattern was then removed from the master, and two holes were punched to serve as reservoirs. Immediately after plasma-treating (PDC-32G, Harrick Scientific, Ossining, NY), the PDMS cast and a glass slide were bonded to form the desired converging-diverging microchannel. After sealing, pure water was introduced into the channel by capillary action. Figure 1 shows a labeled photograph of a convergingdiverging microchannel on a PDMS chip. The insert is a magnified view of the converging-diverging section under a microscope. In this work, the channel width in the straight channel section is 325 µm. The width in the throat, that is, the narrowest part in the converging-diverging section, is 55 µm unless stated otherwise. The cross-sectional area ratio between the straight channel and the throat is, thus, 5.91. The lengths of converging and diverging channels are varied in order to study the effect of channel structure on particle motions. The whole channel between two reservoirs is 30 mm long and 45 µm deep and has a trapezoidal cross section. Experimental Technique. Particles were introduced into the upstream reservoir using a 1-mL plastic syringe. Under the pressure gradient induced by the height difference of liquid (37) Duffy, D. C.; McDonald, J. C.; Schueller, O. J. A.; Whitesides, G. M. Anal. Chem. 1998, 70, 4974-4984.
columns in the two reservoirs, particles were observed freely entering the microchannel and moving closely to the glass surface (i.e., the bottom channel wall). This observation is consistent with our previous study of particle electrophoretic motions in cylindrical capillaries.32 Particle electrophoresis and fluid electroosmosis were driven by a high-voltage DC power source (CZE1000R, Spellman, Hauppauge, NY) through two platinum electrodes placed in the solution in each of the reservoirs. Pressure-driven particle motions were eliminated by carefully balancing the liquid height in the two reservoirs immediately before each measurement. Particle electrophoretic motions in converging-diverging microchannels were visualized through an inverted optical microscope (Leica Microsystems, Richmond Hill, ON) equipped with a progressive CCD camera (Pulnix America Inc., Sunnyvale, CA). A direct current lamp illuminated the view window from the back. The camera was run in video mode at 15 Hz with individual exposure times of 1/250 s. The acquired images (viewed from the top) had a resolution of 640 × 484 pixels, corresponding to a 1108-µm visible channel length unless otherwise stated. A commercial graphic software, Microsoft Paint, was employed to open the images, from which the pixel information about particle positions (specifically, particle centers) with respect to time was extracted manually. Particle velocities were determined by dividing the moving distance between pairs of adjacent images over the time interval (i.e., 1/15 s). Because the reading error in particle centers could be (1 pixel, the error in particle velocity is principally (30 pixel/s, corresponding to (50 µm/s at most. It is, therefore, preferable to make particles move fast, say, at a particle velocity of higher than 0.5 mm/s, by applying relatively high electric fields. RESULTS AND DISCUSSION Accelerated Particle Electrophoretic Separation. The sequential images in Figure 2 illustrate the electrophoretic separation of two particles in a microchannel with a converging-diverging section. The converging and diverging channels are both 400 µm long. The time interval between adjacent images is 1/5 s (from I to VI). The two particles were moving from the right to the left under a 15 KV/m electric field. To compare the particle separation between the case of a straight channel and the case of a converging-diverging channel, we used a 10× microscope objective, instead of the 16× objective in other observations, for a larger field of view. In the straight section of the channel, the leading particle, 21 µm in diameter, moved at 0.58 mm/s, and the lagging particle, 22 µm in diameter, moved at 0.52 mm/s. Their initial separation distance in image I of Figure 2 was 96 µm. After 1/5 s, both particles were still moving in the straight channel, but the separation distance was increased to 108 µm in image II due to their velocity difference. After another 1/5 s, the leading particle moved into the converging section of the channel and was accelerated so that the separation distance became 144 µm in image III instead of 120 µm in the straight channel. When both particles moved into the converging section, they were quickly separated by 335 µm, as shown in image IV, because the leading particle experienced a larger acceleration. Later, when the two particles were both decelerated in the diverging section of the channel, however, the lagging particle was approaching the leading particle, as shown in image V, because the leading particle
Figure 2. Image sequence of an accelerated electrophoretic separation of two particles moving through a converging-diverging microchannel. The time interval between adjacent images in (a) (from I to VI) is 1/5 s. The arrow in image I indicates the moving direction of particles.
