Anal. Chem. 2000, 72, 3512-3517
Computer Simulations of Electrokinetic Injection Techniques in Microfluidic Devices Sergey V. Ermakov,† Stephen C. Jacobson, and J. Michael Ramsey*
Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6142
Computer simulations are used to study electrokinetic injections on microfluidic devices (microchips). The gated and pinched injection techniques are considered. Each injection technique uses a unique sequence of steps with different electric field distributions and field magnitudes in the channels to effectuate a virtual valve. The goal of these computer simulations is to identify operating parameters providing optimal valve performance. In the pinched injection, the conditions of both loading and dispensing steps were analyzed to reach a compromise between the sample plug spatial extent and its concentration. For the gated injection, the condition of leakage free valve operation was found for the sample loading step. The simulation results for the gated valve are compared with experimental data. Microfabricated fluidic devices1-4 (microchips) associated with the Lab-on-a-Chip concept often use electrokinetic manipulations for fluid handling and analysis. These manipulations exploit the phenomena of electrophoresis, which sets electrically charged particles in motion, and electroosmosis, which enables bulk fluid flow. Electrokinetic manipulations can be used to deliver sample to points where it may be chemically modified,5,6 diluted or mixed with other substances,2,7,8 detected, and perhaps used for further analysis by coupling the microchip with other analytical techniques such as mass spectroscopy.9,10 Fluidic valving, particularly in the form of discrete injections, is one of the necessary steps in sample handling. These injections spatially define the portion of sample that will be used in subsequent manipulations and analysis. The † Present address: PE Biosystems, 850 Lincoln Centre Drive, MS 408-2, Foster City, California 94404. (1) Harrison, D. J.; Manz, A.; Fan, Z.; Widmer, H. M. Anal. Chem. 1992, 64, 1926-1932. (2) Harrison, D. J.; Fluri, K.; Seiler, K.; Fan, Z.; Effenhauser, C. S.; Manz, A. Science 1993, 261, 895-897. (3) Jacobson, S. C.; Hergenroder, R.; Koutny, L. B.; Ramsey, J. M. Anal. Chem. 1994, 66, 1114-1118. (4) Jacobson, S. C.; Hergenroder, R.; Koutny, L. B.; Warmack, R. J.; Ramsey, J. M. Anal. Chem. 1994, 66, 1107-1113. (5) Jacobson, S. C.; Hergenroder, R.; Moore, A. W.; Ramsey, J. M. Anal. Chem. 1994, 66, 4127-4132. (6) Jacobson, S. C.; Koutny, L. B.; Hergenroder, R.; Moore, A. W.; Ramsey, J. M. Anal. Chem. 1994, 66, 3472-3476. (7) Seiler, K.; Fan, Z.; Fluri, K.; Harrison, D. J. Anal. Chem. 1994, 66, 34853491. (8) Hadd, A. G.; Raymond, D. E.; Haliwell, J. W.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1997, 69, 3407-3412. (9) Ramsey, R. S.; Ramsey, J. M. Anal. Chem. 1997, 69, 1174-1178. (10) Xue, Q.; Foret, F.; Dunayevskiy, Y. M.; Zavracky, P. M.; McGruer, N. E.; Karger, B. L. Anal. Chem. 1997, 69, 426-430.
