Anal. Chem. 2004, 76, 4968-4976
A Microfluidics Approach to the Problem of Creating Separate Solution Environments Accessible from Macroscopic Volumes Jessica Olofsson,† Johan Pihl,† Jon Sinclair,† Eskil Sahlin,‡ Mattias Karlsson,§ and Owe Orwar*,†
Department of Chemistry and Bioscience, and Microtechnology Centre, Chalmers University of Technology, SE-412 96 Go¨teborg, Sweden, Cellectricon AB, Fabriksgatan 7 SE-412 50 Go¨teborg, Sweden, and Department of Chemistry, Gothenburg University, SE-412 96 Go¨teborg, Sweden
We report on a microfluidic device that generates separate solution environments in macroscopic volumes. Spatially distinct patterns are created by emitting fluids from 16 different sources (closely spaced microchannels) into a solution-filled macroscopic chamber. The fluid in neighboring microchannels couples viscously in the macroscopic container, generating one single interdigitated stream. Scanning nanoelectrode amperometry was used for characterizing the concentration landscape and the diffusion zones between solutions running in parallel at different coordinates in the stream. These experiments were complemented by finite element simulations of the Navier-Stokes and mass transport equations to describe the velocity distributions and the diffusion behavior. For in channel flow velocities of 50 mm‚s-1, patterns could persist on the order of millimeters to centimeters in the open volume. The most narrow diffusion zones with widths less than 10 µm (5-95% concentration change) were found some tens of micrometers out in the macroscopic container. We demonstrate that a 14-µm-diameter nearly spherical object (biological cell) attached to a micropipet can be moved from one solution environment to another by a lateral displacement of only 8 µm. The device is suitable for applications where the solution environment around a microscopic or nanoscopic sensor needs to be changed multiple times, i.e., in order to build layered structures, for obtaining binding isotherms, and kinetic information, for example, on ion channels, enzymes, and receptors as well as in applications where different loci on an object need to be exposed to different environments or where complex solution environments need to be created for studies of interfacial chemistry between two streaming layers. In bulk solutions made out of different species at thermodynamic equilibrium, the probability of finding each component at its respective concentration in any volume element equals unity. Such solutions are homogeneous or perfectly mixed. In a number * Corresponding author: (e-mail)
[email protected]; (phone) + 46 (0)31 772 27 78; (fax) + 46 (0)31 772 27 85. † Chalmers University of Technology. ‡ Gothenburg University. § Cellectricon AB.
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of applications, it would be of interest to achieve the contrary, i.e., inhomogeneous perfectly separate aqueous solution environments as part of the same bulk system at room temperature. To solve the problem with well-defined volume fractions with negligible mixing between different fractions, streaming liquids at low Reynolds numbers can be employed. Previous studies have shown diffusion-limited mixing in parallel fluids entering the same microchannel, creating two or several separate solution environments. Such diffusion-limited mixing in two fluids with preserved laminar behavior has been used to initiate chemical reactions in the diffusion zone to reduce silver ions to metallic microelectrodes,1 to study chemotaxis,2 and to label separate regions of biological cells.3 Also, analytical applications based on differential diffusive behaviors of different species in the mixing zone between two laminar streams have been reported4-6 as well as a variety of approaches to accomplish a well-controlled, rapid mixing behavior.7-12 These applications of microfluidics have been obtained and studied in confined systems and rely on the wellbehaved laminar flow that is characteristic for systems of small dimensions. None the less, the small dimensions involved impose some constraints on the application areas as the flow cannot easily be accessed by external objects, such as sensors, electrodes, or biological materials attached to pipets or other probes. Here we use and characterize a microfluidic device that creates patterned laminar flow accessible from macroscopic volumes. The (1) Kenis, P. J. A.; Ismagilov, R. F.; Whitesides, G. M. Science 1999, 285, 8385. (2) Jeon, N. L.; Baskaran, H.; Dertinger, S. K. W.; Whitesides, G. M.; Van de Water, L.; Toner, M. Nat. Biotechnol. 