- Email: [email protected]
AC electro-osmotic mixing induced by non-contact external electrodes
Biosensors and Bioelectronics 22 (2006) 563–567
AC electro-osmotic mixing induced by non-contact external electrodes Shau-Chun Wang a,∗ , Hsiao-Ping Chen a , Chia-Yu Lee a , Chun-Ching Yu a , Hsueh-Chia Chang b a
b
Department of Chemistry and Biochemistry, National Chung Cheng University, Chia-Yi, Taiwan Center for Microfluidics and Medical Diagnostics and Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN, USA Received 9 February 2006; received in revised form 23 May 2006; accepted 24 May 2006 Available online 11 July 2006
Abstract We demonstrate efficient mixing in a micro-fluidic reservoir smaller than 10 L using ac electro-osmosis driven by field-induced polarization. Our mixing device, of that electrodes are outside of the mixing unit, consists of three circular reservoirs (3 mm in diameter) connected by a 1 mm × 1 mm channel. Unlike dc electro-osmosis, whose polarization is from charged substrate functional groups, this new mechanism uses the external field to capacitively charge the surface and the surface capacitance becomes the key factor in the electrokinetic mobility. The charging and mixing are enhanced at tailor-designed channel corners by exploiting the high normal fields at geometric singularities. The induced surface dielectric polarization and the resulting electric counter-ion double layer produce an effective Zeta potential in excess of 1 V, over one order of magnitude larger than the channel Zeta potential. The resulting ac electro-osmotic slip velocity scales quadratically with respect to the applied field, in contrast to the linear scaling of dc electro-osmosis and at 1 cm/s and larger, exceeds the classical dc values by two orders of magnitude. The polarization is non-uniform at the corners due to field leakage to the dielectric substrate and the inhomogeneous slip velocity produces intense mixing vortices that effectively homogenize solutes in 30 s in a 3 mm reservoir, in contrast to hour-long mixing by pure diffusion. © 2006 Elsevier B.V. All rights reserved. Keywords: Micro-fluidic mixing; AC electro-osmosis; Induced charge; Field leakage
1. Introduction Although micro-fluidic devices are of small dimensions, reactant transport by diffusion still requires an unacceptably long time. For moderately slow analyte diffusion coefficients of D = 5 × 10−6 cm2 /s (organic molecules or short peptides), the transport time t = l2 /D within an l = 1 mm, the characteristic length of a micro-reaction chamber, is approximately 30 min. This long transport time problem is a bottleneck to develop high throughput screening protocols using wet wells or micro-fluidic biochips. Any decrease in the transport time would then produce a corresponding amplification in the throughput. To date, there have been many efforts to produce micro-fluidic mixing devices to overcome the diffusion limitation. Unlike analytical-scale reactors of several mini-liters, small Reynolds numbers (Re < 0.1) of most micro-fluidic flows implies that fluid stirring is difficult. Hence, either turbulent or vortex flows can-
∗
Corresponding author. Fax: +886 5 2721040. E-mail address: [email protected] (S.-C. Wang).
0956-5663/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.bios.2006.05.032
not be easily utilized to accelerate reaction in micro-fluidic devices. Typical static mixers employ a flow splitting (multilamina) technique (Jacobson et al., 1999; Schwesinger et al., 1996; Stroock et al., 2002) to shorten the diffusion length l or use obliquely oriented grooves to speed up transverse components in flows. However, reduction of l below 100 m requires expensive fabrication of micro-splitters and micro-baffles in a long mixing channel. Micro-stirrers and other mixers with moving parts suffer from fabrication difficulties. Long-term reliability of using micro-stirring devices is also questionable. For electrokinetic micro-devices, several simple acceleration strategies have appeared. An apparent electrokinetic mixing instability has been observed in a high-field (103 V/cm) and low frequency (20 Hz) ac field (Oddy et al., 2001). Although electrokinetic mixing devices are straightforward to fabricate, the mixing intensity of these electrokinetic mechanisms, when measured by the vortex velocity, is only at the same order of the electro-osmotic velocity at the same applied field (Oddy et al., 2001). With typical fields of 100 V/cm in practical electrokinetic devices, the electro-osmotic velocity is much less than 1 mm/s. As a result, effective stirring action is not expected. ac electro-osmotic vortices generated by
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S.-C. Wang et al. / Biosensors and Bioelectronics 22 (2006) 563–567
