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Microfluidic Analogy of the Wheatstone Bridge for Systematic Investigations of Electro-Osmotic Flows Adrien Plecis* and Yong Chen Laboratoire de Photonique et de Nanostructures, CNRS, Marcoussis, 91460, France A microfluidic analogy of the electric Wheatstone Bridge has been developed for electrokinetic study of miscellaneous liquid–solid interfaces. By using an optimized glass-PDMS-glass device technology, microfluidic channels with well-controlled surface properties can be fabricated, forming an “H” shaped fluidic network. After solving a set of linear equations, the electro-osmotic flow rate in the center channel can be deduced from indirect measurement of flow rates in the lateral channels. Experimentally, we demonstrate that the electro-osmotic mobility can be monitored every 30 s with accuracy better than 3% for a large dynamic range of electric fields. The results obtained with a borosilicate glass (D-263) and several standard biological buffers are also shown to illustrate the capability of this high throughput method. Electro-osmotic flows (EOF) are of great interest for microfluidic handling and mixing of analytes.1,2 More importantly, they are involved in most of the separation processes that are based on electromigration of species such as in capillary zone electrophoresis,3 gradient electric field focusing4 and field amplified sample stacking.5 Since the separation efficiency of these methods depends on both flow rate and profile,6,7 electrokinetic studies are necessary to improve their efficiency as well as their reproducibility. Moreover, electrokinetic studies are important for the development of novel separation techniques. During the past decade, a number of investigations have already been reported and then reviewed by Santiago8 and Wang.9 The so-called streaming (potential or current) methods10–13 were based on the determination of surface potential of a microchannel * Corresponding author:
[email protected]. (1) Fushinobu, K.; Nakata, M. J. Electron. Packag. 2005, 127, 141–146. (2) Laser, D. J.; Santiago, J. G. J. Micromech. Microeng. 2004, 14, R35–R64. (3) Kuhr, W. G. Anal. Chem. 1990, 62, R403–R414. (4) Petsev, D. N.; Lopez, G. P.; Ivory, C. F.; Sibbett, S. S. Lab Chip 2005, 5, 587–597. (5) Bharadwaj, R.; Santiago, J. G. J. Fluid Mech. 2005, 543, 57–92. (6) Wan, Q. H. J. Chromatogr. A 1997, 782, 181–189. (7) Schwer, C.; Kenndler, E. Chromatographia 1992, 33, 331–335. (8) Devasenathipathy, S.; Santiago, J. G. Micro-and Nano-scale Diagnostic Techniques; Springer Verlag: New York, 2003. (9) Wang, W.; Zhou, F.; Zhao, L.; Zhang, J. R.; Zhu, J. J. J. Chromatogr. A 2007, 1170, 1–8. (10) Erickson, D.; Li, D. Q.; Werner, C. J. Colloid Interface Sci. 2000, 232, 186– 197. (11) Scales, P. J.; Grieser, F.; Healy, T. W.; White, L. R.; Chan, D. Y. C. Langmuir 1992, 8, 965–974. (12) Gusev, I.; Horvath, C. J. Chromatogr. A 2002, 948, 203–223. (13) Gu, Y. G.; Li, D. Q. J. Colloid Interface Sci. 2000, 226, 328–339.
