Anal. Chem. 2001, 73, 658-666
Formation of Natural pH Gradients in a Microfluidic Device under Flow Conditions: Model and Experimental Validation Catherine R. Cabrera,*,† Bruce Finlayson,‡ and Paul Yager†
Department of Bioengineering and Department of Chemical Engineering, University of Washington, Seattle, Washington 98195
A new isoelectric focusing technique has been developed that incorporates natural pH gradient formation in microfluidic channels under flowing conditions. In conjunction, a one-dimensional finite difference model has been developed that solves a system of algebraic-ordinary differential equations that describe the phenomena occurring in the system, including hydrolysis at the electrodes, buffering effects of weak acids and bases, and mass transport due to both diffusion and electrophoresis. A quantitative, noninvasive, optically based method of monitoring pH gradient formation is presented, and the experimental data generated by this method are found to be in good agreement with model predictions. In addition, the model provides a theoretical explanation for initially unexpected experimental results. Model predictions are also shown to match well with experimental results of microfluidic isoelectric focusing of a single protein species. Accounting for the nonuniform velocity profile, characteristic of pressure-driven flow in microfluidic channels, is found to improve predictions of dynamic pH changes close to the electrodes and overall time required to reach steady state, but to reduce the accuracy of dynamic pH change predictions in other regions of the channel. As part of a program to design microfluidic systems for the detection of chemical and biological weapons, this research group has been investigating methods of biological sample preparation that take advantage of the unique conditions found in microfluidic devices. This investigation has been an expansion of previous research into development of “H-filter” technologies that rely on the imposition of a field transverse to the direction of fluid flow for the purposes of sample fractionation or concentration.1 The laminar flow conditions found in microfluidic devices minimize convective mass transport between adjacent fluid streams, so that mass transport occurs primarily via diffusion and migration in an imposed field. The application of an electric field under these conditions allows the integration of continuous-flow electrokinetic techniques with other microfluidic components. Related research * Corresponding author: (e-mail)
[email protected]; (fax) (206) 616-1984. † Department of Bioengineering. ‡ Department of Chemical Engineering. (1) Brody, J.; Osborn, T.; Forster, F.; Yager, P. Transducers ’95, 1995.
658 Analytical Chemistry, Vol. 73, No. 3, February 1, 2001
has included the development of a novel microfluidic electrochemical flow cell2 and demonstrations of its utility in concentrating proteins in static conditions3 and both vegetative bacteria and proteins under flowing conditions.4,5 Isoelectric focusing (IEF) is a fractionation technique that segregates amphoteric particles on the basis of isoelectric point and is commonly used for high-resolution analysis of biological samples, particularly for peptide and protein analysis.6,7 In part because standard methods of IEF require high power and costly ampholyte solutions, the use of IEF for preparative applications is expensive compared to other options and therefore less commonly used.8 The microfluidic IEF device described in this report (see Figure 1) addresses these concerns by generating a pH gradient between two closely spaced electrodes in a “natural” buffer system that requires low power and no synthetic ampholytes. Although a single microfluidic device has a low volumetric throughput, which could be a concern with regards to certain preparative applications, microfabrication techniques lend themselves to massively parallel fabrication, thus facilitating scaleup and the processing of high throughputs. In addition, as the processes to be performed after IEF preparative treatment are themselves miniaturized, the need for a high volumetric throughput will be replaced with a need to optimize handling of small volumes, which will also be met