Reverse of Mixing Process with a Two-Dimensional Electro-Fluid

Feb 18, 2010 - Mixing of two solutions into one is a spontaneous process with a net .... one direction due to diffusion, as calculated by the mass bal...
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Anal. Chem. 2010, 82, 2182–2185

Letters to Analytical Chemistry Reverse of Mixing Process with a Two-Dimensional Electro-Fluid-Dynamic Device Chang Liu,† Yong Luo,‡ E. Jane Maxwell,† Ning Fang,‡ and David D. Y. Chen*,† Department of Chemistry, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada, and Ames Laboratory-U.S. Department of Energy, Department of Chemistry, Iowa State University, Ames, Iowa 50011 Mixing of two solutions into one is a spontaneous process with a net increase in entropy. However, the reverse of the mixing process is usually not possible unless certain conditions are met. A continuous solution stream containing a mixture of two compounds can be separated into two channels, each containing a pure compound, thus reversing the mixing process using a two-dimensional microfluidic electro-fluid-dynamic (EFD) device. When the electric field is strategically applied in the interconnecting channels of an EFD device, the pressure required to direct an analyte into a certain channel can be calculated by using the solutions of electric field and fluid dynamics in the mass balance equation. If the pressure and electric potential at various inlets and outlets satisfy these predetermined conditions, the reverse of a mixing process is observed. Conventional microfluidic devices have been used to introduce samples from interconnecting channels or efficiently mix different solutions into a single channel. The EFD devices expand the spatial separation of analytes from one dimension to two using both the differential migration behavior of analytes and the velocity field distribution in different channel geometries. The devices designed according to these basic physicochemical principles can be used for complete processing of minute samples and to obtain pure chemical species from complex mixtures. Column separation techniques such as chromatography and capillary electrophoresis (CE) can separate a mixture into zones of pure compounds according to their differential migration behavior when interacting with a stationary phase in a flowing stream1 or in an electric field2,3 or when both phenomena occur at the same time.4 Two-dimensional gel electrophoresis separates compounds into different locations along two orthogonal directions * Corresponding author. Phone: (604) 822-0878. Fax: (604) 822-2847. E-mail: [email protected]. † University of British Columbia. ‡ Iowa State University. (1) Martin, A. J. P.; Synge, R. L. M. Biochem. J. 1941, 35, 1358–1368. (2) Hjerten, S. Chromatogr. Rev. 1967, 9, 122–219. (3) Jorgenson, J. W.; Lukacs, K. D. Anal. Chem. 1981, 53, 1298–1302. (4) Terabe, S.; Otsuka, K.; Ichikawa, K.; Tsuchiya, A.; Ando, T. Anal. Chem. 1984, 56, 111–113.

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on a flat surface when a small volume of a sample solution is loaded on a slab gel.5,6 However, most currently used mainstream separation techniques require the loading of a small sample. Free flow electrophoresis (FFE) is another two-dimensional separation method that is capable of continuously processing a mixture and separating different components into streams in a free-flowing liquid continuum so that individual components can be collected in different locations downstream.7,8 Microfluidic devices have been used to introduce samples from interconnecting channels and to efficiently mix different solutions into a single channel.9 Other devices have also been developed for particle sorting that uses the different flow patterns resulting from different channel geometries.10-13 This letter demonstrates that when a two-dimensional electro-fluid-dynamic (EFD) device is used for separation, a mixture can be separated into two separate flow channels and both components can be collected simultaneously in the two separate outlets. EXPERIMENTAL SECTION Rhodamine 110 (Exciton, Dayton, OH), and ethidium bromide (Invitrogen, Eugene, OR) solutions at a concentration of 10 mg/ mL were prepared in the background electrolyte (BGE, 160 mM borate, pH 9.0). The EFD devices shown in Figure 1 were fabricated with PDMS (Sylard184, Dow Coring, Midland, MI) according to established protocols.14 The width of the lateral channels (AC, BC) and the main channel (CD) were 50 and 100 µm, respectively. The depth of all PDMS channels was 200 µm. The positive potentials at points A and B (1000 and 900 V, respectively) were applied by a high-voltage power supply (SL150, Spellman High Voltage Electronics, Hauppage, NY), and the (5) O’Farrell, P. H. J. Biol. Chem. 1975, 250, 4007–4021. (6) Klose, J. Humangenetik 1975, 26, 231–243. (7) Raymond, D. E.; Manz, A.; Widmer, H. M. Anal. Chem. 1994, 66, 2858– 2865. (8) Fonslow, B. R.; Bowser, M. T. Anal. Chem. 2008, 80, 3182–3189. (9) Harrison, D. J.; et al. Science 1993, 261, 895–897. (10) Huang, R. H.; Cox, E. C.; Austin, R. H.; Strum, J. C. Science 2004, 304, 987–990. (11) Yamada, M.; Nakashima, M.; Seki, M. Anal. Chem. 2004, 76, 5465–5471. (12) Kawamata, T.; Yamada, M.; Yasuda, M.; Seki, M. Electrophoresis 2008, 29, 1423–1430. (13) Johann, R.; Renaud, P. Electrophoresis 2004, 25, 3720–3729. (14) Duffy, D. C.; McDonald, J. C.; Schueller, O. J. A.; Whitesides, G. M. Anal. Chem. 1998, 70, 4974–4984. 10.1021/ac902938g  2010 American Chemical Society Published on Web 02/18/2010