asymmetric imbedded electrodes have also been demonstrated to produce enhance mixing (Lastochkin et al., 2004). However, these micro-electrodes within the micro-channel require elaborate fabrication techniques and can contaminate the sample. Wang et al. (2004) developed a micro-stirring scheme using micro-vortices generated via non-linear electrokinetics in a 10 L reaction reservoir. The transport time of this method has been reported to be reduced by two orders using moderate field strength ∼100 V/cm, as compared with the static transport time. When one conducting and ion-selective granule is placed in the uniform field, the electric field lines are attracted into the charged granule and counter-ions carrying the current migrate toward the granule but co-ions are screened. This depletion zone of co-ions breaks the alignment between the streamline and the electric field. Streamlines are no longer irrotational. Generating microvortices therefore becomes possible. Furthermore, the depletion of co-ions creates an overpotential (effective Zeta potential) greater than 1 V across the polarized zone on the granule surface. Non-linear Smoluchowski slip takes place. This fast slip velocity is measured as several cm/s at a moderate field (Barany et al., 1998). In addition, the overpotential decays from the pole to the equator of a granule. So does the slip velocity decreases the same trend to develop a pressure gradient near the granule to produce backflow and ensure flow balance. As a result, intense electro-osmotic vortices are produced. This mechanism of electro-osmotic flow around a granule is first proposed by Dukhin (1991) and has also been confirmed with visualization and theoretical studies (Ben and Chang, 2002; Ben et al., 2002; Mishchuk and Takhistov, 1995). Such a co-ion depletion layer can also be formed at a dielectric surface to create an overpotential via induced polarization when high frequency ac field is applied. When the surface dielectrics are polarized by electric field, the counter-ions in the electrolyte migrate toward the surface to form a field-induced electrical double layer. Because the double layer is essentially charged like a capacitor, this particular charging mechanism is typically referred to as capacitive charging. Such capacitive charging has been studied for double layers on electrodes (Green et al., 2000; Gonzalez et al., 2000) but there exist few studies on capacitive charging of dielectric surfaces away from any electrodes except for the dc study by Thamida and Chang (2002). They show both theoretically and experimentally that intense circulating vortices can develop on both sides of a wedge due to the high normal field at such corners. The advantage of ac charging of dielectric surfaces is that the electrodes can be housed in external reservoirs and, with a sufficiently high frequency, bubble generation can be minimized at these electrodes. More importantly, the electrodes are not in contact with the working sample and hence contamination is avoided. Although the polarity of ac field flips each half cycle, the Smoluchowski slip velocity on the surface still moves toward the same direction because the polarity of induced charge reverses as well. However, this induced charge polarization would cease at low frequencies when the induced charges in the dielectric double layer have time to diffuse back into the bulk. Therefore, a high frequency ac field is required to maintain the polarization of induced charge. On the other hand, the half cycle of ac field has to be long enough to pump counter-ions to the
polarized surface. One hence expects an optimum frequency for the fastest slip velocity that corresponds to the inverse RC time of the double layer, when the double layer capacitor is charged but not excessively by the distributed ohmic resistors of the bulk fluid. Like the flow field close to the conducting surface containing ion exchange functionalities, the electro-osmotic flows are no longer aligned with electric field lines and are highly nonuniform. The existence of vorticity due to pressure-driven back flow becomes possible. Furthermore, when the dielectric surface has a curvature, field leakage across the dielectric medium is enhanced. At the wedge-like corners of mixing reservoir, where the side channels are joined, the enhanced corner electric field lines allow deep penetration through the dielectric substrate. The overpotentials at the two walls of a corner are in opposite polarities. Therefore, the electro-osmotic flows along both surfaces move toward the corner tip to produce a micro-jet and two bounding vortices with extremely high mixing efficiencies (Thamida and Chang, 2002). Channel curvatures and geometric singularities should hence promote the formation and efficiency of the mixing vortices. In this paper, we demonstrate efficient mixing in a microfluidic reservoir smaller than 10 L using ac electro-osmosis driven by field-induced polarization. Our mixing device, of that electrodes are outside of the mixing unit, consists of three circular reservoirs (3 mm in diameter) connected by a 1 mm × 1 mm channel. Intense micro-vortices at the center reservoir corners provide efficient mixing action to homogenize solutes in 30 s in the reservoir of 3 mm in diameter, whereas mixing by pure diffusion would require over an hour. We also study the effects of ac field frequency and field strength on mixing efficiency. 