2002, 20, 826-830. (3) Takayama, S.; Ostuni, E.; LeDuc, P.; Naruse, K.; Ingber, D. E.; Whitesides, G. M. Nature 2001, 411, 1016. (4) Kamholz, A. E.; Weigl, B. H.; Finlayson, B. A.; Yager, P. Anal. Chem. 1999, 71, 5340-5347. (5) Kamholz, A. E.; Yager, P. Biophys. J. 2001, 80, 155-160. (6) Kamholz, A. E.; Schilling, E. A.; Yager, P. Biophys. J. 2001, 80, 1967-1972. (7) Vijayendran, R. A.; Motsegood, K. M.; Beebe, D. J.; Leckband, D. E. Langmuir 2003, 19, 1824-1828. (8) Brody, J. P.; Yager, P.; Goldstein, R. E.; Austin, R. H. Biophys. J. 1996, 71, 3430-3441. (9) Knight, J. B.; Vishwanath, A.; Brody, J. P.; Austin, R. H. Phys. Rev. Lett. 1998, 80, 3863-3866. (10) Liu, R. H. S., M. A.; Sharp, K. V.; Olsen, M. G.; Santiago, J. G.; Adrian, R. J.; Aref, H.; Beebe, D. J. J. Microelectromech. Syst. 2000, 9, 190-197. (11) Song, H.; Ismagilov, R. F. J. Am. Chem. Soc. 2003, 125, 14613-14619. (12) Stroock, A. D.; Dertinger, S. K. W.; Ajdari, A.; Mezic, I.; Stone, H. A.; Whitesides, G. M. Science 2002, 295, 647-651. 10.1021/ac035527j CCC: $27.50
© 2004 American Chemical Society Published on Web 08/05/2004
system opens up possibilities for new applications in areas where separate environments being part of the same solution are needed and flow in closed structures cannot be used. Examples are scanning and deposition applications involving probes as micropipets, electrodes, or patch-clamped cells where microscopic areas need to be exposed to a sequence of solutions in a precise way with fast switching times in the millisecond regime. We have previously reported on the use of a similar device in patch-clamp recordings of ion channel activity, as a tool for rapid solution exchange and sequential delivery of ion channel ligands.13 When running this device in the low Reynolds number regime, the flow exiting the channels couples and advances as one single laminar stream where mixing of the fluids from adjacent channels occurs only through diffusion. To characterize the diffusion behavior and the resulting concentration profiles with submicrometer resolution in the open volume, we performed scanning nanoelectrode amperometry experiments. The study was focused on a moderate in-channel mean velocity of 3 mm‚s-1, suitable for applications involving cells as presented in previous work.13,14 However, the system was also tested for velocities up to 50 mm‚s-1, and at such high velocities, separate solution environments reflecting the loading pattern of the device persists on the order of millimeters to centimeters out in the open volume. This paper presents the first characterization of diffusion between adjacent stream zones in the interface between a microfluidic system and a larger volume as well as the first characterization of a microfluidic system using nanoelectrodes. The velocity profile and the diffusive mixing in the open volume were as well investigated using finite element method simulations. EXPERIMENTAL SECTION Master Fabrication. Six-inch CZ, [100], two sides polished, N-Ph 1-10 Ω‚cm silicon wafers with a thickness of 525 µm (Topsil Semiconductor Materials A/S, Frederikssund, Denmark) were cleaned for 10 min in a 80 °C RCA-2 solution (a 1:1:5 mixture of 32% H2O2/37% HCl/H2O), rinsed in DI water, and dried in a Rinseand-Drier. The wafer was spin coated with MicroChem SU-8 2035 (MicroChem Corp, Newton, MA), yielding a typical thickness of 60 µm, and preexposure baked at 65 °C for 4 min and at 95 °C for 8 min on a hot plate. The wafer was exposed on a Carl Su¨ss MA6 mask aligner through a patterned chrome mask for a dose of 600 mJ‚cm-2. The wafer was postexposure baked at 65 °C for 1 min and at 95 °C for 8 min on a hot plate. The wafer was developed for 6 min in MicroChem XP SU-8 developer, rinsed in 2-propanol, and blow-dried. The master was then silanized for 3 min in a 1% solution of dichlorodimethylsilane in toluene, rinsed in toluene, 2-propanol, and blow-dried. Device Fabrication. The master was mounted in a mold defining the outer dimensions of the chip as well as the sample wells and the recording chamber. The structures on the mold did not make contact with the structures on the master, to prolong the lifetime of the master. Mixed PDMS was injected into the mold, and cured for 10 min at 140 °C. The PDMS piece was dismounted from the mold, and holes were punched through at the sample well and the recording chamber. The PDMS piece (13) Sinclair, J.; Pihl, J.; Olofsson, J.; Karlsson, M.; Jardemark, K.; Chiu, D. T.; Orwar, O. Anal. Chem. 2002, 74, 6133-6138. (14) Sinclair, J.; Olofsson, J.; Pihl, J.; Orwar, O. Anal. Chem. 2003, 75, 67186722.