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characteristics of the injection process determine the quality of the following manipulations and final results. Understanding the mechanisms governing electrokinetic manipulations, particularly discrete injections, is important for optimizing microchip design, choosing appropriate operating conditions, and properly implementing postexperiment data analysis. Unlike traditional capillary electrophoresis (CE) in which both hydrodynamic and electrokinetic injections are used, microchips use almost exclusively electrokinetically driven injections as they have the advantage of only requiring application of electric potentials to the devices. Electrokinetic injections on microchips differ from that of conventional CE, where the injection port is simply a capillary inlet and the sample flux can be rather accurately approximated by a 1-D approach.11 On microchips, the injection valve usually consists of several intersecting channels where the electroosmotic and electrophoretic velocities are summed geometrically as vectors, and the sample flux cannot be accurately estimated using a 1-D approximation. For the channel cross geometry two different injection techniques have been demonstrated: the gated injection valve6 and the pinched injection valve.4 Pinched Valve. The pinched valve is able to generate welldefined short axial extent sample plugs suitable for highperformance separations.4,12 This is achieved by spatially confining the sample in the cross intersection before dispensing it into the separation channel. The sample flow out of the channel 3 (Figure 1, top) is electrokinetically confined by the incoming buffer streams from the vertical channels 2 and 4 and by the electric field distribution in the case of charged species. The extent of sample focusing is regulated by the electric field strength in the vertical channels versus the inlet channel 3. The electric field equipotential lines for the channel cross are shown on the right panels (Figure 1). Once the sample flow has reached a steady state, the electric field is switched to a dispensing step serving also as the separation step (Figure 1, bottom). In this step, to prevent sample leakage into the separation channel and achieve a short axial extent sample plug, an electric field is also applied to channels 1 and 3 to draw sample back from the intersection. During dispensing the equipotential lines in the intersection are convex in the direction of the separation channel resulting in a crescent-like shape for the injected plug. Gated Valve. The gated valve has a loading/separation mode where the sample flows from channel 2 to waste channel 1 while the buffer flows from channel 3 to channels 2 and 4 to prevent (11) Jorgenson, J. W.; Lukacs, K. D. Science 1983, 222, 266-272. (12) Jacobson, S. C.; Culbertson, C. T.; Daler, J. E.; Ramsey, J. M. Anal. Chem. 1998, 70, 3476-3480. 10.1021/ac991474n CCC: $19.00
© 2000 American Chemical Society Published on Web 06/23/2000
Figure 1. Simulated images of the injection sequence for the pinched valve: loading (top); dispensing (bottom). The sample is shown in white with arrows indicating buffer and sample flow direction (left panels). Equipotential lines (right panels) show the electric field distribution in the area close to the channel intersection.
sample leakage and provide continuous buffer supply into the separation channel 4 (Figure 2, top). To make an injection, the field in buffer channel 3 is set to zero allowing a plug of sample to move into the separation channel (Figure 2, middle). In the subsequent separation step, the field is switched back to the loading/separation step. The buffer flow cuts the sample plug, and the injection valve returns to its original state. The electric field arrangement in the gated injection (Figure 2, right panels) explains the slight sample penetration into the buffer channel (Figure 2, middle) and nonsymmetric sample plug tail after dispensing (Figure 2, bottom). The gated valve is capable of dispensing sample plugs of variable volume and provides unidirectional flow in the separation channel. In this paper, the pinched and gated injection techniques described above are studied theoretically by means of computer modeling. Primary attention is paid to studying the effect of the electric field distribution in the channels on sample transport during different phases of injection and to providing injection parameters for optimal sample analysis. The effects of other operating parameters, such as sample diffusion coefficient, electroosmotic mobility, and channel width are also considered.
Figure 2. Simulated images of the injection sequence for the gated valve: loading (top); dispensing (middle); separation/loading (bottom). The sample is shown in white with arrows indicating buffer and sample flow direction (left panels). Equipotential lines (right panels) show the electric field distribution in the area close to the channel intersection.
METHOD Injection studies for microfabricated fluidic devices were conducted using computer simulations based on the mathematical model described previously.13 The model accounts for major transport phenomena: electroosmosis; electrophoretic sample transport; diffusion. Although the simulations are two-dimensional, in many cases this approximation is sufficient to describe electrokinetic sample manipulations quite accurately. Computer code
implementing this model allows the simulation of electrokinetic sample transport in the channels of quite arbitrary geometries for various sample and buffer properties using different initial and boundary conditions for sample concentration, electric field, and velocity. The simulations output the electric field distribution, pressure and velocity fields in the fluid, and the temporal evolution of the sample concentration field. To simulate the detector signal obtained from a single-point detection scheme,14 the average value of the sample concentration over the cross section perpendicular to the separation channel is calculated. The channel width was assumed to be 50 µm unless otherwise stated. The running parameters, i.e., electric field strength and electroosmotic mobility, were taken from the literature.4,15 The channel geometry used for the simulations is similar to Figures 1 and 2. Ei is the electric field strength in the channel i. Actually, Ei is the electric field in that portion of the channel which is far (2-4 channel widths) from the cross intersection and where it is assumed to be uniform and constant. The simulation results will be reported using a relative electric field strength in the channels, i ) Ei/Emax, where Emax is the maximum field value. For convenience we will assume that i is positive if the vector E h is directed toward the channel intersection (node) and negative if directed away. Because we
(13) Ermakov, S. V.; Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1998, 70, 44944504.