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by measuring the potential drop (or current) that arises when a liquid is pushed through it. Alternatively, electro-osmotic flows can be studied on the basis of neutral marker detection during electrokinetic separation processes14–17 or by simply measuring the Ohmic resistance of a channel during current monitoring.18–26 Finally, some more sophisticated methods were developed for transient EOF visualization using particle image velocimetry,27 caged fluorescence28–30 or photobleaching.31,32 These techniques gave important insights into the dynamic of EOF but were not designed for extensive studies of electrokinetic properties as their experimental implementation is often difficult and/or limited to specific geometries or systems. EOF measurements are still challenging in some particular cases when flow rates are small or high accuracy measurements are needed. On the other hand, there appear more and more recipes of the surface treatment by using plasma22 surface chemistry or coating techniques.33,34 These surface engineering techniques are often flexible but suffer from the drawback of limited shelf time and a lack of careful characterization. The (14) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, 1298–1302. (15) Muzikar, J.; van de Goor, T.; Gas, B.; Kenndler, E. J. Chromatogr. A 2002, 960, 199–208. (16) Williams, B. A.; Vigh, C. Anal. Chem. 1996, 68, 1174–1180. (17) Williams, B. A.; Vigh, G. Anal. Chem. 1997, 69, 4445–4451. (18) Huang, X. H.; Gordon, M. J.; Zare, R. N. Anal. Chem. 1988, 60, 1837– 1838. (19) Arulanandam, S.; Li, D. Q. J. Colloid Interface Sci. 2000, 225, 421–428. (20) Li, Q. F.; Zhang, X. Y.; Zhang, H. Y.; Chen, X. G.; Liu, M. C.; Hu, Z. D. Chin. J. Chem. 2001, 19, 581–587. (21) Locascio, L. E.; Perso, C. E.; Lee, C. S. J. Chromatogr. A 1999, 857, 275– 284. (22) Martin, I. T.; Dressen, B.; Boggs, M.; Liu, Y.; Henry, C. S.; Fisher, E. R. Plasma Processes Polym. 2007, 4, 414–424. (23) Ren, L. Q.; Escobedo-Canseco, C.; Li, D. Q. J. Colloid Interface Sci. 2002, 250, 238–242. (24) Sikanen, T.; Tuomikoski, S.; Ketola, R. A.; Kostiainen, R.; Franssila, S.; Kotiaho, T. Lab Chip 2005, 5, 888–896. (25) Sze, A.; Erickson, D.; Ren, L. Q.; Li, D. Q. J. Colloid Interface Sci. 2003, 261, 402–410. (26) Wang, C.; Wong, T. N.; Yang, C.; Ooi, K. T. Int. J. Heat Mass Transfer 2007, 50, 3115–3121. (27) Yan, D. G.; Yang, C.; Nguyen, N. T.; Huang, X. Y. Phys. Fluids 2007, 19. (28) Paul, P. H.; Garguilo, M. G.; Rakestraw, D. J. Anal. Chem. 1998, 70, 2459– 2467. (29) Lempert, W. R.; Magee, K.; Ronney, P.; Gee, K. R.; Haugland, R. P. Exp. Fluids 1995, 18, 249–257. (30) Ross, D.; Johnson, T. J.; Locascio, L. E. Anal. Chem. 2001, 73, 2509–2515. (31) Schrum, K. F.; Lancaster, J. M.; Johnston, S. E.; Gilman, S. D. Anal. Chem. 2000, 72, 4317–4321. (32) Mosier, B. P.; Molho, J. I.; Santiago, J. G. Exp. Fluids 2002, 33, 545–554. (33) Pallandre, A.; de Lambert, B.; Attia, R.; Jonas, A. M.; Viovy, J. L. Electrophoresis 2006, 27, 584–610. (34) Dolnik, V. Electrophoresis 2004, 25, 3589–3601. 10.1021/ac800186c CCC: $40.75 2008 American Chemical Society Published on Web 04/12/2008
dependence of EOF on parameters such as the temperature, the bulk composition, the pH and ionic strength of the solution, the viscosity of the liquid, adsorption properties of the analytes, or even the history of the surface (exposition to water, salts or gases) highly complicates the study of electrokinetic phenomena. That is why high throughput methods for EOF characterization are still necessary to properly understand the influence of all these parameters. In this work, we propose a new strategy for extensive electrokinetic studies. Microfluidic devices were fabricated with a glass-PDMS-glass (GPG) technology35 facilitating the integration of miscellaneous materials as solid to liquid interface. The fluidic network was designed on the basis of an analogy with Wheatstone bridge electronic circuits to enable indirect measurement of microchannel electrokinetic properties. We show that such a microfluidic Wheatstone bridge (µFWB) can provide more than 100 EOF measurements within 1 h with an accuracy of 3% over a large dynamic range. MICROFLUIDIC ANALOGY OF WHEATSTONE BRIDGE CIRCUIT Fluidic Resistance and Flow Actuation. Two typical flow profiles can develop in rectangular