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Pressure-Sensitive Microfluidic Gates Fabricated by Patterning Surface Free Energies Inside Microchannels† Bin Zhao,‡ Jeffrey S. Moore,*,‡ and David J. Beebe§ The Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, and Department of Biomedical Engineering, The University of WisconsinsMadison, Madison, Wisconsin 52706 Received July 24, 2002. In Final Form: October 8, 2002 A series of pressure-sensitive microfluidic gates to regulate liquid flow have been successfully fabricated by patterning surface free energies inside microchannels using self-assembled monolayers in combination with either multistream laminar flow or photolithography. The designs are based on the principles of surface-directed liquid flow previously reported. Aqueous liquids, including protein solutions, are confined to the hydrophilic pathways (or the most hydrophilic pathway) under spontaneous flow conditions and flow into the hydrophobic regions or the less hydrophilic pathways when pressures exceed critical values. A programmable pressure-sensitive liquid delivery device is demonstrated. We have also investigated the initial rate of liquid flow in surface-patterned microchannels under spontaneous flow conditions from both analytical and experimental approaches. The methods described here provide an alternative to the conventional approaches to control liquid flow in the fast-developing field of microfluidic systems.
Valves are critical components of microfluidic devices. Traditionally, microvalves are fabricated from silicon or other stiff materials by micromachining and are categorized as passive or active valves depending on whether they have powered actuation mechanisms.1 Passive valves require no external control (e.g., check valves). Active valves that allow the control of liquid flow by external means provide increased functionality. A variety of actuation mechanisms including thermal expansion, thermopneumatic, electrostatic, and electromagnetic have been employed in developing active valves.1 However, traditional micromachining methods are limited by the need for complex, time-consuming processes and equipment. Alternative approaches using simple and costeffective procedures are being sought. Compared to hard materials typically used in micromachining, soft materials such as poly(dimethylsiloxane) (PDMS) and other polymers have many attractive characteristics including low cost, easy fabrication, disposability, and comformability, and thus they are receiving growing attention in the field of microfluidics.2-11 For instance, Unger et al. have developed multilayer soft lithography using replica mold* To whom correspondence should be addressed. E-mail: moore@ scs.uiuc.edu. † Part of the Langmuir special issue entitled The Biomolecular Interface. ‡ University of Illinois at Urbana-Champaign. § University of Wisconsin at Madison. (1) Kovacs, G. T. A. Micromachined Transducer Sourcebook; McGrawHill: Boston, 1998. (2) Xia, Y.; Whitesides, G. M. Angew. Chem., Int. Ed. 1998, 37, 550. (3) Unger, M. A.; Chou, H. P.; Thorsen, T.; Scherer, A.; Quake, S. R. Science 2000, 288, 113. (4) Quake, S. R.; Scherer, A. Science 2000, 290, 1536. (5) McDonald, J. C.; Metallo, S. J.; Whitesides, G. M. Anal. Chem. 2001, 73, 5645. (6) McDonald, J. C.; Duffy, D. C.; Anderson, J. R.; Chiu, D. T.; Wu, H.; Schueller, O. J. A.; Whitesides, G. M. Electrophoresis 2000, 21, 27. (7) Delamarche, E.; Bernard, A.; Schmid, H.; Michel, B.; Biebuyck, H. Science 1997, 276, 779. (8) Beebe, D. J.; Moore, J. S.; Bauer, J. M.; Yu, Q.; Liu, R. H.; Devadoss, C.; Jo, B. H. Nature 2000, 404, 588. (9) Yu, Q.; Bauer, J. M.; Moore, J. S.; Beebe, D. J. Appl. Phys. Lett. 2001, 78, 2589. (10) Liu, R. H.; Yu, Q.; Beebe, D. J. J. Microelectromech. Syst. 2002, 11, 45.