2. Experimental The fabrication procedures of our micro-fluidic reaction device are the same as those in our previous report (Wang et al., 2004). Co-polyester plastic sheets were obtained from DSM Engineering Plastic Products (Sheffield, MA, USA). The dielectric constant of co-polyester plastics is about 2.4. In order to sufficiently release the bubbles generated at the electrodes when applied ac field is of low frequency, the anode at the left and the cathode at the right were housed in two side-reservoirs. These side-reservoirs were connected by two straight channels to a central mixing reservoir between them. All three reservoirs were 3 mm in diameter and were drilled on one thermoplastic slide (20 mm × 40 mm; 1 mm in thickness). The connecting channels were 1.0 mm in width and each segment between two reservoirs was 10 mm long. The holes and grooves were machined on one plastic slide with conventional drilling and milling tools. The substrate slide was then thermally bonded to the drilled one at 80–100 ◦ C. Pressure was briefly applied using binder clips when the slides were glued together. Electrodes of platinum wires were placed in the two side-reservoirs with their tips bent to dip into the reservoirs to contact the liquids and the remaining part taped on the slides. The electrodes were connected to a high voltage output transformer (Industrial Test Equipment) and rf amplifier (Powertron 250 A, 10 Hz–1 MHz), capable of delivering up to
S.-C. Wang et al. / Biosensors and Bioelectronics 22 (2006) 563–567
6000 V (peak to peak) and 250 W; ac frequencies were produced by a function/arbitrary waveform generator (Hewlett-Packard 33120A). Two drops of glycerin solution stained with or without foodcolor dyes were held in pipette tips to add in the reservoir filled with DI water when the tips were dipped. To determine that the ac electro-osmotic flow field involves closed circulations and to study the diffusion transport across the closed vortices at the top and bottom of the reservoir, the dyes are not placed at the center of the reservoir but rather at its top half. The images of mixing process were recorded with a video camera when the applied field was activated. The images were digitized and transferred into a personal computer as black-and-white pictures to score gray scales at dark regions. Comparison experiments were accomplished without applying an electric field. Gray scale score statistics across the middle of center reservoir along the transverse direction were used to indicate the degree of color heterogeneity. To avoid counting the shadows at the edge, we only used twenty pixels in total inside the reservoir, which cover more than 90% of the diameter. We computed the gray scale standard deviation of these pixels. The standard deviations decreased as the mixing was getting accomplished. 3. Results and discussion Fig. 1 shows the mixing action of dyes in the center reservoir via induced electro-osmotic vortex flows at ac field of sine wave (94 Vrms /cm; 100 kHz). The dye placed in the top half of the reservoir is convected by the strong ac electro-osmotic flow at the top corners towards the two side channels. The induced
565
flow field apparently involves closed vortex pairs at two sides of each corner. Hence, diffusion into the lower reservoir is by slow diffusion and only occurs after 10 s, as seen in Fig. 1. As soon as the dye invades into the lower half, the vortices there mix it rapidly such that the concentration field becomes almost uniform in about 30 s. In contrast, such homogenization over the entire reservoir by diffusion alone would take more than 1 h. In the presence of the ac electro-osmotic vortices, the diffusion length that requires diffusion is reduced to a thin boundary layer between the closed vortices in the top and bottom halves of the reservoir. Transport across such diffusion layers of mixing vortices has been studied by Sawyer et al. (1996). Since the uniformity of the concentration image can be quantified by determining the standard deviation of the pixel intensity values, the curve of gray scale standard deviation versus time measures the mixing action when an ac electric field 94 Vrms /cm is applied across the reservoir. The normalized concentration within the reservoir is expected to approach a homogeneous field exponentially if only diffusion at play. The exponent is −Dt/l2 multiplied by a unit-order factor, where l = 3 mm is the diameter of the reservoir. Hence, a measure of our mixing efficiency can be obtained by assuming a purely diffusive mechanism. As such, the mixing diffusivity can be derived via the linear regression of the logarithm value of standard deviation against time (Fig. 2). The slope of this curve scales linearly with respect to the diffusivity coefficient. As such, we use the slope of the fieldless data in Fig. 2 as reference points (D0 ) and then estimate Deff /D0 by taking the ratio of similar slope, with an applied field to this slope and without an applied field. Data in Fig. 2 fall on a straight line, indicating
Fig. 1. Mixing action using induced ac electro-osmotic vortex flow produced by applying a sine waveform ac field (94 Vrms /cm; 100 kHz) across the mixing reservoir. Two segregated glycerin drops stained with and without food-color dyes in glycerin solution are mixed homogenously in 30 s.