Figure 1. Schematics of the setup: (a) channel geometry of the microfluidic EFD device and (b) a schematic of the device made from a 2.54 cm × 7.62 cm PDMS chip.

pressure induced velocity was precisely controlled through a syringe pump (Harvard Apparatus, Holliston, MA) to achieve the required conditions. Point E is grounded through an electric cable. During the experiment, the analyte mixture was introduced through vial A, while vials B and E were filled with clean BGE. A Nikon Eclipse 80i microscope was used in this study, and the fluorescence signals were recorded by an Andor EM CCD camera (South Windsor, CT). The optical band-pass filters used were from Thorlabs (Newton, NJ), and their full width at half-maximum (fwhm) were 10 nm. When it was necessary to monitor the migration behaviors of two analytes simultaneously, the microscope was operated at two wavelengths using a MAG Biosystems dual-view filter (Optical in Sights, Tucson, AZ) with a 565 nm dichroic filter. A 530 nm filter was used for rhodamine 110, and a 600 nm filter was used for ethidium bromide. THEORETICAL BASIS The migration behavior of analytes in a two-dimensional EFD device, illustrated in Figure 1, can be calculated using a finiteelement-scheme simulation software, COMSOL Multiphysics (COMSOL Inc., Los Angeles, CA). When voltages are applied to different locations, the electric field distribution in the conducting channels can be calculated by solving the Laplace equation(∇2V b ) -∇V. The ) 0), and the electric field at any given point is E boundary conditions are clearly defined by the applied potentials. When the concentrations of the analytes are much lower than that of the background electrolyte (BGE), the effect of analytes on electric field distribution could be omitted. Thus the electric field distribution for a given device mainly depends on the applied potential and the channel geometry. The field strength shown in Figure 2a can be used in the calculation of the fluid velocity field and mass balance equation. The fluid velocity field of a conducting solution can be described by the simplified Navier-Stokes equation -∇p + η∇2b v ) 0, where p is the pressure, η is the viscosity coefficient, and b v is the fluid velocity vector of any point in the fluid field. The

Figure 2. Simulated results of the fork area (ACB) obtained from COMSOL Multiphysics. The channel dimensions used for the simulation are the same as those used in the experiment, as described in the Experimental Section. (a) Electric field distribution under the experimental conditions, where the voltages are 1000 and 900 V for vials A and B, respectively, and vial E is grounded. (b) An example of fluid velocity field when a pressure of 1500 Pa is applied at vial F. (c) An example of concentration distribution of the analyte when both voltages at A and B and a pressure at F are applied. It should be noted that the velocity field in part b shows that the velocity at the wall and that at the center have different orientations because the electroosmotic flow (EOF) and the pressure induced flow are in opposite directions. The net flow of analyte, however, only goes to one direction due to diffusion, as calculated by the mass balance equation. The concentrations from high to low are illustrated from red to blue.