shaped microchannels: (i) Poiseuille type flows, which are pressure driven flows with parabolic velocity profiles, and (ii) electro-osmotic driven flows, which result from externally applied electric fields and exhibit a pluglike profile. Poiseuille type flow is the most frequently met flow profile in microfluidics. It can be generated either by external means like syringe pumps or by pressure pumps. The analytical resolution of Navier-Stokes equations for incompressible Newtonian fluids in rectangular channels was reported by Desmet et al.36 in the case of low Reynolds laminar flows and led to the following expression for the average flow rate J: J)
∫ ∫ b⁄2
w⁄2
-b⁄2
-w⁄2
v(y, z) dz dy )
[
∞
]
4b3w 1 nπw 192b 1- 5 th ∆P 5 12ηL 2b π w n)odd n
∑
( )
(1)
where w is the channel width along the y direction, b is the depth along the z direction, L is the length of the channel, ∆P is the pressure difference between the entrance and the exit of the channel, and η is the viscosity of the liquid. From this equation, one can derive the expression of the fluidic resistance of a channel Rf which is a geometrical coefficient: J ) Rf∆PSIelec ) Relec∆V
(2)
The microfluidic analogy with electrical resistances is due to the proportionality between the applied pressure difference ∆P and the generated flow rate J which is equivalent to Ohm’s law that links the electrical current Ielec to the resistance Relec. This proportionality occurs as long as the regime remains laminar (low Reynold’s number) and the fluid can be considered as incompressible and Newtonian, which is usually the case in microflu(35) Plecis, A.; Chen, Y. Microelectron. Eng. 2007, 84, 1265–1269. (36) Desmet, G.; Baron, G. V. J. Chromatogr. A 2002, 946, 51–58.
Figure 1. Typical microflows and their electrical analogy. (A) The pressure driven Poiseuille flow and the electrical analogy of the voltage source for the pressure gradient. (B) The pluglike electroosmotic flow (EOF) and the electrical analogy of the current source for the induced flow. (C) Superimposition of EOF and a Poiseuille counter flow and its electrical equivalent.
idics. In such an analogy, the pressure difference, which is responsible for the flow in microfluidics, can be seen as a voltage source.37 The electro-osmotic flow (EOF) is the consequence of the counterionic diffuse layer which develops at the liquid–solid interface in response to the surface charge.38 When a transverse electric field is applied, the excess of counterions in the vicinity of the interface is put in motion and drags by viscosity the whole liquid into the microchannel. The velocity gradient occurs in this diffuse layer which has a typical thickness of a few tens of nanometers. As this thickness is much smaller than the section size of the microchannels (a few micrometers) and as the fluid velocity is constant out of this layer, EOF is often referred as a pluglike flow. The homogeneous velocity in the center of the channel is proportional to the electric field E applied along the channel: v ) µEOFE
(3)
µEOF is the EOF mobility, which depends on the surface potential ζ, the viscosity (η), the conductivity (σ) and the permittivity (0r) of the solution. Then, the flow rate can be expressed by
Jeof ) σ
ε0εrζ I η
(4)
where I is the electrical current injected across the microfluidic channel. In such case, the liquid flow rate Jeof is independent of geometrical parameters and only depends on the injected current which is an external setting: the system is in analogy with a current source. These two types of flows and their electrical analogy are depicted in Figure 1. In this scheme, the mass is equivalent to a reservoir at atmospheric pressure. In A, the pressure increase in one of the reservoirs is modeled by a voltage source, and the flow (37) Ajdari, A. C. R. Phys. 2004, 5, 539–546. (38) Hunter, R. J. Zeta potential in colloids science; Academic Press: London, 1981.
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Figure 2. (A) µFWB design and its electrical analogy. (B) During EOF measurement the EOF generated in the center channel is responsible for a pressure distribution into the µFWB and flows proportional to the EOF are generated in the side microchannels. (C) The Poiseuille calibration step together with an EOF calibration step enables evaluation of fluidic resistances of the µFWB.