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nal field. Therefore, like the polarization on the surface of a conducting granule, the induced polarization for ac electroosmosis on dielectric also scales linearly with the applied field strength. Since the Smoluchowski slip velocity is due to the Maxwell force that is the product of the polarization and the applied field, the effective velocity of induced ac electro-osmosis should scale quadratically to the applied field strength. Using the data in Fig. 3 to perform regression, the log–log relation of maximum mixing diffusivity at 100 kHz versus applied field strength approximately yields a straight line of power of two. This quadratic scaling relation confirms our theoretical analysis. Fig. 2. Mixing action quantification is obtained from the global temporal change of the standard deviation (S.D.) of pixel gray scale scores from the digital video of the mixing action inside the reservoir. The mixing diffusivity (curve A) for induced ac electro-osmotic vortex flows in a sine waveform ac field (94 Vrms /cm; 100 kHz) across mixing reservoir is compared to that without a field (curve B).
that the vortex mixing in the reservoir can be accurately represented by a diffusing mixing model with an effective mixing diffusivity Deff . The normalized mixing diffusivity hence represents the effects of electrokinetic flow on mixing relative to the case without flow. Similarly, mixing diffusivity coefficient is obtained in comparison experiment without the application of ac field. The slope of curve A is approximately two orders of magnitude higher than that of curve B in Fig. 2. The mixing efficiency is enhanced about 100-fold using our device. The expected optimum frequency for the slip velocity, roughly corresponding to the inverse RC time of the double layer on the dielectric, is reflected in the mixing efficiency. Fig. 3 shows normalized mixing diffusivity dependence on applied field frequency. All curves in Fig. 3 have maximum mixing efficiency around 100 kHz. This optimum frequency for slip velocity is consistent with that measured on electrodes for dilute electrolyte solutions (Gagnon and Chang, 2005). The co-ion depletion layer of induced ac electro-osmosis is created when the surface dielectrics is polarized by an exter-
4. Conclusion Effective mixing two orders of magnitude higher than molecular diffusion has been achieved in a small size reservoir (less than 10 L) with vortex flows at a through-flow Reynolds number of less than 1. These micro-vortices resulted from fluid circulation created by non-uniform polarization of dielectric wedges inserted in an ac electric field (35–94 Vrms /cm; 50–140 kHz). The applicability of this unique mixing mechanism was demonstrated under moderate electric fields and without internal electrodes, flow splitting by baffles or mechanical stirrers with moving parts. Although diffusive mixing would take more than 1 h for the low diffusivity dye, the new mechanism is able to achieve complete mixing in 30 s corresponding to a two-order reduction in mixing time. Although there is only one mixing chamber in our device, replicating hundreds of them on one substrate disk should be a straightforward fabrication effort. Channel geometries with additional corners or other geometric singularities should promote faster and longer-range mixing. Electrodes can be fabricated by depositing conductive materials on the edge of the reservoirs. The mixing action can also initiate the instant the final reactants are released into the wet wells. Unlike the previous mixing chamber using a conducting granule of 1 mm in diameter, this novel device employs non-linear electro-osmosis without the presence of granule. Therefore, there should be no difficulty to scale down to micro-fluidic mixing chambers smaller than 100 m. In addition, since the maximum mixing efficiency of this device is achieved at very high ac frequency 100 kHz, bubble generation at the electrodes is no longer problematic when this device is in enclosed format. Acknowledgements The financial support by National Science Council, Taiwan (NSC 94-2113-M-194-015) and National Chung Cheng University is acknowledged. References
Fig. 3. Measured effective mixing diffusivity as a function of ac frequency for four different applied fields (94, 71, 47, and 35 Vrms /cm). The maximum mixing diffusivity appears at 100 kHz.
Barany, S., Mishchuk, N.A., Prieve, D.C., 1998. J. Colloid Interf. Sci. 207 (2), 240–250. Ben, Y., Chang, H.-C., 2002. J. Fluid Mech. 461, 229–238. Ben, Y., Demekhin, E.A., Takhisov, P.V., Chang, H.-C., 2002. J. Chin. Inst. Chem. Eng. 33, 15–24. Dukhin, S.S., 1991. Adv. Colloid Interf. Sci. 35, 173–196.
S.-C. Wang et al. / Biosensors and Bioelectronics 22 (2006) 563–567 Gagnon, Z., Chang, H.-C., 2005. Electrophoresis 26, 3725–3737. Gonzalez, A., Ramos, A., Green, N.G., Castellanos, A., Morgan, H., 2000. Phys. Rev. E. 61, 4019–4028. Green, N.G., Ramos, A., Gonzalez, A., Morgan, H., Castellanos, A., 2000. Phys. Rev. E 61, 4011–4018. Jacobson, S.C., Mcknight, T.E., Ramsey, J.M., 1999. Anal. Chem. 71, 4455–4459. Lastochkin, D., Zhou, R., Wang, P., Ben, Y., Chang, H.-C., 2004. J. Appl. Phys. 96, 1730–1733. Mishchuk, N.A., Takhistov, P.V., 1995. Colloid Surf. A 95, 119–131.