ing and bonding of elastomeric materials to build active microfluidic systems containing on-off valves, switching valves, and pumps.3,4 McDonald et al. have fabricated single-use valves by PDMS molding.5 Stimuli-responsive hydrogels that exhibit volume changes in response to environmental conditions such as pH and temperature have been used in our group to fabricate microfluidic valves capable of regulating liquid flow without external control by self-adjusting in response to the liquid constituents.8-10,12 These types of valves can be made in a short length of time, and the processes do not require clean room conditions. Here we report on a different approach to fabricate microfluidic gates with functions similar to those of valves. The designs and fabrication are based on the principles of surface-directed liquid flow and the methods of patterning surface free energies that we developed.13-15 While surface patterns on one substrate can be achieved by a variety of techniques,2,16-18 our methods allow us to pattern surface free energies on the top and bottom substrates of microchannels simultaneously. The initial rate of liquid flow in surface-patterned microchannels under spontaneous flow conditions is also investigated. In previous publications, we described patterning surface free energies inside microchannels by use of selfassembled monolayers (SAMs) in combination with either multistream laminar flow or photolithography to direct liquid flow. Aqueous liquids flow only along the hydrophilic pathways when the pressure is maintained below a critical value. The gas-liquid interface is pinned precisely at the boundary between the hydrophilic and hydrophobic (11) Yu, C.; Xu, M.; Svec, F.; Frechet, J. M. J. J. Polym. Sci., Part A: Polym. Chem. 2002, 40, 755. (12) Zhao, B.; Moore, J. S. Langmuir 2001, 17, 4758. (13) Zhao, B.; Moore, J. S.; Beebe, D. J. Science 2001 291, 1023. (14) Zhao, B.; Moore, J. S.; Beebe, D. J. Anal. Chem. 2002, 74, 4259. (15) Zhao, B.; Viernes, N. O. L.; Moore, J. S.; Beebe, D. J. J. Am. Chem. Soc. 2002, 124, 5284. (16) Husemann, M.; Morrison, M.; Benoit, D.; Frommer, K. J.; Mate, C. M.; Hinsberg, W. D.; Hedrick, J. L.; Hawker, C. J. J. Am. Chem. Soc. 2000, 122, 1844. (17) Xia, Y.; Qin, D.; Yin, Y. Curr. Opin. Colloid Interface Sci. 2001, 6, 54. (18) Aizenberg, J.; Black, A. J.; Whiteside, G. M. Nature 1999, 398, 495.
10.1021/la026294e CCC: $25.00 © 2003 American Chemical Society Published on Web 11/12/2002
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Figure 2. Schematic illustration of the tip of a liquid flowing through the hydrophilic pathway. The top and bottom are hydrophilic glass substrates; the hydrophobic virtual walls on the two sides are separated by a distance of w. Figure 1. (a) Schematic illustration of multistream laminar flow of HD, a solution of OTS in HD, and a solution of HFTS in HD. (b) Optical micrograph of an aqueous dye solution flowing (a) along the hydrophilic pathway under spontaneous flow conditions, (c) into the OTS region under a pressure of 26 mmH2O, and (d) into the HFTS region under a pressure of 39 mmH2O.
regions. Because there are no physical walls on the sides of liquid streams, liquids are referred to as being confined by virtual walls. The maximum pressure that virtual walls can withstand in a straight liquid stream is Pmax ) (2γ/h) sin(θn - 90°), where γ is the liquid surface tension, h is the channel depth, and θn is the advancing contact angle of liquid on the hydrophobic region. A higher value of θn will result in a higher maximum pressure. Experimentally, we have confirmed this equation by patterning channel surface free energies using multistream laminar flow in combination with SAMs of either octadecyltrichlorosilane (OTS) or heptadecafluoro-1,1,2,2-tetrahydrodecyltrichlorosilane (HFTS). The values of θn of water on SAMs of OTS and HFTS are 112° and 118°, respectively; γwater is 72.1 mN/m. Calculations show that the values of Pmax are 300 N/m2 (30.6 mmH2O) and 376 mN/m2 (38.4 mmH2O) for OTS-patterned and HFTS-patterned channels with a height of ∼180 µm. Experimental values are 31 and 37 mmH2O for OTS and HFTS monolayers, respectively, in good agreement with calculated values. On the basis of the maximum pressure differences for SAMs of OTS and HFTS, we designed and fabricated θn-dependent pressuresensitive microfluidic gates. As illustrated in Figure 1a, hexadecane (HD), a solution of OTS in HD, and a solution of HFTS in HD were pumped into the channels and maintained under laminar flow for a predetermined period of time.19 SAMs formed on the top and bottom substrates of channels simultaneously in the areas where OTS and HFTS solutions flowed through, while the other areas remained hydrophilic. Once the surface was patterned, aqueous dye solutions flowed only along the hydrophilic pathway under spontaneous flow conditions (Figure 1b). Liquid flowed into the OTS region when the applied (19) The channels used here were made from glass slides and glass coverslips according to the method described in previous publications (refs 8 and 12). HD (99%) was purchased from Aldrich and used as received. The concentrations of OTS and HFTS in HD were 0.5% w/v. Syringe pumps (Harvard Apparatus PHD 2000 programmable) were used to pump HD and solutions into the channels. HD was always introduced into the channel prior to the silane solution to eliminate the formation of SAMs in unwanted areas. At the end of process, flow of the silane solution was always halted before stopping the flow of pure solvent. The flow rates of solvent and solution were usually the same, either 1 or 2 mL/min; the flow time was 2-3 min (contact angle measurement showed that SAMs with full coverages formed on cover glasses in less than 2 min). The channels were cleaned by sequentially flushing with 10 mL of hexane and 10 mL of methanol followed by drying with a stream of clean air or nitrogen.