rate J corresponds to the current generated. In B, the EOF is represented by a current source which delivers a flow rate J ) Jeof, which only depends on the surface potential and the injected electrical current (eq 2). In C, a particular case is shown where an EOF is generated in a channel where the outlet was plugged. In the electrical analogy, this can be represented by the open switch preventing the current to reach the mass (J ) 0). In electrical systems, the current crosses the resistance and a potential drop is created. In microfluidic devices, a pressure drop and the associated counter flow Jp are generated in the microchannel so that the mass conservation of the liquid is fullfilled, which leads to J ) Jp + Jeof ) 0. Physically, velocity profiles of each component of the flow (EOF and Poiseuille) are superimposed, resulting in a zero net flow. This example shows that, depending on the fluidic (respectively electrical) system to which it is connected, an EOF (respectively current source) can also generate various pressure (respectively voltage) drops. Microfluidic Wheatstone Bridge. As a consequence, one can design a microfluidic Wheatstone bridge based on the above analogy. Figure 2 shows the microfluidic design as well as its electrical equivalent. When an electric field is applied across the center channel (Figure 2B), an EOF is generated. For negatively charged surfaces, this results in the fluid moving toward the cathode. The conservation law of the fluid creates a pressure gradient that causes a flow in all four arms of the “H” configuration. Clearly, the flow rate of the generated Poiseuille flow is proportional to the EOF. By measuring the flow rate Ji in one of the four arm channels, it is possible to deduce the EOF velocity in the center channel. For example, the flow rate measured in the fourth arm of the “H” configuration, J4, is proportional to Jeof as defined in Figure 3: Jeof ) R4 J4 g1g2 + g2g3 +
i
i
R4 ) gi )
∑g
(g1 + g3)g4
(5)
Rp Ri
where the proportionality factor R4 is deduced using the electrical analogy (see Supporting Information); gi (i ) 1, 2, 3, 4) are the relative fluidic conductance values calculated from the fluidic resistance Ri of the ith channel and Rp of the center channel. 3738
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Figure 3. Schematic of the µFWB fabrication process based on glass-PDMS-glass technology. Here, the PDMS layer is used for both microfluidic network patterning and adhesion between the upper and the lower glass substrates. In the present study, this layer was 2 µm in height.
Fluidic Resistance Calibration. Although the microfluidic resistance of the four arms can be theoretically calculated (eq 1), it is however preferable to establish an experimental calibration procedure because of the technological uncertainty on the effective dimensions of the channels. Considering an EOF experiment as presented in Figure 2B, it is possible to measure the fluid velocity Ji in the four arms of the FWB. Because of the conservation of the liquid flow, only three of these measurements are independent (J4 ) J1 + J3 - J2 for example). We have then only three independent equations of the type Jeof ) f( g1, g2, g3, g4, Ji) (i ) 1, 2, 3)
(6)
for five variables (gi(i)1-4) and Jeof), which is not sufficient for determining the fluidic resistances and thus solving the Ri coefficients. Therefore, we have to consider a second and independent calibrationsthe “Poiseuille step”swhich is performed by applying a pressure gradient across the FWB. Then, the flow distribution depends on the ratio of the fluidic resistances. By breaking the symmetry in the device design, a liquid flow is forced through the center channel, as shown in Figure 2C. With the Poiseuille step, three additional equations can be deduced from flow rate measurements in arms 1, 2 and 3. Again, the fourth measurement is not independent of the three first ones (J4 ) J1 + J3 - J2). These equations have the following form:
Jp ) f ( g1, g2, g3, g4, Ji) (i ) 1, 2, 3)
(7)
where Jp is the flow rate cross the center channel, which is an additional unknown of the problem. Combining the two calibration steps will result in a system of six independent equations for six variables that can be determined uniquely. The expression of the Ri coefficients as a function of the six measured velocities can be expressed generally as (see also Supporting Information for complete mathematical expression): Rj ) fj( Ji, Ji) (i,j ) 1, 2, 3)
(8)