was decelerated more. This approaching did not end until the lagging particle moved out of the diverging section, as seen in image VI, where the two particles were separated by only 148 µm. This separation distance is close to that in a straight channel within the same period of time (156 µm based on the velocity difference of the two particles). However, the dramatic enhancement of particle separation that occurred in the throat region (image IV in Figure 2) can facilitate both the identification and the separation of reaction intermediates and other transient species (e.g., short-lived molecules).15 This locally enhanced particle separation can also benefit the separation of a single cell or particle from the others using either a lateral optical38 or electrical39 force. (38) Wang, M. M.; Tu, E.; Raymond, D. E.; Yang, J. M.; et al. Nat. Biotechnol. 2005, 23, 83-87. (39) Xuan, X.; Li, D. submitted.
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Figure 3. Velocity variations of 20-µm particles moving along the center line of a converging-diverging microchannel under different electric fields. The converging and diverging channels are both 400 µm long. The axial distance (abscissa) zero represents the throat of the converging-diverging channel section (i.e., the narrowest part). The lines are used only to guide the eye.
Because the accelerated particle electrophoretic separation is attributed to the locally enhanced particle motion in the converging channel, it is, thus, natural and necessary to examine the potential effects on particle electrophoretic motions in converging-diverging microchannels. In this work, we have studied the effects of electric field, particle size, particle trajectory, and channel structure, which will be presented below. For the first three experiments, a converging-diverging channel structure identical to that in Figure 2 was employed. Effect of Electric Field. Three different electric fields (10, 15, and 20 KV/m) were applied to generate electrophoretic motion of 20-µm particles. At each electric field, we noticed that the vast majority of particles were moving within the middle 2/3 of the channel width. However, all particles behaved (migrating in the straight section, accelerating in the converging section, and decelerating in the diverging section) similarly if they followed a similar trajectory. These trajectories were symmetric about the throat of the converging-diverging channel section. Those particles moving along the channel center line were chosen for our study of the effect of electric field strength on particle electrophoretic motion. The effect of particle trajectory will be discussed later in this paper. Figure 3 summarizes the velocity variations of 20-µm particles moving along the center line of a converging-diverging microchannel at different electric fields. In the figure, the axial distance (abscissa) zero indicates the throat (the narrowest part) of the channel. The data points for each curve in Figure 3 are from the measurements of four individual particles. The lines are used only to guide the eye. As anticipated, particles undergo acceleration and deceleration when they pass through the converging and diverging channels. Their velocity curves are symmetric about the throat. The highest particle velocity we measured was ∼1.5 mm/s. Because the fluid velocity is on the same order as the particles, the Reynolds number of liquid flow in the throat is far less than 1. Figure 4 shows the ratio of the particle velocity in the converging-diverging channel to that in the straight channel at 4326 Analytical Chemistry, Vol. 77, No. 14, July 15, 2005
Figure 4. Velocity ratios of 20-µm particles moving along the center line of a converging-diverging microchannel under different electric fields. The lines are used only to guide the eye.