conservation of mass principle gives the relationship of ∇ · b v ) 0, which is used in conjunction with the Navier-Stokes equation to solve for the pressure and velocity. The boundary condition is controlled by the applied hydrodynamic pressure at vial F in Figure 1, and the electroosmotic flow is generated from the walls of the individual channels. The velocity vector and pressure at each point can be calculated. Figure 2b demonstrates a simulated fluid velocity field in the microdevice when a pressure is applied against the electric field. The migration behavior of the analytes in the EFD device is determined by numerically solving the mass balance equation (∂c/ b) · ∇c + ∇ · (-D∇c) ) 0, where c is the analyte ∂t) + (v b + µepE concentration at a specific location, D is the diffusion coefficient, Analytical Chemistry, Vol. 82, No. 6, March 15, 2010

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Figure 3. Behavior of one analyte: (a) simulated concentration distribution of R110 when (1) the pressure flow from F is high, preventing R110 from entering the device, (2) the pressure from F is adjusted so that R110 flows along ACB, (3) the pressure is adjusted so that R110 flows along both ACB and ACDE directions, and (4) the pressure is so small that all R110 flows along the ACDE direction. The concentration of the analyte from high to low is depicted by the color scheme of red to blue. (b) Experimental verification using R110. The fluorescence images of the fork of ACB were recorded using a CCD camera. (c) The boundary conditions for R110 to be localized in vial A, moving along ACB, moving along both ACB and ACDE, and moving along ACDE only.

µep is the electrophoretic mobility of the analyte, and the values of b v and b E are obtained from the previous calculation for electric field and fluid field. Thus the analyte concentration and its variation with time at any location can be calculated to determine the analyte migration behavior, as shown in Figure 2c. The steady state velocity of a charged particle that is moving b+ in the channel can be written as b v)b vep + b veo + b vp ) µepE b µeoE + b vp, where electrophoretic velocity (v bep) is discriminative and determined by its electrophoretic mobility (µep), which is a intrinsic property for a particular analyte. On the other hand, the electroosmotic velocity (v beo) and pressure-induced velocity (v bp) are nondiscriminative and affect all components equally. With careful control of nondiscriminative velocities, analytes with similar µep can be made to migrate in opposite directions. The limiting factor in this case is the resolution of the pressure control system, which can be highly precise when a syringe pump is used. The syringe pump used in this work has a resolution of 0.001 µL/min (1 nL/min). With a flow rate of 300 nL/min in the channels, the ∆µep is in the range of 2-4 × 10-10 m2 V-1 s-1. For the EFD device shown in Figure 1, lateral channels AC and BC are symmetrical about the main channel and the width of the main channel (CD) is twice that of the lateral channels. Therefore the value of pressure-induced velocity is consistent in channels AC, BC, and CD. The electric field strength in the main channel CD is the average of the values in the two lateral channels. In this experiment, the potential applied in vial A is higher than that in vial B, so that the electric field strength in AC is higher than CD, which is in turn higher than that in BC. Therefore, when the reverse pressure from F decreases, the flow in AC will start in the forward direction first, before the flow in CD. The forward flow in BC will start only when the pressure in F is further reduced. Figure 3a shows the simulated concentration distributions of a single analyte in the microchannels as the pressure-induced 2184

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velocity is varied from high (1) to low (4). The direction of the steady-state analyte velocity in the channels is indicated as well. When the pressure from vial F is high, the steady state velocity of the analyte in any channel of AC, BC, and CD has the same direction as b vp. In this case, the analyte stays at the injection vial A and never migrates into AC or any other channel, as illustrated in the first case (a1) in Figure 3. As the magnitude of b vp decreases, the steady state velocity of the analyte reverses in channel AB first, forcing all of the analyte to migrate through point C to the collection vial B, as demonstrated in the second case (a2) in Figure 3. In case 3, |v bp| decreases to be small enough to let the analyte reach point D but at the same time not so small that it would stop the flow of the analyte in the C-B direction. When the pressure is very low, as in case 4, all of the analyte migrates along the direction of electric field, from injection vial A, through point C and D, and toward the collection vial E because the steady state velocity of the analyte in any channel of AC, BC, and CD has the opposite direction with b v p. The boundary values of |v bp| for these four migration cases in the EFD device are indicated in Figure 3c. Because these values are analyte specific and are determined by the analyte electrophoretic mobility (µep), when a mixture of analytes is continuously injected from vial A, the pressure can be adjusted so that specific analytes will migrate to different vials according to the predetermined boundary values, achieving the reverse process of mixing. In order for such a process to be possible, the second boundary value (Y in Figure 3c) for the slower component needs to be less than the third boundary value (Z in Figure 3c) for the bBC|(µeo + µep,fast). bCD|(µeo + µep,slow) < |v faster component: |E bp| < |E The value of electric fields in different channels can be altered by changing the voltage applied at vials A and B. Therefore, so long as there is an electrophoretic mobility difference between two analytes, the proper electric field and pressure values can be chosen to demonstrate the reverse of the mixing process.