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Oddy, M.H., Santiago, J.G., Mikkelsen, J.C., 2001. Anal. Chem. 73, 5822– 5832. Sawyer, D.R., Sen, M., Chang, H.-C., 1996. Chem. Eng. J. 64, 129–142. Schwesinger, N., Frank, T., Wurmus, H., 1996. J. Micromech. Microeng. 6, 99–102. Stroock, A.D., Dertinger, S.K.W., Ajdari, A., Mezic, I., Stone, H.A., Whitesides, G.M., 2002. Science 295, 647–651. Thamida, S., Chang, H.-C., 2002. Phys. Fluid 14, 4315–4328. Wang, S.C., Lai, Y.W., Ben, Y., Chang, H.-C., 2004. Ind. Eng. Chem. Res. 43, 2902–2911.
AC electro-osmotic mixing induced by non-contact external electrodes Shau-Chun Wang a,∗ , Hsiao-Ping Chen a , Chia-Yu Lee a , Chun-Ching Yu a , Hsueh-Chia Chang b a
b
Department of Chemistry and Biochemistry, National Chung Cheng University, Chia-Yi, Taiwan Center for Microfluidics and Medical Diagnostics and Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, IN, USA Received 9 February 2006; received in revised form 23 May 2006; accepted 24 May 2006 Available online 11 July 2006
Abstract We demonstrate efficient mixing in a micro-fluidic reservoir smaller than 10 L using ac electro-osmosis driven by field-induced polarization. Our mixing device, of that electrodes are outside of the mixing unit, consists of three circular reservoirs (3 mm in diameter) connected by a 1 mm × 1 mm channel. Unlike dc electro-osmosis, whose polarization is from charged substrate functional groups, this new mechanism uses the external field to capacitively charge the surface and the surface capacitance becomes the key factor in the electrokinetic mobility. The charging and mixing are enhanced at tailor-designed channel corners by exploiting the high normal fields at geometric singularities. The induced surface dielectric polarization and the resulting electric counter-ion double layer produce an effective Zeta potential in excess of 1 V, over one order of magnitude larger than the channel Zeta potential. The resulting ac electro-osmotic slip velocity scales quadratically with respect to the applied field, in contrast to the linear scaling of dc electro-osmosis and at 1 cm/s and larger, exceeds the classical dc values by two orders of magnitude. The polarization is non-uniform at the corners due to field leakage to the dielectric substrate and the inhomogeneous slip velocity produces intense mixing vortices that effectively homogenize solutes in 30 s in a 3 mm reservoir, in contrast to hour-long mixing by pure diffusion. © 2006 Elsevier B.V. All rights reserved. Keywords: Micro-fluidic mixing; AC electro-osmosis; Induced charge; Field leakage
1. Introduction Although micro-fluidic devices are of small dimensions, reactant transport by diffusion still requires an unacceptably long time. For moderately slow analyte diffusion coefficients of D = 5 × 10−6 cm2 /s (organic molecules or short peptides), the transport time t = l2 /D within an l = 1 mm, the characteristic length of a micro-reaction chamber, is approximately 30 min. This long transport time problem is a bottleneck to develop high throughput screening protocols using wet wells or micro-fluidic biochips. Any decrease in the transport time would then produce a corresponding amplification in the throughput. To date, there have been many efforts to produce micro-fluidic mixing devices to overcome the diffusion limitation. Unlike analytical-scale reactors of several mini-liters, small Reynolds numbers (Re < 0.1) of most micro-fluidic flows implies that fluid stirring is difficult. Hence, either turbulent or vortex flows can-
∗
Corresponding author. Fax: +886 5 2721040. E-mail address: [email protected] (S.-C. Wang).