After this calibration, the indirect determination of the EOF in the center channel can be deduced from the measurement of the flow rate in any of the four channels. This calibration procedure was designed according to the electrical analogy, which offers a very elegant way to solve the incertitude on the fluidic resistance distribution across the device. Moreover, this calibration step is very quick to perform (8 measurements represent less than 10 min; see experimental details) and makes it possible to detect leakages or electrical problems by checking the fluid flow conservation. Using dedicated mathematic software such as Matlab or Mathematica, the determination of the Ri coefficients is almost immediate and the determination of the EOF can rapidly begin in the desired entrance channel. This calibration can also be achieved at any moment to check for the eventual change in fluidic resistance of the device (channel clogging for example). EXPERIMENTAL SECTION Device Fabrication. A glass-PDMS-glass (GPG) sandwich configuration, which facilitates the integration of miscellaneous patterned surfaces, was used for device fabrication. As shown in Figure 3, the fluidic network was patterned into the PDMS layer prior adhesive bonding of the upper substrate. The open channels in the PDMS layer could be obtained by either molding35 or reactive ion etching.39 The final devices consisted of two patternable surfaces (the upper and lower glass surface) and PDMS sidewalls of a few microns height. Thanks to the rigidity of the substrate, large microchannels (up to 1 mm) could be achieved leading to negligible contribution of PDMS sidewalls to the EOF. Comparing to other sandwich configurations, the use of PDMS as an intermediate bonding layer has several advantages.40 First, a strong and permanent bonding with any silicon based substrate (as well as some polymers as polyethylene) can be achieved after a gentle oxygen plasma treatment of PDMS. Second, PDMS has a low Young modulus and is sufficiently deformable so that microelectrodes and other surface patterns can be easily integrated without leakage. Fluid Control and Flow Rate Measurements. Microfluidic connections to the external control units were ensured through access holes microblasted in the upper layer glass plate. A thick PDMS layer was used as a gasket between the chip and a homemade chip-holder as shown in Figure 4. The sample solution could be easily changed into the reservoirs using syringes with (39) Plecis, A.; Chen, Y. Microelectron. Eng. 2008. DOI: 10.1016/j.mee.2008. 01.097. (40) Niklaus, F.; Stemme, G.; Lu, J. Q.; Gutmann, R. J. J. Appl. Phys. 2006, 99.
Figure 4. Schematic of a glass-PDMS-glass device mounted in a homemade assembly apparatus with fluidic connections and electronic wiring.
Figure 5. Fluidic connections and pressure control with an electrovalve automatically to switch from flushing phases (a pressure gradient is imposed through the µFWB in order to inject fresh solution) to equilibrium phase (the same pressure is applied at the four entrances to stop completely the flow) during which EOF measurements are performed.
needles. The reservoirs were then connected to flexible tubes filled with deionized water. The external connection scheme of the tubing is presented in Figure 5. Pressure sources consisted of one reservoir at atmospheric pressure (P0) and a pressurized reservoir (P1 ) P0 + 1 bar). Exits 2 and 3 were connected to the reservoir at atmospheric pressure while entrances 1 and 4 could be switched between the pressurized reservoir (flushing state) and the atmospheric one (equilibrium state). A computer controlled electrovalve was used to control the dynamic state of the device. Four electrodes (E1, E2, E3 and E4) were introduced in the tubes outside of the device. Their potential was set to the same value as their respective microelectrode (dotted lines in Figure 5) in order to ensure the zero electric field in the four lateral channels of the FWB. Fluid velocities were measured using fluorescent beads as tracers (Estapor Microsphere; 0.02% in mass). In order to determine the flow rate within a few seconds, a particle image anemometry (PIA) was developed based on a full frame crosscorrelation algorithm.41 This technique performs a fast and Analytical Chemistry, Vol. 80, No. 10, May 15, 2008
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accurate (3% standard deviation) determination of flow rates in microchannels. Tween 20 (0.02%, Sigma-Aldrich) was added to the investigated solutions in order to reduce particle adsorption on glass surfaces. Calibration and EOF Measurements. Calibration steps were performed prior to measurements. The EOF calibration step was first achieved by successively repeating the same EOF experiment (Figure 2B) four times and measuring the velocity in each arm of the µFWB. The flow rates in channels 1, 2 and 4 were stored under Matlab environment, and the flow rate in channel 3 was compared to the J1 + J2 - J4 in order to check the conservation law of the fluid. Then the Poiseuille step (Figure 2C) was performed by applying a small pressure difference (typically a few mbar instead of 1 bar) between the reservoirs without electric field. The flow rates J1, J2 and J3 were also compared to J4 and then injected in eq 8 (full expression is detailed in the Supporting Information) in order to determine the Ri coefficients. Then, one arm of the µFWB was chosen for EOF monitoring and EOF measurements could be successively performed every 30 s. EOF monitoring consisted of 2 successive steps: first, the flow was stopped and the electric field applied. A