pressure was 26 mmH2O (Figure 1c).20 At a pressure of 39 mm, liquid flowed through the entire channel as shown in Figure 1d. Since surface hydrophobicity can be tuned by use of mixed SAMs of two different trichlorosilanes, the liquid flow direction in surface-patterned channels can be well controlled. In surface-directed liquid flow as shown in Figure 1b, liquid is confined by two hydrophilic physical walls separated by distance h and two virtual walls spaced by a width w. The advancing contact angle of water on virtual walls can be viewed as 180° as small water drops assume a round shape in air. Figure 2 shows the tip of a liquid stream advancing along a hydrophilic pathway. R1 and R2 are the radii of curvature of the liquid tip surface in directions vertical and parallel to the liquid stream. The capillary force generated from the hydrophilic surfaces produces a side-view profile with a negative R1, dragging liquid forward. The retraction force from the hydrophobic virtual walls results in a top-view profile with a positive R2, dragging liquid backward. These two forces interplay with each other and determine the critical geometry for spontaneous liquid flow. If |R2| > |R1|, ∆P < 0 and water spontaneously wets the hydrophilic pathway. If |R2| < |R1|, ∆P > 0 and water cannot spontaneously flow through the hydrophilic region. The critical condition for spontaneous flow occurs when |R2| is equal to |R1|, that is, w ) h/(cos θp), where θp is the advancing contact angle of liquid on the hydrophilic region. If θp ) 0°, the critical width is equal to the channel depth. A higher liquid contact angle on the hydrophilic region requires a larger width for liquid flow to take place spontaneously. On the basis of the critical width equation, we have designed and fabricated θp- and width-dependent, pressure-sensitive microfluidic gates to control liquid flow. Here, a more flexible method, photolithography in combination with photocleavable SAMs, was used to generate hydrophilic/hydrophobic surface patterns for fabricating microfluidic gates. Upon exposure to UV irradiation, the o-nitrobenzyl-oxygen bond in the SAM of 2,2,3,3,4,4,5,5,6,6,7,7,8,8,8-pentadecafluoro-1-octyl 4-(11trichlorosilyl-1-oxoundecyloxymethyl)-3-nitrobenzoate (FSAM) is cleaved. The carboxylic acid groups are thus exposed to the air interface, making the surface hydrophilic (Figure 3a).14,15,21 Two UV light sources were employed to deprotect F-SAM deposited on cover glasses and photopattern surface free energies inside microchannels. One is from an Olympus Epi-Fluorescent microscope and another one is Novacure.21 Figure 3b shows the relationship between UV irradiation time and water advancing contact angle (θa) on a F-SAM-coated cover glass by use (20) The surface tension of the aqueous Rhodamine B dye solution is lower than that of deionized water, resulting in a lower maximum pressure.