0956-5663/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.bios.2006.05.032
not be easily utilized to accelerate reaction in micro-fluidic devices. Typical static mixers employ a flow splitting (multilamina) technique (Jacobson et al., 1999; Schwesinger et al., 1996; Stroock et al., 2002) to shorten the diffusion length l or use obliquely oriented grooves to speed up transverse components in flows. However, reduction of l below 100 m requires expensive fabrication of micro-splitters and micro-baffles in a long mixing channel. Micro-stirrers and other mixers with moving parts suffer from fabrication difficulties. Long-term reliability of using micro-stirring devices is also questionable. For electrokinetic micro-devices, several simple acceleration strategies have appeared. An apparent electrokinetic mixing instability has been observed in a high-field (103 V/cm) and low frequency (20 Hz) ac field (Oddy et al., 2001). Although electrokinetic mixing devices are straightforward to fabricate, the mixing intensity of these electrokinetic mechanisms, when measured by the vortex velocity, is only at the same order of the electro-osmotic velocity at the same applied field (Oddy et al., 2001). With typical fields of 100 V/cm in practical electrokinetic devices, the electro-osmotic velocity is much less than 1 mm/s. As a result, effective stirring action is not expected. ac electro-osmotic vortices generated by
564
S.-C. Wang et al. / Biosensors and Bioelectronics 22 (2006) 563–567
asymmetric imbedded electrodes have also been demonstrated to produce enhance mixing (Lastochkin et al., 2004). However, these micro-electrodes within the micro-channel require elaborate fabrication techniques and can contaminate the sample. Wang et al. (2004) developed a micro-stirring scheme using micro-vortices generated via non-linear electrokinetics in a 10 L reaction reservoir. The transport time of this method has been reported to be reduced by two orders using moderate field strength ∼100 V/cm, as compared with the static transport time. When one conducting and ion-selective granule is placed in the uniform field, the electric field lines are attracted into the charged granule and counter-ions carrying the current migrate toward the granule but co-ions are screened. This depletion zone of co-ions breaks the alignment between the streamline and the electric field. Streamlines are no longer irrotational. Generating microvortices therefore becomes possible. Furthermore, the depletion of co-ions creates an overpotential (effective Zeta potential) greater than 1 V across the polarized zone on the granule surface. Non-linear Smoluchowski slip takes place. This fast slip velocity is measured as several cm/s at a moderate field (Barany et al., 1998). In addition, the overpotential decays from the pole to the equator of a granule. So does the slip velocity decreases the same trend to develop a pressure gradient near the granule to produce backflow and ensure flow balance. As a result, intense electro-osmotic vortices are produced. This mechanism of electro-osmotic flow around a granule is first proposed by Dukhin (1991) and has also been confirmed with visualization and theoretical studies (Ben and Chang, 2002; Ben et al., 2002; Mishchuk and Takhistov, 1995). Such a co-ion depletion layer can also be formed at a dielectric surface to create an overpotential via induced polarization when high frequency ac field is applied. When the surface dielectrics are polarized by electric field, the counter-ions in the electrolyte migrate toward the surface to form a field-induced electrical double layer. Because the double layer is essentially charged like a capacitor, this particular charging mechanism is typically referred to as capacitive charging. Such capacitive charging has been studied for double layers on electrodes (Green et al., 2000; Gonzalez et al., 2000) but there exist few studies on capacitive charging of dielectric surfaces away from any electrodes except for the dc study by Thamida and Chang (2002). They show both theoretically and experimentally that intense circulating vortices can develop on both sides of a wedge due to the high normal field at such corners. The advantage of ac charging of dielectric surfaces is that the electrodes can be housed in external reservoirs and, with a sufficiently high frequency, bubble generation can be minimized at these electrodes. More importantly, the electrodes are not in contact with the working sample and hence contamination is avoided. Although the polarity of ac field flips each half cycle, the Smoluchowski slip velocity on the surface still moves toward the same direction because the polarity of induced charge reverses as well. However, this induced charge polarization would cease at low frequencies when the induced charges in the dielectric double layer have time to diffuse back into the bulk. Therefore, a high frequency ac field is required to maintain the polarization of induced charge. On the other hand, the half cycle of ac field has to be long enough to pump counter-ions to the
polarized surface. One hence expects an optimum frequency for the fastest slip velocity that corresponds to the inverse RC time of the double layer, when the double layer capacitor is charged but not excessively by the distributed ohmic resistors of the bulk fluid. Like the flow field close to the conducting surface containing ion exchange functionalities, the electro-osmotic flows are no longer aligned with electric field lines and are highly nonuniform. The existence of vorticity due to pressure-driven back flow becomes possible. Furthermore, when the dielectric surface has a curvature, field leakage across the dielectric medium is enhanced. At the wedge-like corners of mixing reservoir, where the side channels are joined, the enhanced corner electric field lines allow deep penetration through the dielectric substrate. The overpotentials at the two walls of a corner are in opposite polarities. Therefore, the electro-osmotic flows along both surfaces move toward the corner tip to produce a micro-jet and two bounding vortices with extremely high mixing efficiencies (Thamida and Chang, 2002). Channel curvatures and geometric singularities should hence promote the formation and efficiency of the mixing vortices. In this paper, we demonstrate efficient mixing in a microfluidic reservoir smaller than 10 L using ac electro-osmosis driven by field-induced polarization. Our mixing device, of that electrodes are outside of the mixing unit, consists of three circular reservoirs (3 mm in diameter) connected by a 1 mm × 1 mm channel. Intense micro-vortices at the center reservoir corners provide efficient mixing action to homogenize solutes in 30 s in the reservoir of 3 mm in diameter, whereas mixing by pure diffusion would require over an hour. We also study the effects of ac field frequency and field strength on mixing efficiency. 