was bonded to a 71 × 41 mm microscope slide with a thickness of 0.6 mm or a No. 1 coverslip with a thickness of 130 µm (VWR International, Stockholm, Sweden), depending on whether the device was intended for use with the electrochemical probe, fluorescence microscopy, or confocal laser scanning microscopy. The microscope slide and the PDMS piece were exposed to an oxygen plasma (Plasmatherm RIE m-95, 15 s, 85 W, 250 mTorr, 10 cm3‚m O2) and immediately afterward aligned and brought together, forming an irreversible seal. Cell Culture. Adherent PC-12 cells were cultivated on circular coverslips in Petri dishes for 4-8 days in (DMEM/F12) medium supplemented with antibiotics and antimycotin (0.2%), fetal calf serum (10%), and L-glutamine. Before the fluorescence experiments, cells were washed and detached in a HEPES-saline buffer containing (in mM): 10 HEPES, 140 NaCl, 5 KCl, 1 CaCl2, 1 MgCl2, and 10 D-glucose (pH 7.4). All chemicals used in the cell culturing were from Sigma-Aldrich Sweden AB (Stockholm, Sweden). Microfluidic Device and the Basic Setup. The device presented in this article has 16 channels of dimensions 50 × 57 µm (w × h) individually addressing 16 sample reservoirs and exiting into a macroscopic open volume. At the point of exit, the channels are separated by 22-µm-thick walls. The volume of the 16 sample reservoirs is 80 µL, and the dimensions of the open volume are 35 × 20 × 4 mm (w × l × h). Prior to experiments, the sample reservoirs were loaded with different solutions using a micropipet. A 2-mm-thick polycarbonate lid was attached over the sample reservoirs using double adhesive tape (3M, Stockholm, Sweden) in order to create a closed system. The lid was connected to a syringe with PE tubing, and a syringe pump (CMA/100, microinjection pump, Carnegie Medicine, Cambridge, U.K.) was used to compress the air enclosed by the lid to initiate a welldefined pressure-driven flow in the channels. Finally, the open volume was filled with solution. Fluorescence Microscopy. A device was placed on an inverted microscope (Leica DM IRB, Leica, Wetzlar, Germany) equipped with a 488-nm Ar+ laser (2025-05, Spectra Physics Laser Inc., Mountain View, CA). To obtain epifluorescence, a spinning disk was placed in the beam path to break the coherence and scatter the laser light. The light was reflected off a polychroic beam splitter and sent through a 5×, 10×, or 40× objective. Fluorescence images were obtained by a CCD camera. The device was loaded with MilliQ water in every second channel alternated with carboxylate-modified fluorescent polystyrene microspheres (0.027-µm diameter, Molecular Probes, Eugene, OR) diluted to 0.1% solids in MilliQ water. Carbon Fiber Nanoelectrodes. Carbon fiber nanoelectrodes were fabricated from 11-µm-diameter carbon fibers (Goodfellow Cambridge Ltd., Huntingdon, England) and borosilicate capillaries with 0.58-mm inner diameter and 1-mm outer diameter (Harvard Apparatus Ltd., Edenbridge, Kent, U.K.). A carbon fiber was inserted into a capillary that was pulled apart using a Sutter P-2000 micropipet puller (Sutter Instruments Co, Novato, CA), forming two micropipets connected by the carbon fiber and enclosing it. The carbon fiber was split, and the resulting endings protruding from the micropipets were flame etched in a candle flame and pulled back into the micropipet so that only ∼100 µm protruded. The glass was melted to fix and enclose the carbon fiber through Analytical Chemistry, Vol. 76, No. 17, September 1, 2004
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moving the micropipet tip quickly through the candle flame. The carbon fiber was connected to a silver wire from inside the glass pipet using conductive epoxy (ELFA, Ja¨rfa¨lla, Sweden). The flameetched carbon fiber was insulated through electrodeposition of phenol (Merck, Darmstadt, Germany) and 2-allylphenol (SigmaAldrich Sweden AB) as described by Strein and Ewing.15 Finally, the insulating coating was removed from the tip of the flameetched carbon fiber so that an electroactive electrode was exposed. This was accomplished by scratching the tip against a vertical silicon surface under the microscope. The steady-state current of the electrode in a nonstirred solution of 10 mM ferrocyanide with 0.5 M KCl as supporting electrolyte in MilliQ water was 120 pA. The diameter of the electroactive area of the electrode was estimated to be in the order of 100 nm by the relation I ) 4rnFDC, holding for disk electrodes in nonstirred solution and where r is the radius of the electrode, n the stoichiometric number of electrons involved in the electrode reaction, F the Faraday constant, D the diffusion coefficient of the electroactive species, and C the bulk concentration of these species.16 The diffusion coefficient of ferrocyanide in 0.5 M KCl was calculated to 7.37 × 10-10 m2‚s-1. The contour of the electrode was made as slim as possible in order to minimize disturbances of the flow during concentration profile measurements. Concentration Scans Using Carbon Fiber Nanoelectrodes. A 16-channel device was loaded with 10 mM potassium ferrocyanide (Sigma-Aldrich Sweden AB) and 0.5 M KCl (Merck) in MilliQ water in channels 2, 4, 6, 8, 9, 11, 13, and 15 alternated with 0.5 M KCl in MilliQ water. The device was placed on a microscope (Leica DM IRB) equipped with a motorized scanning stage (Proscan, Prior Scientific, Cambridge, U.K.) and a CCD camera (C166157-01, Hamamatsu, Kista, Sweden). This equipment, together with micromanipulators (Narishige, Tokyo, Japan), was placed on a vibration-isolated table inside a Faraday cage. A carbon fiber nanoelectrode connected to a HEKA EPC-10 triple patchclamp amplifier (HEKA Elektronik, Lambrecht/Pfalz, Germany) was positioned outside the channels with the micromanipulators, and an Ag/AgCl electrode (Axon Instruments, Foster City, CA) was placed in the open volume and used as a combined counter and reference electrode. A flow of an in-channel mean velocity of 3 mm‚s-1 was started, and a potential of +0.8 V (vs Ag/AgCl) was applied to the carbon fiber nanoelectrode. The nanoelectrode was scanned outside the channel outlets through translating the scanning stage, and the concentration profile of ferrocyanide in the open volume was measured using amperometry. In amperometry, the steady-state current response is linearly dependent on the bulk concentrations of electroactive species. This also holds for experiments in stirred solutions or performed under flow conditions. Changes in flow velocity in general affect electrode currents as the mass transport to it changes. Due to the small size of the electrodes used, the velocity dependence was not noticeable even when the velocity varied as much as from 0.5 to 3.9 mm‚s-1. The current-concentration translation scale for the scans was set by peak and dip plateau values corresponding to full ferrocyanide concentration and zero concentration within the scans. Due to electrode fouling during the measurements, the current corresponding to a specific concentration was slowly (15) Strein, T. G.; Ewing, A. G. Anal. Chem. 1992, 64, 1368-1372. (16) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, 2nd ed.; Wiley: New York, 2001.