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Figure 3. (a) Photodeprotection of F-SAM upon exposure to UV irradiation and (b) the effect of UV irradiation time on the surface wettability of F-SAM. (b) Advancing contact angle of water; (9) advancing contact angle of pH ) 11.8 NaOH solution.
of UV from the microscope. Water θa decreases fast in the beginning but levels off after 90 min. X-ray photoelectron (21) Glass slides and glass cover slips were treated with “piranha” solution (70/30, v/v, concentrated H2SO4/30% aqueous H2O2) at 60 °C for 30 min before the use for microchannel assembly (caution: piranha solution reacts violently with many organic materials and should be handled with great care). For F-SAM deposition, in a typical experiment, 2,2,3,3,4,4,5,5,6,6,7,7,8,8,8-pentadecafluoro-1-octyl 4-(11-trichlorosilyl1-oxoundecyloxymethyl)-3-nitrobenzoate (22 mg) was dissolved in toluene (8.00 g) in a scintillation vial. The solution was allowed to age for a certain period of time until 1 min immersion of piranha-treated cover glasses resulted in a H2O advancing contact angle of 118°. The aging time varied depending on the ambient humidity and water content in toluene and was determined in each experiment. The solution was filtered by use of a 0.45 µm poly(tetrafluoroethylene) filter encased by polypropylene (Alltech) if it became cloudy upon standing. Once the optimal aging time was determined, the silane solution was injected into the microchannels and was flushed away by hexane after 1 min. The channel was then rinsed with methanol and dried with a stream of clean air. A photomask was placed on top of a F-SAM-coated channel filled with 0.1 M HCl, and a coverslip was placed on top of the photomask to ensure that it was flat. Two UV light sources were employed to generate hydrophilic/hydrophobic surface patterns. One is from an Olympus Epi-Fluorescent microscope (BX-60) passing through a nearUV filter cube (U-MNUA, type BP 360-370 nm) with a band-pass of 360-370 nm wavelength. A 2× lens was used. Another one is Novacure (EFOS, model N2001-A1). Typical irradiation conditions are as follows: the UV intensity is preset at 5700 mW/cm2, the distance between the lens and F-SAM is 20 mm, and the exposure area is 12 mm in diameter. The introductory pathways on the two ends were also irradiated in order that aqueous solutions spontaneously fill the channel. The channel was sequentially flushed with 10 mL of deionized water and 10 mL of methanol and then dried with a stream of clean air or nitrogen.
spectroscopy (XPS) analysis on a F-SAM irradiated by UV light for 2.5 h showed that the nitrogen peak belonging to the nitro group was not detectable. However, the fluorine peak did not totally disappear, indicating that the reaction is close to complete but not quantitative.14 A curve similar in shape to that in Figure 3b was obtained by use of Novacure, but water θa decreases about 60 times faster under the typical Novacure irradiation conditions. The UV light source in Novacure has a much higher power. Obviously, the surface wettability of F-SAM can be readily controlled by UV irradiation time. We have taken advantage of this ability to fabricate θp-dependent pressuresensitive microfluidic gates. Figure 4a shows the photomask that was used to fabricate hydrophilic-hydrophobic surface patterns inside microchannels. The widths in both pathways are 625 µm. Region A on the left side of the dashed line was irradiated with UV light from the microscope for 120 min, and region B on the right side of the dashed line was irradiated for only 60 min. Thus, the water advancing contact angles on the two sides of the dash line are different, and consequently, so are the critical widths that support spontaneous water flow. According to Figure 3b, the values of H2O θp on regions A and B are 69° and 76°, respectively, corresponding to the critical widths of 502 and 744 µm. Therefore, under the spontaneous flow condition, water wets region A but does not flow into region B as shown in Figure 4b. Increasing
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Figure 4. θp-Dependent pressure-sensitive microfluidic gates. (a) Optical micrograph of the photomask that was used in patterning surface free energies inside a microchannel; the widths in pathways A and B are 625 µm. (b) Optical micrograph of a water stream under spontaneous flow conditions. (c,d) Optical micrographs of water flow under a pressure of 12 mmH2O recorded at different times. A circle is used to fit the liquid tip in region B, and the diameter of the fitting circle is 680 µm.