by developing an effective microfluidic implementation of IEF. The vast majority of IEF devices employed in biological applications generate pH gradients through the migration of a heterogeneous mixture of carrier ampholytes in an electric field or through the interdiffusion of large reservoirs of acid and alkaline buffers.6 In contrast, the device described below takes advantage of the electrolysis-driven production of H+ and OH- ions at the anode and cathode, respectively, to form a “natural pH gradient” in a simple buffer system. The idea of using a “natural” buffer system, rather than a complex mixture of ampholytes, has been (2) Holl, M.; Macounova, K.; Cabrera, C.; Yager, P. Electrophoresis, submitted. (3) Macounova, K.; Cabrera, C.; Holl, M.; Yager, P. Anal. Chem. 2000, 16, 3745-51. (4) Cabrera, C.; Macounova, K.; Holl, M.; Yager, P. 1st Annual International IEEE EMBS Special Topics Conference on Microtechnology in Medicine and Biology, Lyon, France, 2000; pp 359-62. (5) Yager, P.; Cabera, C.; Hatch, A.; Hawkins, K.; Kamholz, A.; Macounova, K. MicroTAS, Twente, The Netherlands, 2000; pp 319-22. (6) Righetti, P.; Bossi, A. Anal. Chim. Acta 1998, 372, 1-19. (7) Rodriguez-Diaz, R.; Wehr, T.; Zhu, M. Electrophoresis 1997, 18, 2134-44. (8) Evans, L.; Burns, M. Bio/Technology 1995, 13, 46-62. 10.1021/ac000495a CCC: $20.00
© 2001 American Chemical Society Published on Web 12/29/2000
Figure 1. Schematic of microfluidic electrochemical flow cell. (a) Actual device, consisting of two gold electrodes sandwiched between layers of Mylar and held together with pressure-sensitive adhesive; (b) schematic of the main sample channel (note: figure not to scale), including axes locations and channel dimensions. Note that the electrodes (dark gray) actually occupy only ∼50% of the height of the channel wall; Mylar and adhesive layers (light gray) form the top and bottom of the side walls.
investigated by a number of researchers,9-12 but there appears to be no published method that relies solely on the products of hydrolysis interacting with a buffer in solution to create the pH gradient. These hydrolysis products migrate, via diffusion and electrophoresis, toward the center of the channel, ultimately forming a steady-state pH gradient that remains stable for the duration of the experiment. Because the total distance between the electrodes is small, diffusion and electrophoresis are sufficiently rapid to allow formation of a pH gradient within seconds. A similar device was previously built and used to apply an electric field transverse to the direction of flow, but it was intended to perform electrophoresis and no pH gradient was intentionally created.13 Giddings and colleagues first proposed the idea of applying an electric field transverse to the direction of fluid flow for the purposes of microfluidic sample fractionation.14 However, the intended use of the field was as a selective force in field flow fractionation (EFFF), a batch technique that ultimately relies on the different position of particles in a parabolic flow profile to achieve separation.15 Since then, several other groups have investigated this approach.16-18 Chmelik published the first study on pH gradient formation in an EFFF device using phenol red as a representative ampholyte.19,20 Giddings and colleagues later presented the idea of a continuous-flow electrophoretic binary separator device, using a split-flow thin cell (SPLITT cell) in which (9) Nguyen, N.; Salokangas, A.; Chrambach, A. Anal. Biochem. 1977, 78, 28794. (10) Prestidge, R.; Hearn, M. Anal. Biochem 1979, 97, 95-102. (11) Slais, K. J. Microcolumn Sep. 1993, 5, 469-79. (12) Svensson, H. Acta Chem. Scand. 1961, 15, 325-41. (13) Liu, G.; Giddings, J. Anal. Chem. 1991, 63, 296-9. (14) Caldwell, K.; Keaner, L.; Myers, M.; Giddings, J. Science 1972, 176, 2968. (15) Schure, M.; Caldwell, K.; Giddings, J. Anal. Chem. 1983, 58, 1509-16. (16) Chmelik, J.; Thormann, W. J. Chromatogr. 1992, 600, 306-11. (17) Chmelik, J.; Thormann, W. J. Chromatogr. 1992, 600, 297-304. (18) Thormann, W.; Firestone, M.; Dietz, M.; Cecconie, T.; Mosher, R. J. Chromatogr. 1989, 461, 95-101. (19) Chmelik, J. J. Chromatogr. 1991, 539, 111-21. (20) Chmelik, J. J. Chromatogr. 1991, 545, 349-58.