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decreasing. To account for this decrease not only between scans but also within scans, each current peak was normalized individually in scans where possible (all scans but for y ) 150 µm). In scans where plateau values were only found outside channels 8 and 9 (all scans for y ) 150 µm), this plateau value was used for normalization of the whole scan. The scanning velocity during measurements was 10 µm‚s-1 and the sample frequency 200 Hz, resulting in a spatial sample frequency corresponding to 20 data points/µm. Data were filtered with a 30-Hz FFT low-pass filter. Confocal Laser Scanning Microscopy. A 16-channel device was used where the normal bottom microscope slide had been exchanged for a coverslip with a thickness of 130 µm in order to able to utilize high-magnification, high-aperture optics with short working distance. Three channels of the chip were loaded with extracellular buffer solution together with 50 µg‚mL-1 FM 4-64 membrane staining, red fluorescent dye (Molecular Probes) and 5 mg‚mL-1of a fluorescein-labeled dextran with a average molecular mass of 2 MDa (Dex-fl 2MD, Molecular Probes) having a diffusion coefficient of ∼6 × 10-12 m2‚s-1 (estimated from D ) kBT/6πηrg in conjunction with approximations of the radius of gyration (rg) for the dextran polymer17). The remaining channels were loaded with 50 µL/mL FM4-64 in extracellular buffer. A channel flow of 3 mm‚s-1 was started. Cells were added to the open volume of the device, and one of them patch-clamped. The patch-clamped cell was placed 30 µm above the bottom outside a channel not containing Dex-fl 2MD for a few minutes, moved to the border of a channel containing Dex-fl 2MD, and slowly moved into that channel using a high-graduation micromanipulator (Narishige MC-35A, Tokyo, Japan). The x-coordinate of the cell was changed in small steps while the z- and y-coordinates were kept constant. The following switching of solution around the cell was studied using a Leica TCS RS SP2 laser scanning confocal microscopy system equipped with a PL AP 63× magnification 1.32 NA oil immersion lens (Leica, Wezlar, Germany). Finite Element Method Simulations. To estimate flow velocities and flow directionality close to and at the orifices of the microchannels, the flow was simulated with the finite element method program FEMLAB (Comsol, Stockholm, Sweden). An application mode based on the Navier-Stokes equations was used and the equations
-∇‚η(∇u + (∇u)T) + F(u‚∇)u + ∇p ) F ∇‚u ) 0 where η is the viscosity, u the velocity, F the density, p the pressure, and F body forces were solved for the geometry shown in Figure 2A. The geometry corresponds to two half-channels separated by a wall and a reduced open volume. In the simulations, gravity was omitted and the body force F set to zero. The fluid density F was set to 103 kg‚m-3 and the viscosity η to 1 mPa‚s. The inflow velocity was set to 3 mm‚s-1 for the whole cross section of the channel inlets (u(x,y,z) ) (0,3,0) mm‚s-1), and on the curved border, an outflow boundary condition defined by the pressure and the normal component of the viscous force equaling zero was used (p ) 0, n‚η(∇u + (∇u)T) ) 0, where n is the normal to the (17) Andrieux, K.; Lesieur, P.; Lesieur, S.; Ollivon, M.; Grabielle-Madelmont, C. Anal. Chem. 2002, 74, 5217-5226.