pressure leads to water flowing into region B (Figure 4c,d). Because basic solutions ionize acidic groups making the surface more wettable,14 θp of pH ) 12.6 NaOH solution on region B is lower than 70°. As a consequence, this solution spontaneously flows through regions A and B. In another words, this pressure-sensitive microfluidic gate is also pH sensitive. Similar considerations allowed us to fabricate a widthdependent pressure-sensitive microfluidic gate. Figure 5a shows the photomask that was used to pattern the surface. The widths in two pathways are 450 and 650 µm. The UV irradiation time for both regions was 100 min, which affords a water θp of 70°, corresponding to a critical width of 526 µm (the diameter of the fitting circle is 518 µm). Thus, water can flow spontaneously through the hydrophilic pathway A (Figure 5b,c) and cannot flow into the branch pathway B unless a pressure is applied (Figure 5d). Like in the θp-dependent pressure-sensitive microfluidic gate, this surface pattern is not selective to the pH ) 12.6 NaOH solution under spontaneous flow conditions (Figure 5e,f). If pressure is applied to a liquid stream confined in a wedge-shaped hydrophilic pattern, it will penetrate further into the narrower region. The relationship between the smallest width of liquid stream and the external pressures is given by the equation 1/w ) (Fg/2γ)H + cos θp/h, where w is the smallest width under a pressure expressed in liquid height H, F is the liquid density, and g is the gravitational force constant.14 Although there is a discrepancy between our experimental results and the calculated values,14 the trend of decreasing width with increasing external pressure enables us to design and fabricate programmable pressure-sensitive microfluidic gates by patterning surface free energies via photolithography. An example is shown in Figure 6. Under spontaneous flow conditions, liquid flowed only into the left hydrophilic pathway (Figure 6b). When the pressure was 4 mmH2O, water flowed into the central hydrophilic
pathway (Figure 6c). Further increasing the pressure (e.g., 14 mmH2O in Figure 6d) pushed the liquid into the narrowest hydrophilic pathway. This device demonstrates programmable liquid delivery based on the width difference of the hydrophilic pathways. It is also possible to program liquid flow in the hydrophilic pathways of the same widths but different surface wettabilities. Because many of the current and anticipated uses for microfluidics involve protein solutions, we tested a 1:10 dilution of fetal bovine serum and a 0.2% aqueous solution of gelatin. The virtual walls were stable to these solutions. However, once collapsed, the contact angle of the hydrophobic surface dropped to approximately 45° and the virtual walls could not be reused. If the protein solutions were withdrawn without collapse, the device can be reused. Because the equilibrium adsorption of proteins to the surfaces took an appreciable amount of time, roughly 2 min, compared to the time necessary to fill the channels, the critical width of the hydrophilic pathway that would support spontaneous flow during initial use was little affected by the protein solutions. In practical applications, it is very important to investigate the flow rate and the velocity distribution of liquid flow in virtual walls. Here in this section we put our emphasis on the analytical and experimental studies of the initial rate of liquid flow in surface-patterned microchannels under spontaneous flow conditions. For a pipe with a circular cross section, assuming laminar flow and a Newtonian fluid, flow is given by the Hagen-Poiseuille equation, Q ) πr4∆P/(8ηL), where Q is the volume flow rate, r is the channel radius, L is the channel length, η is the liquid viscosity, and ∆P is the pressure difference.1 The corresponding linear flow rate is ν ) r2∆P/(8ηL). For noncircular channels, the hydraulic radius RH is used instead of radius r. RH is defined as the ratio of the cross-sectional area to the wetted perimeter (e.g., for a circular channel, RH ) (πr2)/(2πr) ) r/2). Thus,
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Figure 5. Width-dependent pressure-sensitive microfluidic gates. (a) Optical micrograph of the photomask that was used to pattern surface free energies inside a microchannel. (b,c) Optical micrographs of a water stream under spontaneous flow conditions recorded at different times. (d) Optical micrograph of water flow under a pressure of 12 mmH2O. We use a circle to fit the liquid tip in the narrow pathway. The diameter of the fitting circle is 518 µm. (e,f) Optical micrographs of pH 12.6 NaOH solution flowing spontaneously recorded at different times.
the linear flow rate can be expressed by the following equation: ν ) RH2∆P/(2ηL). For a liquid filling in a circular capillary (the surface tension γ is the driving force and dominant), ∆P ) 2γ cos θ/r ) γ cos θ/RH, where θ is the contact angle of water on the capillary surface. Therefore, the initial rate of liquid flow in a capillary is ν ) RHγ cos θ/(2ηL). L in this equation is considered as the length of the column of liquid.22 For liquid flow in surface-patterned microchannels under spontaneous flow conditions, ∆P ) (2γ cos θp/h) (2γ/w). The first component on the right of the equation is the capillary force dragging liquid forward. The second component is the retraction force due to the virtual walls. Because the liquid stream wets only the top and bottom substrates, the hydraulic radius RH ) (wh)/(2w) ) h/2. The initial rate of liquid flow in virtual walls is expressed as follows:
ν ) dL/dt ) RH2 ∆P/(2ηL) ) (hγ/4ηL)[cos θp - (h/w)] Thus, the initial flow rate in virtual walls under spon(22) Kim, E.; Whitesides, G. M. J. Phys. Chem. B 1997, 101, 855.