different electric fields. This velocity ratio will also be used to study other effects hereafter. At a higher electric field and, thus, a higher moving speed, particles gain a lower velocity increase in the converging-diverging channel. For example, the maximum ratio of particle velocity in the throat is ∼2.9 at 10 KV/m, but it is only ∼2.2 when the electric field is increased to 20 KV/m. More importantly, the maximum velocity ratio attained in the throat is much lower than the ratio of the cross-sectional areas between the straight channel and the throat (5.91 for the convergingdiverging microchannel used in this study). There is no double that if very small particles, such as ions, move in the convergingdiverging microchannel, the maximum velocity ratio will be identical to the cross-sectional area ratio because these small ions have neither influence on the externally applied electric field nor inertial effects. As particles become larger, however, the electric field is distorted due to the presence of nonconducting particles and becomes nonuniform in the converging-diverging section, although the particle inertia is still negligible under the experimental conditions. Therefore, both the particle electrophoresis and the liquid electroosmosis are affected. Figure 5 displays the computed contour of the electric field in a converging-diverging microchannel with a 20-µm particle positioned in the middle of the throat. The inset is a zoom-in view of the electric field distribution around the particle. The converging-diverging section has the same dimensions as the actual channel. To save computation time, only a 5-mm-long channel with the converging-diverging section in the middle was selected as the computational domain. The total voltage drop applied to this 5-mm-long channel is 100 V, that is, an average electric field 20 KV/m. The 2D numerical simulation was conducted using Fluent 6. As seen from this figure, the electric field varies significantly in the converging/diverging channel, especially around the particle, but it is almost uniform in the straight channel. The largest electric field (167 KV/m) appears around the two poles of the particle and is ∼1.38 times as high as that adjacent to the channel walls in the throat (121 KV/m). The electric field at the channel wall generates the electroosmotic flow, which in turn affects the particle motion. The particle electrophoretic motion (opposite to the electroosmotic fluid flow) is controlled by its surrounding electric field. The difference in these two electric
Figure 5. Computed contour of the electric field in a converging-diverging microchannel with dimensions identical to those of the actual channel used in the experiment. The average electric field across the channel is 20 KV/m. The color bar shows the contour levels of electric field in V/m.
fields might explain why the maximum particle velocity ratio in the throat is significantly smaller than the actual area ratio. The real underlying mechanism may have to resort to detailed numerical simulations of particle (either positively changed or negatively charged or neutral) electrophoretic motion in converging-diverging microchannels. The lower ratio of particle velocity in the throat at a higher electric field may be attributed to the dielectrophoretic force FDEP that is generated by the nonuniform electric field E (Figure 5) in the converging-diverging section of the channel40
FDEP ) -2πfa3E∇E
(1)
where f is the liquid permittivity and a is the particle radius. Note that the so-called Clausius-Mossotti factor, K ) -1/2, has been invoked in eq 1 for nonconducting particles and the DC electrical field employed in our experiments. This force points to the lower electric field region (called the negative dielectrophoresis) and, thus, tends to retard the particle electrophoretic motion. At higher electric fields, FDEP grows larger, resulting in a smaller particle velocity ratio in the channel throat. In addition, eq 1 shows that the dielectrophoretic force is also dependent on the particle size. The particle size effects will be discussed in the following section. Effect of Particle Size. Particle velocities of different sizes were measured through the same converging-diverging microchannel. To isolate the size effect, we selected only the particles moving along the center line of the straight channel. The electric field for each particle size was carefully chosen so that particles of different sizes were moving at approximately the same speed in the straight channel. Specifically, the applied electric fields were 20, 12, and 16 KV/m for 20-, 10.35-, and 5.7-µm particles. The velocity ratios of these particles are shown in Figure 6. There is a clear trend that small particles are accelerated more than big (40) Pohl, H. A. Dielectrophoresis; Cambridge University Press: Cambridge, 1978.
Figure 6. Velocity ratios of particles of different size moving along the center line of a converging-diverging microchannel. The applied electric fields were 20, 12, and 16 KV/m for 20-, 10.35-, and 5.7-µm particles, respectively. All particle velocities were ∼0.5 mm/s in the straight channel. The lines are used only to guide the eye.
particles when passing through the converging-diverging channel section. This phenomenon can be attributed to the smaller negative dielectrophoretic force for smaller particles, as predicted by eq 1. Effect of Particle Trajectory. We have mentioned above that almost all 20-µm particles were observed moving within the middle 2/3 of the channel width region. For smaller particles used in the experiments, we found that they could move along any trajectory except very close to the channel walls. We chose 10.35µm particles to investigate the trajectory effect on the particle electrophoretic motion. The channel cross section was divided into three regions, that is, along the center line ((1/3 channel half width originating from the channel center line), intermediate region (about (1/3 to (2/3 channel half width) and close to channel walls (about (2/3 to (1 channel half width). The applied electric field was 15 KV/m. Figure 7 shows the velocity ratios of particles moving within the three different regions. Not surprisAnalytical Chemistry, Vol. 77, No. 14, July 15, 2005
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Figure 7. Velocity ratios of 10.35-µm particles moving along different trajectories between the lateral walls of a convergingdiverging microchannel. The rectangular, circular, and triangular symbols indicate the particle velocity ratios along the channel center line, in the intermediate region, and close to channel walls, respectively. The ranges of these regions are referred to the text. The applied electric field was 15 KV/m. The lines are used only to guide the eye.