Figure 4. Behavior of two analytes: (a) relative boundary conditions that determine the flow directions of R110 and EB and the relative conditions used in the experiment and (b) fluorescence images at 530 nm for R110 and 600 nm for EB taken simultaneously to demonstrate (1) R110 flowing along ACB and EB flowing along both ACB and ACDE, (2) R110 flowing along ACB and EB flowing along ACDE only, demonstrating the reverse of a mixing process, and (3) R110 flowing along both ACB and ACDE but EB only flowing along ACDE.

RESULTS AND DISCUSSION To verify the results from the theoretical predictions, we used the fluorescent dye rhodamine 110 to demonstrate the four different migration paths in the EFD devices for a single analyte, as the pressure-induced velocity is varied from high to low. The images in Figure 3b clearly show that the analyte migration in different branches of the EFD device can be controlled by adjusting the pressure at vial F in Figure 1, once proper voltages at different inlet and outlet vials are set. To experimentally demonstrate the reverse process of mixing, a mixture of two fluorescent dyes was used as the injection stream. Rhodamine 110 (upper part in parts a and b of Figure 4) has a smaller µep than ethidium bromide (lower part in parts a and b of Figure 4) under the experimental conditions. In the first condition depicted in Figure 4, a relatively high pressure pushes rhodamine 110 to collection vial B, while ethidium bromide is collected in both vial B and vial E. Condition 2 is the state in which the mixture is separated into two channels each containing one dye. Rhodamine 110 and ethidium bromide from the injection mixture in vial A diverge into different channels at point C. In this case, vial B collects pure rhodamine 110 and vial E collects pure ethidium bromide. If the applied pressure is further reduced, some rhodamine 110 may enter vial E as well, comigrating with ethidium bromide (condition 3 in Figure 4). It should be pointed out that animated simulation results showed that it is possible for some analytes to go into the wrong channels initially because of the different velocity field at different locations of the channels cross section (e.g., parabolic flow profile) or because of diffusion. However, because the steady state flow defines the net migration behavior, the molecules are forced to go back to the proper channel if the length of the channel is long enough. The distance the analyte travels to the other channel is related to the width of the channel and the angle of the fork, as determined by fluid

dynamics, as shown in Figure 2. This phenomenon was also confirmed by the experiment. CONCLUSIONS The geometry of flow channels can be used to enhance the separation of chemical or biological materials, in addition to the commonly used driving forces such as chemical equilibrium and electric or magnetic field. The continuous demixing achieved with the simple EFD devices allows complete processing of small samples to obtain pure compounds from complex matrixes. The results demonstrated in Figure 2 show that analytes can either be forced to stay in vial A or forced to go into channel CB or CD depending on their intrinsic electrophoretic mobilities, suggesting that a pure component from a mixture can be collected in vial B if proper voltages and pressure are set. The predictable nature and ease of operation could lead to a new generation of purification devices to serve the needs of biomedical research and other commercial and academic activities. ACKNOWLEDGMENT The first two authors contributed equally to this work. D.D.Y.C. was supported by the Natural Sciences and Engineering Research Council of Canada, and N.F. was supported by the Director of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, U.S. Department of Energy (DOE). The Ames Laboratory is operated for DOE by Iowa State University under Contract No. DE-AC02-07CH11358.

Received for review December 22, 2009. Accepted February 11, 2010. AC902938G

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