(14) Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1996, 68, 720-723. (15) Jacobson, S. C.; Ramsey, J. M. Anal. Chem. 1997, 69, 3212-3217.
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by the sample velocity v, σ ) σtv. The Cmax value was taken from the temporal signal. We also searched for optimal parameters in the loading step; an integral criterion θ for an average Cmax/σ value over the injection chamber is used:
θ)
Figure 3. Example of the electric field schemes for the pinched valve for the loading and dispensing steps. Arrows show the direction of the field, and numbers correspond to the relative electric field strength i in the channels.
consider only channels of equal width and solutions with constant conductivity, the following equation reflecting Kirchhoff’s law is valid:
∑ ) 0
(1)
i
i
An example of one of the electric field distributions used in our studies for the pinched injection is depicted in Figure 3. The pinched injection consists of a loading and dispensing step, and therefore, two electric field distributions are specified. The term “injection chamber” refers to the square region defined by the channel intersection. In the pinched injection, however, during the loading step the focusing sample stream sometimes spreads into the channels 2 and 4. In such cases the integral characteristics are calculated over the larger region taking into account those portions of channels 2 and 4 (Figure 1) where the sample concentration is above zero. RESULTS Pinched Valve. Two requirements are deemed desirable for the pinched valve: the sample plugs should have (i) minimal spatial extent (or variance) and (ii) maximal sample concentration. However, these requirements result in opposite trends. Sample plugs with smaller standard deviations (σ) are obtained through stronger sample confinement, which reduces the sample concentration (Cmax) in the stream. In the present study, we attempted to find electric field distributions producing sample plugs with the criterion Cmax/σ maximized. Here, σ represents the standard deviation of the sample peak C ) C(t) monitored in channel 4, 100 µm downstream from the edge of the injection chamber (Figure 1). First, a standard deviation σt was calculated from the temporal signal using a formula for the second central statistical moment,16
∫ t c(t - t ) dt ) ∫ c(t) dt ∞ 2
2
σt
0
0
∞
(2)
0
Here t0 is the peak elution time calculated from the first statistical moment. Then, to eliminate the velocity bias, σt was multiplied (16) Giddings, J. C. Unified Separation Science; Wiley: New York, 1991.