Comparison of Experimental and Simulated Concentration Profiles. The agreement between the normalized measured and simulated concentration profiles was analyzed through estimating the correlation coefficient, n
∑(x - jx)(y - jy) i
r)
i
i)1
x
x
n
n
∑(x - jx) ∑(y - jy) 2
i
i)1
2
i
i)1
where xi are simulated concentration values and yi corresponding experimental values from the zones outside channels 6 and 7. As well, the mean of the squared difference defined as n
∑(y - x )
2
Figure 1. (A) SEM image of the channel outlets acquired prior to bonding of the bottom microscope slide. The width of the channels is 50 µm, and the height is 57 µm. The width of the walls separating the channels is 22 µm. In (B), a patterned flow obtained at an inchannel flow velocity of 50 mm‚s-1 is shown. The channels are loaded with MilliQ water and green fluorescent polystyrene microspheres (0.027-µm diameter in MilliQ water) in an interdigitated fashion. The picture was acquired through a 5× objective. Scale bar is 100 µm. (C) shows a closeup of two channel outlets taken with 40× objective. The left and right channels were respectively loaded with red and green fluorescent polystyrene microspheres (0.027-µm diameter) in Milli Q water, and the flow velocity was 3 mm‚s-1. (D) shows a light microscopy image of the channel outlets with a carbon fiber nanoelectrode placed outside the outlets. In (A), (C), and (D), the scale is given by the channel width, 50 µm.
boundary surface). On the sides of the geometry, symmetry boundary conditions were used (n‚u ) 0, t1‚η(∇u + (∇u)T) ) 0, t2‚η(∇u + (∇u)T) ) 0, where t1 and t2 are the tangentials to the boundary surface). On all other boundaries, no-slip conditions (u ) 0) were used. The meshing of the geometry was refined until a convergence plot showed no further changes in values of the solution for chosen control spots in the geometry. In control simulations, the position of the curved border and the boundary settings on it was varied and the results were compared with the simulation presented here in order to make sure that this imposed boundary did not influence the fluidics very close to the channel outlets considerably. Simulations of the concentration profiles in the open volume were performed by coupling a mass balance equation to the simulated velocity profile. The equation ∇ ‚(-D∇c + cu) ) 0, where c is the concentration and D is the diffusion coefficient, was solved for the geometry. The first and second terms in the flux vector (-D∇c + cu) are the diffusive and the convective contributions, respectively. The following boundary conditions were used. A fixed concentration of 1 at the inlet of the left channel (c ) 1), 0 concentration at the inlet of the right channel (c ) 0), mass transport only through convection over the curved border (n‚(-D∇c) ) 0), and no mass transport over the remaining borders (n‚(-D∇c + cu) ) 0) of the geometry were used. The concentrations were kept in a dimensionless form and can be scaled to hold for any choice of absolute values. The diffusion coefficient was set to 7.37 × 10-10 m2‚s-1.
i
i
i)1
n was calculated. RESULTS AND DISCUSSION A Low Reynolds Number-Featured System. The microfluidic device consists of a PDMS mold plasma-bonded to a glass slide. The chip contains 16 sample reservoirs individually addressing a channel system that emanates as a tightly packed array into a container with the size of 35 × 20 × 4 mm (w × l × h). At the loci of exit, the 50-µm-wide and 57-µm-high channels are closely spaced and separated by 22-µm-thick walls (see Figure 1A). The Reynolds number of fluid flow inside the channels was estimated to ∼0.2 at an average flow velocity of 3 mm‚s-1 by using the hydraulic radius rh ) 4A/P, where A is the cross-sectional area of the channel and P the wetted perimeter, as the typical length scale of the system.4 The Reynolds number is the estimate of the influence of inertia versus viscous forces in fluid systems and is defined by Re ) ULF/ η, where U is the characteristic velocity in the system, L the characteristic length scale, F the density, and η the viscosity. Low Reynolds numbers imply that inertia forces are of minor importance, that the flow is laminar, and that mixing between adjacent layers occurs only through diffusion.18 Whereas the in-channel Reynolds number can be exactly calculated, the Reynolds number of the channel-macroscopic volume system is harder to define. However, as the length scale of the system increases, the velocity decreases (see Figure 2D), indicating that the Reynolds number of the system should remain fairly constant in the proximity of the channel exits. Velocity Profiles in the Interfacial Region. As fluid exits a channel, it starts to spread in all directions and follows the contour of the channel roof and the endings of the channel-separating walls. Outside the channel exits, fluid from adjacent channels meet and couple so that one single laminar stream is created. Due to this coupling between streams, the sideway spreading of the fluid is suppressed and thereafter takes place mainly in the forward (18) Landau, L. D.; Lifshitz, E. M. Fluid Mechanics, 2nd ed.; Pergamon Press: New York, 1987.