the electric field was imposed transverse to the direction of flow.21-23 Related work led to the development of a microfluidic electrochemical flow cell for EFFF, in which, as with the device presented here, the electrodes themselves formed the channel walls.13 As with the SPLITT cell, no pH gradient was deliberately formed. A recent publication presents the results of using such a device in conjunction with EFFF to fractionate a heterogeneous mixture of polystyrene beads.24 The authors use unbuffered water and note an unexpected “wall repulsion” effect that caused experimental results to deviate from theory predictions. It is probable that this repulsive effect is actually a result of pH gradient formation leading to isoelectric focusing. Since the method of pH gradient formation described in this paper is novel, it is not surprising that there are few published mathematical models that include all the relevant electrochemical phenomena relevant to this process. Typically, those models that do allow a dynamic pH gradient either neglect electrolysis at the electrodes25 or neglect the buffering effects of weak acids/bases present in the solution. The model of Bier and colleagues26,27 does include all relevant phenomena except the effects of a nonuniform flow profile. The derivation of the model presented in this paper generally follows that of the Biers model. The method of model implementation is different, and the system to which the model is applied, particularly the method of pH gradient formation, is different. To our knowledge, this is the first published model that accounts for the effects of a parabolic flow profile on the dynamics of pH gradient formation. MATERIALS AND METHODS Apparatus. All experiments were performed in microfluidic electrochemical flow cells made of layers of Mylar (material obtained from Fraylock, an division of Lockwood Industries, Inc., San Carlos, CA), cut with a CO2 laser and assembled using preapplied pressure-sensitive adhesive.2,3 To form the electrode walls, 99.99% pure gold was sputtered directly onto O2 plasmaactivated Mylar, which was then wrapped around a core piece of Mylar coated with pressure-sensitive adhesive to form the electrodes. The channel dimensions were 0.4 mm thick × 1.25 mm wide (between electrodes) × 40 mm long (from channel inlet to outlet, the electrodes were 38.5 mm; see Figure 1. Flow was pressure-driven with syringe pumps (Kloehn Co., Ltd., Las Vegas, NV). The pumps and device were plumbed together with Upchurch (Oak Harbor, WA) tubing, fittings, and other accessories, as well as custom-built fluidic interconnects.3 Theory of Device Operation. During operation, pressuredriven fluid enters the channel, flowing along the z-axis, and an electric field is applied perpendicular to the direction of flow (see Figure 1). The applied voltage results in hydrolysis at the electrodes, with production of H+ at the anode and OH- at the cathode. The migration and diffusion of these species, combined with the equilibrium reactions of the weak acids in solution, (21) Levin, S.; Myers, M.; Giddings, J. Sep. Sci. Technol. 1989, 24, 1245-59. (22) Levin, S. Isr. J. Chem. 1990, 30, 257-62. (23) Fuh, C.; Giddings, J. Sep. Sci. Technol. 1997, 32, 2945-67. (24) Tri, N.; Caldwell, K.; Beckett, R. Anal. Chem. 2000, 72, 1823-9. (25) Saville, D.; Palusinski, O. AIChE J. 1986, 32, 207-14. (26) Bier, M.; Palusinski, O.; Mosher, R.; Saville, D. Science 1983, 219, 12817. (27) Palusinksi, O.; Graham, A.; Mosher, R.; Bier, M.; Saville, D. AIChE J. 1986, 32, 215-23.