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1 w
∫
w
Cmax(x)
0
σ(x)
dx
(3)
Here w is the channel width. This accounts for the concentration distribution in the entire injection chamber and not just in one cross section. Here the standard deviation σ is calculated for the concentration profile in the cross section perpendicular to the sample stream while the integration is being performed over the chamber width w. The integration coordinate x coincides with the axis of the sample channel. A series of simulations have been performed for injections of a neutral sample with different electric field distributions. Dimensionless sample concentration was set equal to 1.0 in the sample reservoir. All spatial variables were made dimensionless dividing them by the channel width. The convective sample transport, e.g. electroosmosis, was dominant over diffusive transport as estimated by the diffusional Pe´clet number Ped,
Ped )
vw D
(4)
where v is the net sample velocity and D is the sample diffusion coefficient. In our simulations, Ped was set to 250, but in many cases its effective value is lower since the sample velocity depends on the magnitude of the local electric field strength. Still Ped was never below 50 in the separation channel where the interplay between convection and diffusion is most important. Only symmetric electric field distributions have been simulated; that is, in the loading step the confining electric fields in the buffer and the separation channels (Figure 3) were equal, 2L ) 4L, and during the dispensing step the pullback electric fields in the sample and waste channels were equal, 1D ) 3D. Here, a second subscript, L and D, denotes the loading and dispensing step, respectively. In such cases the field distribution can be characterized by an absolute value of the electric field in just one of the channels. In the loading step the electric field in the sample channel |3L| is used, since |2L| ) |4L| ) (|1L| - |3L|)/2 ) (1 - |3L|)/2. Similarly for the dispensing step the absolute value for the electric field in the separation channel |4D| is used, because |1D| ) |3D| ) (|2D| - |4D|)/2 ) (1 - |4D|)/2. In the text below the electric field distribution for the pinched injection will be referenced with a pair of values, |3L| and |4D|. In all simulations the electric field scale was set to Emax ) 500 V/cm, and the electroosmotic mobility (µeo) was equal to 3 × 10-4 cm2/(V‚s). The sample loading confinement is defined as weak if |3L| > |2L|, strong if |3L| < |2L|, and medium if |3L| ≈ |2L|. Similarly in the dispensing step, the sample pullback is weak if |4D| > |1D|, strong if |4D| < |1D|, and medium if |4D| ≈ |1D|. In Figure 4 the criterion Cmax/σ is plotted as a function of |3L| and |4D|. A maximum is observed at |3L| ) 0.6, |4D| ) 0.3. This distribution can be described as a weak pinch during loading combined with a medium sample pullback during dispensing. As seen in Figure
Figure 4. Injection characteristics (Cmax/σ) as a function of loading (|3L|) and dispensing (|4D|) electric field schemes.
4, for a fixed electric field distribution during loading a medium sample pullback (|4D| ) 0.3-0.4) usually provides the maximal Cmax/σ compared to other pullback electric fields. If during dispensing the pullback electric field is strong (|4D| ) 0.2), a larger portion of the sample plug is drawn back into the channels 1 and 3, while a smaller percentage is dispensed into the separation channel 4 (Figure 5a). This leads to a substantial loss of sample plug mass and as a result a smaller Cmax compared to optimal pullback (|4D| ) 0.33, Figure 5b). Conversely, for a weak pullback (|4D| > 0.5) the sample plug is not cut effectively from the sample stream during sample dispensing (Figure 5c). Sample bleeds out of channels 1 and 3 into channel 4, resulting in strongly tailing sample plugs with large σ values. The behavior of the Cmax/σ ratio becomes more evident if Cmax and σ are considered independently (Figure 6a,b, respectively). For medium and strong pullback electric fields, |4D| e 0.4, σ changes very little because it is determined primarily by the loading step, and the plug is “cleanly” dispensed. For weak pullbacks (|4D| > 0.4), the standard deviation grows very quickly due to tailing, while Cmax remains essentially unchanged. Another observation made from the simulation results is the electric field distribution demonstrating the best sample loading performance, as defined by the criterion θ (eq 3), does not lead to the best overall performance as defined by Cmax/σ. Figure 7 shows the