stack of 5 images in one of the measurement points was stored under Matlab environment during the first seconds of the EOF generation (from 0.1 to 5 s at very low electric fields). Buffer changes induced by electrochemical reactions at the electrodes remained negligible when measuring the EOF in the earlier times. The second step consisted in flushing the µFWB with fresh solution during 30 s, while images were processed directly under Matlab environment for flow rate determination. EOF measurement could then be repeated every 30 s. This frequency was limited by the PIA crosscorrelation algorithm but can be increased using faster computer and/or optimized cross-correlation algorithms. As a last remark, it was possible to get rid of the unknown electrophoretic velocity of latex beads by measuring the fluid velocity in the entrance channels where the electric field is zero. As a consequence, several buffer solutions could be investigated without fastidious calibration of the electrophoretic mobility of the fluorescent beads (which depends on the buffer type). Moreover, once the fluidic resistances of the chip were calibrated using one buffer solution, successive solutions could be injected and characterized immediately without the need for a new calibration. Indeed, the fluidic resistance ratios do not depend on the buffer. So the calibration steps are only performed once and a large number of buffers can then be investigated within a very short experimental time. RESULTS AND DISCUSSION Accuracy of the µFWB Method. The EOF mobility of D-263 glass surfaces was measured for three different solutions, i.e., PBSA (potassium monobasic phosphate 0.4 mM), PBSB (potassium dibasic phosphate 0.4 mM) and NaCl (2 mM). Figure 6 shows a comparison of the electrokinetic properties of the microchannels immediately after the fabrication of the device and after a 12 h exposition to deionized water (one night typically). The Gaussian distribution of the EOF mobilities as measured with the PBSA solution immediately after the device fabrication (inset of Figure 6) is a consequence of the uncertainty on flow rate determination. The typical standard deviation for EOF (41) Plecis, A.; Malaquin, L.; Chen, Y. Proc. MicroTAS 2007.
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Figure 6. EOF mobility of D-263 glass channels for three different solutions as measured both immediately after the device fabrication and after injecting deionized water in the device for one night. These results clearly show that the EOF mobility of the samples depends sensitively on the preconditioning of the device. Inset: Statistics of the EOF mobility of PBSA solution (potassium monobasic phosphate 0.4 mM) measured immediately after the device fabrication, showing a standard deviation of 3.2% for 100 consecutive measurements, which is among the best accuracy for existing EOF techniques.
measurement is 3% but increases when the flow rates are in the limit of the PIA technique or when experimental parameters are not properly set (concentration of microbeads, time grabbing interval of the camera, etc.49). Comparatively to previously reported techniques, this standard deviation is among the best, but the precision can even be considered as better as averaged mobility is not calculated from a couple of experiments but more than one hundred. Indeed, it is clear from the inset in Figure 6 that fitting the distribution with a Gaussian enables the precise determination of the center of the distribution with a precision higher than 3%. This is statistically possible because the FWB enables fast repetitive measurements. With such accuracy, slight differences between EOF mobilities of glass interfaces in contact with different buffers can clearly be observed with the µFWB method. As expected by the dependence of the zeta potential on the ionic strength of the solution,42 the 2 mM NaCl (pH ) 6.75) solution shows an EOF mobility smaller than that of the 0.4 mM PBS solutions, whereas the difference between the EOF mobilities of PBSA and PBSB solutions can be explained by the effect of the pH (5.95 and 7.44 respectively) on the silanol protonation equilibrium. The more basic is the solution, the greater will be the negative charge of the glass surface and thus the EOF. This graphic also demonstrates that EOF mobilities highly depend on the preconditioning or history of the microdevice. Comparing to measurements achieved immediately after microdevice fabrication, the surface exhibits a higher mobility after injecting deionized water in the microfluidic device for 12 h. This is due to surface reorganization processes 43,44 that are usually difficult to monitor and poorly understood until now. In these experiments, the center channels were 50 µm in width and 2 µm in height. As a consequence, PDMS sidewalls contribute (42) Xu, X.; Gao, J. P.; Bao, X. L. Chin. J. Chem. 2006, 24, 85–88. (43) Devreux, F.; Barboux, P.; Filoche, M.; Sapoval, B. J. Mater. Sci. 2001, 36, 1331–1341. (44) Doremus, R. H. Glass science, 2nd ed.; Wiley: New York, 1994.