2. Experimental The fabrication procedures of our micro-fluidic reaction device are the same as those in our previous report (Wang et al., 2004). Co-polyester plastic sheets were obtained from DSM Engineering Plastic Products (Sheffield, MA, USA). The dielectric constant of co-polyester plastics is about 2.4. In order to sufficiently release the bubbles generated at the electrodes when applied ac field is of low frequency, the anode at the left and the cathode at the right were housed in two side-reservoirs. These side-reservoirs were connected by two straight channels to a central mixing reservoir between them. All three reservoirs were 3 mm in diameter and were drilled on one thermoplastic slide (20 mm × 40 mm; 1 mm in thickness). The connecting channels were 1.0 mm in width and each segment between two reservoirs was 10 mm long. The holes and grooves were machined on one plastic slide with conventional drilling and milling tools. The substrate slide was then thermally bonded to the drilled one at 80–100 ◦ C. Pressure was briefly applied using binder clips when the slides were glued together. Electrodes of platinum wires were placed in the two side-reservoirs with their tips bent to dip into the reservoirs to contact the liquids and the remaining part taped on the slides. The electrodes were connected to a high voltage output transformer (Industrial Test Equipment) and rf amplifier (Powertron 250 A, 10 Hz–1 MHz), capable of delivering up to
S.-C. Wang et al. / Biosensors and Bioelectronics 22 (2006) 563–567
6000 V (peak to peak) and 250 W; ac frequencies were produced by a function/arbitrary waveform generator (Hewlett-Packard 33120A). Two drops of glycerin solution stained with or without foodcolor dyes were held in pipette tips to add in the reservoir filled with DI water when the tips were dipped. To determine that the ac electro-osmotic flow field involves closed circulations and to study the diffusion transport across the closed vortices at the top and bottom of the reservoir, the dyes are not placed at the center of the reservoir but rather at its top half. The images of mixing process were recorded with a video camera when the applied field was activated. The images were digitized and transferred into a personal computer as black-and-white pictures to score gray scales at dark regions. Comparison experiments were accomplished without applying an electric field. Gray scale score statistics across the middle of center reservoir along the transverse direction were used to indicate the degree of color heterogeneity. To avoid counting the shadows at the edge, we only used twenty pixels in total inside the reservoir, which cover more than 90% of the diameter. We computed the gray scale standard deviation of these pixels. The standard deviations decreased as the mixing was getting accomplished. 3. Results and discussion Fig. 1 shows the mixing action of dyes in the center reservoir via induced electro-osmotic vortex flows at ac field of sine wave (94 Vrms /cm; 100 kHz). The dye placed in the top half of the reservoir is convected by the strong ac electro-osmotic flow at the top corners towards the two side channels. The induced
565
flow field apparently involves closed vortex pairs at two sides of each corner. Hence, diffusion into the lower reservoir is by slow diffusion and only occurs after 10 s, as seen in Fig. 1. As soon as the dye invades into the lower half, the vortices there mix it rapidly such that the concentration field becomes almost uniform in about 30 s. In contrast, such homogenization over the entire reservoir by diffusion alone would take more than 1 h. In the presence of the ac electro-osmotic vortices, the diffusion length that requires diffusion is reduced to a thin boundary layer between the closed vortices in the top and bottom halves of the reservoir. Transport across such diffusion layers of mixing vortices has been studied by Sawyer et al. (1996). Since the uniformity of the concentration image can be quantified by determining the standard deviation of the pixel intensity values, the curve of gray scale standard deviation versus time measures the mixing action when an ac electric field 94 Vrms /cm is applied across the reservoir. The normalized concentration within the reservoir is expected to approach a homogeneous field exponentially if only diffusion at play. The exponent is −Dt/l2 multiplied by a unit-order factor, where l = 3 mm is the diameter of the reservoir. Hence, a measure of our mixing efficiency can be obtained by assuming a purely diffusive mechanism. As such, the mixing diffusivity can be derived via the linear regression of the logarithm value of standard deviation against time (Fig. 2). The slope of this curve scales linearly with respect to the diffusivity coefficient. As such, we use the slope of the fieldless data in Fig. 2 as reference points (D0 ) and then estimate Deff /D0 by taking the ratio of similar slope, with an applied field to this slope and without an applied field. Data in Fig. 2 fall on a straight line, indicating
Fig. 1. Mixing action using induced ac electro-osmotic vortex flow produced by applying a sine waveform ac field (94 Vrms /cm; 100 kHz) across the mixing reservoir. Two segregated glycerin drops stained with and without food-color dyes in glycerin solution are mixed homogenously in 30 s.