ingly, the trajectory has negligible effect on the particle electrophoretic motion in a converging-diverging microchannel considering the pluglike velocity profile of electroosmotic flow. In other words, two particles of exactly the same speed in the straight section will not be more dispersed after passing through the converging-diverging channel relative to a straight channel. It should be pointed out that, although we greatly diluted the particle solutions in the experiments so that the particle-particle interactions were negligible, there were still several particles close to each other (but not in contact) and migrating through the converging-diverging channel. We observed that all these particles underwent a process similar to that of an isolated particle. However, when two or more particles stuck to each other, their mutual motion became significantly retarded. Sometimes we found that these particles formed a chain along the direction of electric field lines before the channel throat, especially at high electric fields. This pearl-chain phenomenon is believed to be the result of the dielectrophoretic force.41,42 Effect of Channel Structure. To examine the effect of channel structure on particle electrophoretic motion in convergingdiverging microchannels, the length of the converging or diverging section was varied among 200, 400, and 600 µm while their total length was fixed at 800 µm. The converging-diverging channel can be symmetric or asymmetric about the throat. Because the electric properties may not be exactly identical between different microchannels, we integrated these converging-diverging channel sections into one PDMS chip. The actual width of the throats is 55 µm for all three structures. Figure 8 demonstrates the velocity ratios of 10.35-µm particles migrating along the center lines of the above asymmetric convergingdiverging channels. One can see that the particle velocity attains the highest increase in the symmetric structure. The asymmetric structure has insignificant effect on particle electrophoretic mo(41) Cummings, E. B.; Singh, A. K. Anal. Chem. 2003, 75, 4724-4731. (42) Lapizco-Encinas, B. H.; Simmons, B. A.; Cummings, E. B.; Fintschenko, Y. Anal. Chem. 2004, 76, 1571-1579.
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Figure 8. Velocity ratios of 10.35-µm particles moving along the center line of asymmetric converging-diverging microchannels with fixed total length of the converging and diverging parts. The labels Lc and Ld indicate the lengths of converging and diverging channels, respectively. The applied electric field was 10 KV/m. The lines are used only to guide the eye.
tions due to the negligible influence of the length of converging or diverging channel. CONCLUSIONS This paper has presented a detailed experimental study of particle electrophoretic motion in converging-diverging microchannels. The whole process of particle acceleration and deceleration through the converging and diverging channels was visualized by optical microscopy. We have demonstrated the accelerated particle electrophoretic separation in converging-diverging microchannels. We have also examined individually the effects of electric field, particle size, particle trajectory, and channel configuration on particle electrophoretic motion. The ratio of the particle velocity in the throat to that in the straight channel has been used throughout the paper to study the above effects. This ratio is insensitive to both the particle trajectory and the length of converging/diverging channel, but it increased for smaller particles moving through symmetric converging-diverging channels under lower electric fields due to the lower dielectrophoretic force that is generated by the nonuniform electric field. Moreover, we find that the particle velocity ratio in electrically driven flows is significantly lower than the cross-sectional area ratio of the straight channel to the throat. We have attributed this to the particle-induced distortion in the electric potential distribution. The computed contour of electric field in a converging-diverging microchannel has revealed that the electric field is locally higher around the two poles of a particle than all other regions inside the channel. ACKNOWLEDGMENT Financial support from the Natural Sciences and Engineering Research Council (NSERC) of Canada through a research grant to D. Li is gratefully acknowledged. Received for review December 1, 2004. Accepted May 6, 2005. AC048216X