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Figure 2. (A) Geometry used in the finite element method simulations of the fluidics. The geometry corresponds to two half-channels separated by a wall and emanating into an open volume. (B) and (C) show side views of the velocity profiles obtained in front of the center of a channel (x ) 0 µm) and in front of a wall (x ) 36 µm), respectively, for an in-channel mean velocity of 3 mm‚s-1. (D) shows the velocity profile for a slice 28.5 µm above the bottom of the device (z ) 28.5 µm). The velocities can be read out from the color bar, and the direction of the flow is shown by the arrows. At the walls, the velocity of the fluid is zero due to the use of no-slip boundary conditions. For low Reynolds numbers, particles and walls influence the behavior of flow over considerably long distances and it takes ∼ 50 µm before differences in velocity for different x-values level out to less than 20%. In (B) and (C), it is shown that there is no preference for the forward direction compared to the upward direction on a length scale on the order of the channel dimensions, indicating a low Reynolds number flow dominated by viscous forces.
and the upward directions. Fluid exiting the end channels (channels 1 and 16) behaves slightly different because they couple only to a flowing stream in one lateral dimension and to the stagnant bulk fluid in the other. In Figure 2B-D, velocity profiles obtained from finite element method simulations are shown in cross section plots for x ) 0 µm, x ) 36 µm, and z ) 28.5 µm. At the walls, the fluid velocity is zero due to the use of no-slip boundary conditions. However, further away from the channelseparating walls, the fluid velocity increases through viscous coupling to faster moving fluid. That sideway spreading is suppressed by fluid exiting adjacent channels is indicated by the minor broadening of the zones in Figure 1B. A fluorescence micrograph of a region outside a channel wall is displayed in Figure 1C, showing the outlets of two adjacent channels loaded with 27-nm-diameter beads and run at an average in-channel velocity of 3 mm‚s-1. Concentration Profiles and Diffusion Zones in the Macroscopic Volume. When loading the sample reservoirs with different substances, an interdigitated flow is created in the open volume with mixing between different solution environments occurring through diffusion only. Figure 1C shows the sharp interface obtained outside the wall endings when loading adjacent 4972 Analytical Chemistry, Vol. 76, No. 17, September 1, 2004
streams with slow-diffusing 27-nm-diameter beads (D ∼ 1.6 × 10-11 m2‚s-1, estimated from D ) kBT/6πηrg) and having an average in-channel velocity of 3 mm‚s-1. Although sharp interfaces are obtained close to the channel outlets, diffusion starts as soon as the fluids couple into one stream and finally, at some distance from the channel outlets, the solutions will be perfectly mixed. The degree of mixing at different coordinates of the open volume depends on the flow velocity and the diffusion coefficients of the different species involved. Using flow velocities of 50 mm‚s-1, and fluorescently labeled polystyrene beads with D ∼ 1.6 × 10-11 m2‚s-1, the pattern persists tens of millimeters out in the open volume. The first millimeter of such flow is shown in Figure 1B. Figure 3 shows concentration profiles for ferrocyanide in the open volume for an average in-channel velocity of 3 mm‚s-1. The curves were obtained using scanning nanoelectrode amperometry. As can be seen, the positions of the peaks are virtually constant along the x-axis for y-values as high as 100 µm. When combining the simulated velocity profile with the mass balance equation describing convective and diffusive flux (for details, see Experimental Section), it results in a concentration landscape that agrees well with the experimental data. This can be seen in Figure 4, where the shapes of experimentally derived
Figure 3. (A) Schematic of channel outlets showing how coordinates are defined. (B-F) show concentration profiles for different heights above the bottom of the device (different z-values) obtained from detection with a carbon fiber nanoelectrode. All curves are normalized so that maximum response (i.e., 10 mM ferrocyanide) corresponds to 1. The distance between the gridlines on the plot corresponds to a step from 0 to 1 in concentration. The concentration profiles can be scaled to hold for other initial concentration choices on the assumption that the diffusion coefficient does not change. For z ) 80 and 100 µm, the concentration profile at y ) 10 µm was never measured as the chip wall had corrugations on the order of 10 µm that high up. The center-to-center distance for the channels is 72 µm (which is also the distance between the grid lines on the x-axis). The edge channels (channels 1 and 16) support the middle channels, and as can be seen, only slight broadening of the solution zones have taken place in the x-direction even as far from the channels as y ) 100 µm. At y ) 150 µm, solution zones originating from channels 2 and 15 have broadened considerably in the x-direction for high z-values. In amperometric concentration measurements, changes in flow velocity in general affect the electrode current as the mass transport to the electrode surface is changed. For small electrodes, this dependence is less pronounced and no dip is seen in the curves when passing the wall between channels 8 and 9, although the velocity in front of the wall falls to less than 15% of the maximum velocity for z ) 20 µm and y ) 10 µm.