Figure 7. (A) Variation of the EOF mobility for the NaCl solution (2 mM) as a function of time obtained after injecting deionized water in the device for one night. The observed time evolution of the EOF mobility can be explained by considering surface adsorptions and chemical reactions at the liquid–solid interfaces. (B) Variation of the EOF mobility of the PBSB solution (potassium dibasic phosphate 0.4 mM) as a function of the intensity of applied electric field obtained after injecting deionized water in the device for one night. It shows a constant mobility, except a slight deviation at higher voltages.
to 4% of the total mobility. As regards the accuracy of the method, this contribution to the measured mobilities is negligible, especially as the mobility of PDMS surfaces is usually close to the one of silica. However, if the aspect ratio of the fabricated center channel is small or the surface charge of the intermediate layer is significantly different from the upper and lower surface materials, the contribution of lateral walls should be taken into account in the interpretation of the results. Real Time Monitoring of Surface Modifications. As the EOF mobility can be deduced in a few seconds, the monitoring of interface modifications can also be achieved on a much shorter time scale. Figure 7A shows the variations of the EOF mobility as a function of time when the buffer is changed into the microfluidic device. The observed short time dynamic of the EOF mobility is attributed to surface adsorptions and chemical reactions with silanol groups at the liquid–solid interfaces. Future systematic investigations will be performed in order to explain this dynamic. This monitoring is quite different from the one proposed by Pittman45 in which the electric field is applied continuously and the EOF velocity is measured by photobleaching. Here, the electric field is switched off between each measurements, which enables surface modifications to be followed without the influence of a strong electric field and its Joule effect. However, comparative studies are possible by applying the electric field during the flushing phase in order to clearly understand the influence of strong electric fields on surface modifications. Dynamic Studies As a Function of the Electric Field. Finally, the dependence of the EOF mobility of surfaces as a function of the electric field strength can also be investigated over a wide range. As the central channel across which we apply the electric field is only 1 mm in length, reasonable voltage differences (for example 100 V) result in high electric fields (1000 V/cm) comparable to the one used during separation processes. Figure 7B reports the EOF mobility as a function of the applied voltage. Error bars show the standard deviation for 5 measurements and exhibit a strong increase for electric fields above 700 V cm-1. Two hypotheses can explain this behavior. The first one depends on experimental limitations: as the CCD camera was (45) Pittman, J. L.; Henry, C. S.; Gilman, S. D. Anal. Chem. 2003, 75, 361–370.
limited to 30 frames per second, these measurements (corresponding to fluid velocities of 1.7 mm s-1) are close to the upper limit of the PIA technique.41 This problem should be corrected with the use of a faster CCD. The second hypothesis consists in considering either EOF of “the second kind” at microchannel entrance (a recirculation of fluorescent beads was observed for high electric fields) or electrokinetic instabilities46,47 as responsible for measurement uncertainty and velocity decrease. Joule heating does not seem to explain this behavior as it should increase the mobility (higher temperature results in lower viscosity). Further investigations should bring an answer to this observation, but this regime is difficult to compare with previous results from literature as all quantitative studies on the dependence of EOF with electric fields were either performed under 300V cm-1 or did not mention acceptable standard deviations. The curve presented in Figure 7B was measured within one hour, which illustrates the flexibility of the µFWB as a general tool for electrokinetic investigations. As a last remark, there is no potential limitation in applying sinusoidal or any type of non-dc electric fields. By applying asymmetric electric fields with zero net current, it is also possible to measure the nonlinearity of the EOF for a surface if the measured average flow rate is not zero. CONCLUSION A microfluidic analogy of the well-known electrical Wheatstone bridge circuits has been used for high throughput indirect measurements of the electrokinetic properties of microfluidic channels. The results obtained with a D-263 glass surface in contact with different buffers showed a very high accuracy determination of the EOF mobility (standard deviations