criterion θ as a function of |3L|. The θ value reaches a maximal value at |3L| ) 0.1, which corresponds to a strong pinch. For this loading field distribution, the sample stream is relatively thin and depleted, and the losses in the sample mass are large resulting in low Cmax values (Figure 6a). During the dispensing step, a low Cmax outweighs the benefits of strong sample confinement. Note here that the optimal loading field distribution is different from the one found in Ermakov et al.13 because an average Cmax/σ is used (eq 3). Strong sample confinement and strong sample pullback reduce the mass of the sample plug compared to weak confinement and weak pullback. Different combinations of these steps produce various results. For quantitative purposes it is important to have an estimate of the mass dispensed versus the electric field distribution. Figure 8 shows the mass of the plug dispensed into the separation channel 4 as a function of the electric field in this channel. The seven lines correspond to different sample confinements during the loading step. The dispensed mass is expressed in relative units obtained by dividing by the “mass of the injection chamber”. The “mass of the injection chamber” is equal to the amount of sample with concentration 1 completely filling the injection chamber. By using relative units the results become independent of the channel width and, thus, more general. For reference, the mass which is contained in the injection chamber during the loading step is shown by markers to the right of the graph. The amount of mass dispensed in the plug ranges from mdisp ) 0.14 for |3L| ) 0.1 and |4D| ) 0.2 to mdisp ) 2.35 for |3L| ) 0.82 and |4D| ) 0.8, a factor of 16 variation. For the same sample confinement and different pullback fields the difference in the mass dispensed can be as much as 5-fold as in the case |3L| ) 0.1, and difference in mass dispensed is smaller for weak pinches. Gated Valve. During sample loading, the sample stream flowing from sample channel 2 (Figure 2) to the waste channel 1 has to be effectively isolated from the separation channel 4. Sample leakage into the separation channel will increase the background signal affecting detection. Theoretically, in the absence of diffusion, all sample will flow into the waste channel (valve off) if |2/1| e 1 and eq 1 holds. In practice, however, due to diffusion the valve off condition is more restrictive. The ratio |2/1| must be further decreased as diffusion increases relative to convective sample transport. This is illustrated in Figure 9a using experimental data,17 and Figure 9b shows the results of simulations performed under similar conditions. The equal concentration contour lines in the figures correspond to 7% of the maximum sample concentration taken at different electric field strengths Emax and a fixed value for |2/1|. The thick solid line (line 5) in Figure 9b shows the
Figure 5. Simulated images of dispensed sample plug for different pullback electric fields: (a) strong pullback |4D| ) 0.2; (b) optimal pullback |4D| ) 0.33; (c) weak pullback |4D| ) 0.8. The arrows show the direction of the field (electroosmotic flow). See text for more details.
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Figure 8. Injected sample mass as a function of the separation channel electric field |4D| for 7 different confining fields, |3L| ) 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.82. The sample mass in the injection chamber before dispensing is marked to the right of the graph. The mass is normalized by the “mass of an injection chamber”. For details, see text.
Figure 6. Maximum concentration in the sample plug (a) and the sample plug axial standard deviation (b) as a function of |4D|. Different lines correspond to different loading schemes (the values of the field in the sample channel are given by the legend).
Figure 9. Experimental (a) and simulated (b) concentration contour lines during sample loading. Different contour lines correspond to different reference electric fields: (1) Emax ) 38 V/cm, (2) Emax ) 97 V/cm, (3) Emax ) 190 V/cm, and (4) Emax ) 380 V/cm, for constant relative electric field strength 1 ) -0.68, 2 ) 0.42, 3 ) 1.0, and 4 ) -0.74. Line 5 shows the sample stream boundary in the absence of diffusion. (Part a reprinted with permission from ref 17, copyright 1999 American Chemical Society.)
Figure 7. Integral criterion θ as a function of electric field in the sample channel |3L|.
theoretical contour of the sample stream in the absence of diffusion for all Emax. In reality even at a relatively high electric field strength (line 4) the contribution of diffusion is quite noticeable since the 7% line lies well below the limiting line 5. This effect is more pronounced for the lower electric fields (lines 1 and 2) when leakage becomes apparent. (17) Jacobson, S. C.; Ermakov, S. V.; Ramsey, J. M. Anal. Chem. 1999, 71, 32733276.
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Experimental and simulated contour lines agree well at higher electric fields (lines 3 and 4), but there is a discrepancy for lower electric fields. One reason is the 2-D approximation adopted in the model assumes a constant channel width (42 µm), but the channels on the real microchip have a variable width going from 49 µm at the top of the channel down to 35 µm at the bottom due to isotropic etching of the glass substrate. The CCD images and contour lines obtained experimentally correspond to a fluorescence signal integrated over the channel depth, while in simulations it corresponds to a fixed cross section. Thus, experimentally, the thickness of the fluorescent dye layer is smaller near the channel edges, and hence, the signal is weaker. As a result, line 1 in Figure 9a has a second branch near the right wall of the
Figure 10. Percentage of sample leakage into the separation channel for different Ped and |2/1| parameters. The sizes of the circles reflect the magnitude of leakage. Stars correspond to experimental results shown by Figure 9a. See text for more details.