diffusion zones are displayed together with profiles obtained from simulations. The good agreement shows that the fluid mechanics and the diffusion behavior of the device have been simulated
accurately as well as that the carbon fiber nanoelectrodes did not considerably affect the diffusion zones (see figure text for details). Given the small cross section of the nanoelectrodes in the Analytical Chemistry, Vol. 76, No. 17, September 1, 2004
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Figure 4. Closeups of the measured concentration profiles presented in Figure 3 shown together with the corresponding simulated profiles. The experimental curves show the diffusion zones between solutions originating from channels 6 and 7. The average correlation coefficient and the average of the means of the squared difference between respective pairs of simulated and experimentally measured concentration values were 0.999 29 and 0.000 508 for normalized concentrations. If excluding the curve for z ) 20 µm and y ) 150 µm (contains errors due to nonindividual normalization; see Experimental Section, r )0.99948 and mean of the squared difference 0.003 91), the least correlation obtained were 0.996 75 and the largest mean of the squared difference 0.001 97 (both for z ) 20 µm and for y ) 80 µm). The simulated and the measured curves deviate very little from each other, and the deviations often are dominated by measurement noise, showing that the system has been simulated accurately as well as that the experimental characterization method has little influence on the system itself. However, for some curves, mainly including curves for z ) 20 µm, the measured diffusion slightly lags the simulated. Close to z ) 20 µm, the derivative of the velocity is high, and the measurements are sensitive to the exact position of the electrode. The largest point value difference in concentration found between simulated and experimentally curves was 0.096 75 (expressed in normalized concentration). The discrepancies can be explained by the insecurity in positioning the electrodes, being ∼(2 µm in the z-axis, together with possible mismatches between real values of a number of parameters, as for example diffusion coefficients, and the theoretical values used of these parameters in the simulations.
direction of the flow compared to the channel and wall dimensions, this is well in line with theoretical predictions. At the contact zones where fluids exiting adjacent channels first meet and couple, the concentration gradient is steep and fluid moves slowly due to the close presence of the channel-separating walls (see Figure 2C and D). Thus, there is a large driving force as well as relatively long periods of time available for the diffusion zones to evolve before reaching the first measuring points in the experiments (y ) 10 µm). Further out, the concentration gradient is less steep, and importantly, the slowly moving fluid has gained velocity through momentum transfer from fluid passing closer to the centers of the channels. This results in a slower evolution of diffusion zones if measured in spatial coordinates along the y- and z-axes. As can be seen in the traces from the scanning nanoelectrode experiments displayed in Figure 3B and C, the solution pattern remained fairly constant for coordinates reaching some tens of micrometers above the bottom of the chip (the z-direction) and some tens of micrometers out from the channels (the y-direction). The most narrow diffusion zones are not found in 4974 Analytical Chemistry, Vol. 76, No. 17, September 1, 2004
the very vicinity of the channel but some tens of micrometers further out as can be seen in Figure 5. The explanation to this phenomenon is the increase in velocity outside the channelseparating walls, resulting in a convergence of streamlines and a narrowing of the diffusion zones, as well as the upward spreading of the fluid. Complex Concentration Patterns in Open Volumes. By loading the sample reservoirs with different chemical species, complex concentration patterns in three-dimensional fluid space can be created using a large number of different substances. Due to diffusional spreading, not only environments containing the pure loading solutions will be found but also environments containing different mixtures of the species involved. In the characterization experiments shown in Figure 3, the concentration profile from one single substance was measured. However, loading the chip with a larger number of substances, overlapping concentration profiles can be created and it would be possible to expose, for example, a probe not only to a sequence of pure solutions but also to different mixtures of them evolved through diffusion. As
Figure 5. Plot showing experimentally measured widths for the diffusion zones, defined as the distance over which a 5-95% concentration switching occurs. Note that the diffusion zones are not narrowest closest to the wall but some tens of micrometers further out. This phenomenon is also seen in the simulated concentration profiles. The explanation is the increase in velocity outside the channel-separating walls, resulting in a convergence of streamlines and a thinning of the diffusion zones, as well as the upward spreading of the fluid. The y-values with the narrowest diffusion zones are slowly shifting for increased z-values, following the shifting of highest fluid velocities. The narrowest diffusion zones are found for z ) 20 µm and y ) 10-30 µm. Here the concentration shifts from 5 to 95% of maximum concentration over less than 10 µm.
these systems can accurately be simulated with finite element methods, as shown in Figure 4, computer simulations can be used in the design and characterization of different loading patterns. Systems with flow trajectories and velocity profiles easier to describe than the ones presented here can be achieved through adding large support channels essentially functioning as fluid walls and thereby restricting the broadening of the flow. Prevention of broadening also results in maintenance of velocity, which increases the length scale of pattern persistence considerably. Other possible refinements involve extension of the one-dimensional channel arrays into two dimensions and to systems having both inflow and outflow channels with individual pressure control in order to direct the flow within the open volume. For example, by altering the positions for negative pressure application, switching between different flow paths for the fluid exiting the outlet channels can be accomplished. Further, the approach of exiting microchannels into open volumes can also be implemented together with previously developed microfluidic systems, i.e., T-sensors4 or gradient generation systems.19,20 Solution patterns created using microfluidics systems entering into macroscopic containers can be used for solution exchange around objects that are too large for microchannels or are attached to macroscopic structures. It is also possible to expose different parts of such objects to different solutions, here demonstrated for a biological cell censor in Figure 6D. In contrast to previously presented subcellular patterning methods, the cell can be accessed by probes for electrochemical or patch-clamp measurements. In (19) Dertinger, S. K. W.; Chiu, D. T.; Jeon, N. L.; M., W. G. Anal. Chem. 2001, 73, 1240-1246. (20) Jeon, N. L.; Dertinger, S. K. W.; Chiu, D. T.; Choi, I. S.; Stroock, A. D.; Whitesides, G. M. Langmuir 2000, 16, 8311-8316
Figure 6. Confocal fluorescence images showing solution switching around a cell. A patch-clamped cell with a radius of ∼7 µm is moved in small steps between the zones outside two adjacent channels. The following switching of solution around the cell was studied with confocal laser scanning microscopy. The cell is stained with the red fluorescent dye FM 4-64, and one of the channels contains green fluorescent Dex-fl 2MD. The fluid is forced to take new paths due to the presence of the cell and follows the contour of it, most pronousedly seen in (E). The distance moved between (C) and (E), resulting in a full switching of the fluid flowing around the cell, is less than 10 µm. The scale bar is 10 µm.