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nal field. Therefore, like the polarization on the surface of a conducting granule, the induced polarization for ac electroosmosis on dielectric also scales linearly with the applied field strength. Since the Smoluchowski slip velocity is due to the Maxwell force that is the product of the polarization and the applied field, the effective velocity of induced ac electro-osmosis should scale quadratically to the applied field strength. Using the data in Fig. 3 to perform regression, the log–log relation of maximum mixing diffusivity at 100 kHz versus applied field strength approximately yields a straight line of power of two. This quadratic scaling relation confirms our theoretical analysis. Fig. 2. Mixing action quantification is obtained from the global temporal change of the standard deviation (S.D.) of pixel gray scale scores from the digital video of the mixing action inside the reservoir. The mixing diffusivity (curve A) for induced ac electro-osmotic vortex flows in a sine waveform ac field (94 Vrms /cm; 100 kHz) across mixing reservoir is compared to that without a field (curve B).
that the vortex mixing in the reservoir can be accurately represented by a diffusing mixing model with an effective mixing diffusivity Deff . The normalized mixing diffusivity hence represents the effects of electrokinetic flow on mixing relative to the case without flow. Similarly, mixing diffusivity coefficient is obtained in comparison experiment without the application of ac field. The slope of curve A is approximately two orders of magnitude higher than that of curve B in Fig. 2. The mixing efficiency is enhanced about 100-fold using our device. The expected optimum frequency for the slip velocity, roughly corresponding to the inverse RC time of the double layer on the dielectric, is reflected in the mixing efficiency. Fig. 3 shows normalized mixing diffusivity dependence on applied field frequency. All curves in Fig. 3 have maximum mixing efficiency around 100 kHz. This optimum frequency for slip velocity is consistent with that measured on electrodes for dilute electrolyte solutions (Gagnon and Chang, 2005). The co-ion depletion layer of induced ac electro-osmosis is created when the surface dielectrics is polarized by an exter-
4. Conclusion Effective mixing two orders of magnitude higher than molecular diffusion has been achieved in a small size reservoir (less than 10 L) with vortex flows at a through-flow Reynolds number of less than 1. These micro-vortices resulted from fluid circulation created by non-uniform polarization of dielectric wedges inserted in an ac electric field (35–94 Vrms /cm; 50–140 kHz). The applicability of this unique mixing mechanism was demonstrated under moderate electric fields and without internal electrodes, flow splitting by baffles or mechanical stirrers with moving parts. Although diffusive mixing would take more than 1 h for the low diffusivity dye, the new mechanism is able to achieve complete mixing in 30 s corresponding to a two-order reduction in mixing time. Although there is only one mixing chamber in our device, replicating hundreds of them on one substrate disk should be a straightforward fabrication effort. Channel geometries with additional corners or other geometric singularities should promote faster and longer-range mixing. Electrodes can be fabricated by depositing conductive materials on the edge of the reservoirs. The mixing action can also initiate the instant the final reactants are released into the wet wells. Unlike the previous mixing chamber using a conducting granule of 1 mm in diameter, this novel device employs non-linear electro-osmosis without the presence of granule. Therefore, there should be no difficulty to scale down to micro-fluidic mixing chambers smaller than 100 m. In addition, since the maximum mixing efficiency of this device is achieved at very high ac frequency 100 kHz, bubble generation at the electrodes is no longer problematic when this device is in enclosed format. Acknowledgements The financial support by National Science Council, Taiwan (NSC 94-2113-M-194-015) and National Chung Cheng University is acknowledged. References
Fig. 3. Measured effective mixing diffusivity as a function of ac frequency for four different applied fields (94, 71, 47, and 35 Vrms /cm). The maximum mixing diffusivity appears at 100 kHz.
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