separation channel, and line 2 has a characteristic V-shape near the channel corner. These features are absent in simulated results. Sample leakage can be estimated as a function of the diffusional Pe´clet number (eq 4). The Pe´clet number is small when the diffusion coefficient is large, the channel width is small, or the sample velocity is small. The latter may occur if the sample moves slowly due to a low electric field strength or the sample is an anionic compound with an electrophoretic mobility close to the electroosmotic mobility. All these cases were simulated for different |2/1| ratios in order to find conditions where sample leakage is significant. The sample leakage was characterized by the percent of the sample flux entering the separation channel relative to the total sample flux transported into the intersection. The first three series of simulations were performed to study the influence of the electric field intensity and the |2/1| ratio on sample leakage. The sample used in the simulations was a neutral compound. The field intensity in the waste channel was set to either 500, 200, or 100 V/cm which corresponded to Ped ) 250, 100, or 50, and the ratio |2/1| was changed from 0.5 to 1.0. In the second series the channel width was varied from 50 to 10 µm, and the field strength in the waste channel E ) 200 V/cm and |2/1| ) 0.6 were kept constant. This corresponded to Ped ) 100, 60, 40, and 20. The last series showed the effect of different sample species on leakage. A cation with electrophoretic mobility µep ) 2.0 × 10-4 cm2/(V‚s) (Ped ) 166.7) and an anion with µep ) -2.0 × 10-4 cm2/(V‚s) (Ped ) 33.3) were simulated at 200 V/cm in the waste channel at various |2/1| ratios. Electroosmotic mobility was the same in all cases µeo ) 3.0 × 10-4 cm2/(V‚s). The results are shown in Figure 10, where the leakage is presented as a function of the |2/1| ratio and Ped number. The size of the circle reflects the magnitude of the sample leakage.
Three conclusions can be drawn. First, sample leakage increases as the |2/1| ratio increases. Second, as the total electric field strength increases, the leakage decreases. Third, anions leak more than cations because the anions have longer transit times through the valve. As seen in Figure 10, the sample leakage exceeds 1% if |2/1| and Ped corresponding to the running parameters lie to the right of the line plotted in the Ped - |2/1| plane. The experimental data shown in Figure 9a were analyzed and are indicated by the stars in Figure 10. For those experiments, |2/1| ) 0.57, and Ped calculated for the channel width 42 µm were 16.8, 42.6, 83.8, and 167.6 for lines 1-4, respectively, in Figure 9a. The stars for lines 1 and 2 lie below the 1% line indicating leakage greater than 1%, and the stars for lines 3 and 4 are above the 1% line indicating leakage is below 1%. This correlates with the experimental data shown in Figure 9a, where the leakage is obvious in the cases corresponding to lines 1 and 2, while for lines 3 and 4 the leakage is insignificant. CONCLUSIONS Computer modeling results of two injection techniques in the channel cross geometry helped identify a set of running parameters providing optimal performance. For the pinched valve a weak pinching electric field during the loading step combined with a medium pullback electric field during the dispensing step provides the sample plugs with Cmax/σ maximized. For the gated injection a set of running parameters was found providing leakage-free valve operation during the loading step. Compared with experimental data, these predictions showed good agreement. Presented in the dimensionless form for both the pinched and gated valves, the results can be easily used as a guide for proper valve operation over a wide range of experimental conditions. ACKNOWLEDGMENT This research is sponsored by the Office of Research and Development in the U.S. Department of Energy. Oak Ridge National Laboratory is managed by Lockheed Martin Energy Research Corp. for the U.S. Department of Energy, under Contract DE-AC05-96OR22464. The research was supported in part by an appointment for S.V.E. to the Oak Ridge National Laboratory Postdoctoral Research Associates Program administered jointly by the Oak Ridge National Laboratory and the Oak Ridge Institute for Science and Education. The authors thank Dr. Christopher T. Culbertson for helpful discussions.
Received for review December 28, 1999. Accepted April 7, 2000. AC991474N
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