scanning applications, either an object can be moved across the channel outlets or the flow velocities may be varied so that the environment at different positions in the open volume can be changed. Several parameters such as flow velocity and diffusion coefficients can be used to tune the degree of diffusion and mixing at different coordinates. Predictable flow systems of this type further have the advantage of mapping time into the spatial domain. Diffusion and chemical reactions are dynamic processes evolving in time. As different times are coupled to different coordinates in the open volume through flow trajectories and velocities, the time evolution can be read out in a static picture. Solution Switching around Objects. If a spherical object is placed in a flow having a sufficiently low Reynolds number, the fluid will split at a stagnation point as it reaches the object and then spread in different directions to follow the contour of the object. The object will thus be surrounded by fluid that, in principle, originates from the same point.18 This is also true for many objects that are not spherical but axisymmetric with the Analytical Chemistry, Vol. 76, No. 17, September 1, 2004
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symmetry axis in the direction of the flow. For systems where diffusion is negligible, such objects in theory only have to be moved an infinitesimal distance in order to experience a switching between two solutions emanating from adjacent channels on a chip. In such ideal systems, the size of the object should not influence this distance. In reality, these statements rarely hold for two reasons. First, most objects are not perfectly spherical/ perfectly symmetric. Second, diffusion is in general not negligible close to objects as the velocity of the fluid passing is slowed by the object itself. The slower the fluid moves (which depends on the in-channel velocity, the positioning of the object, and the size of the object), and the higher the diffusion coefficient of the species in the two solutions is, the more diffusive exchange take place between the fluids as they pass the object, and the more the diffusion zone is broadened. Thus, the object has to be moved a correspondingly longer distance before experiencing a total switching of its solution environment. We have previously reported on the usefulness of the device described here for solution exchange around patch-clamped cells.13 To investigate the solution switching around a patchclamped cell with a geometry deviating from a perfect sphere, and being attached to a glass micropipet, confocal microscopy studies were performed. In Figure 6, a sequence of confocal microscopy images describing the switching is shown. The cell is moved from a solution containing a high molecular weight fluorescein-labeled dextran having a very small diffusion coefficient (D ) 6 × 10-12 m2‚s-1) and a solution not containing this species. As can be seen, the cell experiences a complete switching of fluid environment by being moved only 8 µm. Note that we here consider stationary situations. In a dynamic, time-dependent situation, for instance, where the cell is moved fast between the fluid environments, the situation becomes more complex due to drag along of the fluid.18 CONCLUSIONS We have presented and characterized a microfluidic device generating patterned laminar flow in open volumes. By varying the loading patterns of the device, it is possible to obtain complex concentration landscapes of one or several substances as well as
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discrete environments of a multitude of substances. This is the first characterization of fluid flow and diffusion in the interface of a microfluidic system and a larger volume as well as the first characterization of a microfluidic system using nanoelectrodes. The velocity profile and the diffusive mixing in the open volume were also investigated using a finite element method, and good agreement was seen between experimental and theoretical data, indicating that these systems can be simulated accurately and that they can be designed with the help of computers. As the concentration landscapes are created in an open volume, they are accessible for different sensors as exemplified by cells connected to structures of macroscopic dimensions such as patchclamp pipets and electrodes. Other applications, for example, building of layered structures, studies on solvent extraction, various aspects of interfacial chemistry, and onset characterization of chemical reactions, should be equally feasible to conduct using this technology. The main objective of the work presented here has been to create and characterize spatially distinct solution environments with length scales of tens to hundreds of micrometers accessible in open volumes. For applications involving larger structures, the channel dimensions can be scaled up or channel velocities increased. It is also possible to downscale the system for applications involving scanning of submicrometer objects across collimated streams. ACKNOWLEDGMENT This work was supported by the Royal Swedish Academy of Sciences, the Swedish Research council (VR), and the Swedish Foundation for Strategic Research (SSF) through a donation from the Wallenberg Foundation. We express our gratitude to Daniel Fagerlund for help with editing digital images and figures and to Leica for allowing us to use their confocal scanning microscopy system.
Received for review December 22, 2003. Accepted June 8, 2004. AC035527J