Analytical Chemistry, Vol. 73, No. 3, February 1, 2001
659
Table 1. pKa Values for Chemicals Used in Experiments compound
pKa1
pKa2
pKa3
bromocresol purple histidine phosphate
∼1.5 1.8 2.2
6.3 6.0 7.2
9.0 12.4
generate a dynamic pH gradient that ultimately reaches a steadystate configuration.3 The development of this gradient is complicated by the nonuniform velocity profile in the channel, which itself is caused by the combination of pressure-driven flow and laminar conditions (Reynolds number between 0.01 and 0.43 in the experiments presented here). The flow adjacent to the walls of the channel is much slower than the flow in the center of the channel, so that there is effectively a longer residence time at the walls of the channel than along the channel midline. Residence time refers to the amount of time the fluid spends in the channel. Reagents. Buffered solutions of colored pH indicator dye were used to monitor pH gradient formation in the microfluidic device. All reagents were used without further purification. The acid form of the pH indicator dye bromocresol purple (BCP) was used (Aldrich Chemical, Milwaukee, WI). The buffers used were L-histidine (Avocado Research Chemicals, Karlsruhe, Germany) and sodium phosphate (Baker Chemicals, Phillipsburg, NJ). The pKa values for these chemicals are summarized in Table 1. Protocol. All experiments were carried out in 1 mM buffer, 0.1 mM Na2SO4, and 0.2 mM BCP. The electrolyte, Na2SO4, was added to increase the conductivity of solution. The flow rate was 80 nL/s unless otherwise noted. Image collection began only after a minimum of three device volumes had passed through the channel, to allow the system to stabilize. A HP 6612C power supply (Hewlett-Packard, Palo Alto, CA) was used to apply a constant voltage of 2.4 V. On the basis of the current through the system (∼6-9 µA, depending on the experimental conditions) and conductivity of the solution (3.8 × 10-3 S/m for histidine/BCP), the voltage drop across the 1.27-mm channel was actually closer to 1.8 V. The conductivity was calculated using data taken from a resistivity meter. This difference in applied versus calculated voltage suggests that there is a significant voltage drop immediately at the electrode surfaces. Image Capture. To track the formation and position of pH gradients, color images of the channel were taken using transmitted incandescent light as the illumination source. The channel was imaged with a color three-chip CCD camera (Oncor, Inc., Gaithersburg, MD) mounted to a microscope (Carl Zeiss, Inc., Thornwood, NY), and images were captured using a frame grabber (Scion CG-7, manufactured by Scion Co., Frederick, MD). The images were taken with a 10× objective; the final field of view was 1.46 × 1.1 mm. Images were taken at fixed positions down the channel, starting at z ) 0 mm and continuing to z ) 22 mm. The microscope stage was manually advanced past the microscope objective in either 1- or 2-mm increments, as measured with the micrometer incorporated into the microscope stage. Image Processing. Overview. All image processing was performed with software written in-house in Matlab. The extent of pH gradient development, as indicated by changes in indicator dye color, was extracted from each image at two fixed locations, separated by a distance of 0.5 mm in the z-direction, so that each 660 Analytical Chemistry, Vol. 73, No. 3, February 1, 2001
Figure 2. Effect of correcting for illumination variation. (a) Transmitted light image of experimental device at 2.5 mm from the inlet of the channel; (b-d) intensity profile taken at inlet of channel (black line) and intensity profile taken at 2.5 mm downstream from inlet of channel (gray line). (b) Data after image segmentation and smoothing; (c) after correction for image-to-image illumination variation; (d) after further correction for intraimage illumination variation. Experimental conditions: 0.2 mM phenol red in 1 mM phosphate buffer, 0.1 mM Na2SO4, current density 0.40 Α/m2.
image generated two pixel intensity profiles. For each intensity profile, the location of the channel walls formed by the electrodes was determined by locating pixels with values higher than the dark threshold on the red channel, which was saturated at all pH values. The pixel intensity values were then extracted for the region between the walls (see Figure 2) at two fixed locations, separated by 0.5 mm, in each image. Each intensity profile was resampled to a consistent number of pixels, smoothed with a lowpass filter, and corrected for variations in illumination. The log of these pixel levels was used as a comparison to model predictions. Illumination Variation Correction. Two kinds of illumination variation were observed in the experimental data: variation between images taken at different points in the channel and variation across the channel for a given image (intraimage). The image-to-image illumination variation was an artifact of the experimental apparatus, which reduced the intensity of the illumination close to the inlet, causing those images taken near the inlet to appear darker than images taken in the center of the channel. To correct for this variation, images were taken of the channel filled with pH indicator dye, under no-voltage and noflow conditions, and pixel intensity profiles were taken as described above. The deviation from the initial intensity profile, at z ) 0, was calculated for each subsequent profile by taking the ratio of the initial image to that of the profile of interest, on a pixel-by-pixel basis, generating a matrix of normalizing values, Mn (number of images, number of pixels). The intraimage variation may have been caused by slight height differences in the Mylar viewing window. To correct for
this variation, a second set of normalization values was generated by dividing the initial intensity profile of the background image series by its maximum pixel value (occurring approximately at the center of the channel), again on a pixel-by-pixel basis, generating a vector of normalizing values, Vn (number of pixels). Experimental data were first corrected for image-to-image illumination variation by multiplying each intensity profile by the normalizing values, Mn, that correspond to the appropriate position down the channel (see Figure 2c). The data were then corrected for intraimage variation by dividing each intensity profile by the second set of normalizing values, Vn (see Figure 2d). Model of pH Gradient Formation in a Microfluidic Electrochemical Flow Cell. 1-D Electrophoresis-Diffusion Model of pH Gradient Formation. The mathematical formulation of the processes occurring in the microfluidic electrochemical flow cell is based on the equation of continuity (eq 1), in which c(x,y,z,t) is
(
)
∂c ∂c ∂c ∂c ∂J ∂J ∂J + vx + vy + vz ) + + ∂t ∂x ∂y ∂z ∂x ∂y ∂z
(1)
the concentration of a given species, v(x,y,z,t) is the velocity, and J(x,y,z) is the mass flux. By assuming steady state (e.g., the concentration of a species at a given point in the channel does not change with time), the first term on the left-hand side of the equation may be neglected. Given the laminar flow conditions, the assumption of time-invariant fluid velocities for a given constant pump rate is valid. In essence, the length dimension (z-axis) is functioning as a pseudotime variable. The fluid velocity in the x- and y-directions is assumed to be zero, so the left-hand side of eq 1 reduces to a single term, vz∂c/∂z. The flux includes electrophoresis, diffusion, and loss and/or generation due to chemical reactions,
J ) -Fvz∇φ - D∇c + Rc
(2)
where F is the Faraday constant, ν is the absolute mobility of the species, z is the charge number of the species, φ is the electric field, D is the diffusion coefficient of the species, and Rc is the reactant term for the species. The reaction term is zero for all cases since the only reactions occurring in the channel are either acid/base equilibria, which are accounted for elsewhere in the model, or electrolysis of water, which occurs only at the electrode surface and is accounted for in the boundary conditions. The electric field is applied parallel to the x-axis, so electromigration along the y- and z-axes can be neglected. Because the y-dimension is small relative to the other dimensions (see Figure 1), it is assumed that diffusion is rapid along the y-axis and that there are no concentration gradients along the y-axis. Finally, diffusion along the z-axis is neglected because convective transport is assumed to be significantly faster than diffusion along the z-axis. The validity of this assumption is discussed in more detail in the Results and Discussion section. These approximations allow eq 1 to be simplified to the following continuity equation for steady-state, 1-D laminar flow:
[
]
∂c(x,z) dJ(x) 1 ) dz dx v(x)
(3)
To solve for concentration at any point in the channel, this PDE is transformed to an ODE in the x-direction by applying finite difference methods (eq 4).28 The species included in the model
[(
)]
i dcin Jj+1 - Jij 1 ) dz ∆x v(n)
(4)
are the following: H+, OH-, carbonic acid (both HCO3- and H2CO3), the two charged forms of the indicator dye (Dye- and Dye2-), all protonation states of the buffer (e.g., For MES: C6H12NO4S-, C6H13NO4S, C6H14NO4S+), Na+, SO42-, O2, and H2. The fully protonated form of the pH indicator dye is neglected because the pKa for that equilibrium reaction is very low (