taneous flow conditions is proportional to cos θp when L and w are constants and is proportional to (-1/w) if L and θ are constants. To investigate the relationship between the initial flow rate and the width of the hydrophilic pathway, we used a photomask consisting of a series of stripes with different widths to generate a surface pattern inside a microchannel by use of Novacure. The UV irradiation times for all stripes are identical (2 min under the typical photopatterning conditions described in ref 21). Figure 7 shows optical micrographs of water filling into three hydrophilic pathways with widths of 900, 825, and 750 µm, respectively. Water was held at the same starting line by use of a syringe and then allowed to flow spontaneously after the removal of the syringe. Figure 7a,b shows the positions of three streams at times of t1 and t2 (∆t ) t2 - t1 ) 5.2 s). It is clear that water in the wider hydrophilic stripe moves faster. In the experiment, we found that the absolute flow rates varied from experiment to experiment. The absolute initial rate could be affected by the degree of surface hydration in the hydrophilic pathways, the distance between the water reservoir and the starting line, and external factors such as the syringe. Rather than trying to control all possible parameters, we made a comparison of the relative moving rates of the three water streams on the assumption
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Figure 6. Programmable width-dependent pressure-sensitive microfluidic gates. (a) Optical micrograph of the photomask used in surface patterning. Optical micrographs of a water stream (b) under spontaneous flow conditions, (c) under a pressure of 4 mmH2O, and (d) under a pressure of 14 mmH2O.
Figure 7. Optical micrographs of three water streams with widths of 900, 825, and 750 µm at time t1 (a) and t2 (b); t2 - t1 ) 5.2 s. (c) Plot of the relative flow rate (distance from t0 to t1) versus (-1/w). (d) Plot of the relative flow rate (distance from t1 to t2) versus (-1/w).
that all other factors were the same in each experiment. The distances that the water streams moved were measured and were plotted versus (-1/w). In Figure 7c, the Y axis is the distance that water moved from time t0 to t1; in (d), the Y axis is the distance that the liquid moved from time t1 to t2. Fitting results show that straight lines are obtained by linear regression with R values larger than 0.997, which is roughly in agreement with our analytical results. To study the relationship between the initial rate and θp, a photomask consisting of three rectangular stripes with equal widths was employed to make a surface pattern by Novacure. The irradiation times were 60, 80, and 100 s for three stripes in an order from left to right. Considering the possible variation of the UV light intensity and the
Figure 8. Optical micrographs of three water streams held at the same starting line (a), at time t1 after releasing (b), and at time t2 (c). Plots of relative flow rates from t0 to t1 (d), from t0 to t2 (e), and from t1 to t2 (f) versus cos θp.
quality of F-SAM, we used circles to fit the liquid shapes in the corners of each hydrophilic stripe (not shown in the micrographs) and calculated cos θp by use of the critical width equation cos θp ) h/D, where D is the diameter of the fitting circle.14 Figure 8 shows the optical micrographs of water flowing into the three hydrophilic pathways and plots of the relative flow rates versus cos θp. Water was initially held at the same starting line by use of a syringe
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and then was allowed to flow spontaneously. Images b and c were recorded at times t1 and t2. Clearly, water moved faster in the more hydrophilic stripe. An excellent straight line was obtained by linear regression in plot d, but the values of R in plots e and f were 0.997 and 0.996, respectively. Nevertheless, we can draw a conclusion that the experimental results are roughly consistent with the analytical flow rate equation. In conclusion, we described the design and fabrication of a series of pressure-sensitive microfluidic gates to regulate liquid flow by use of SAMs in combination with either multistream laminar flow or photolithography. The designs are based on the principles of surface-directed liquid flow. Specifically, we used the maximum pressure that virtual walls can withstand, the critical width of the hydrophilic pathways that support spontaneous liquid
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flow, and the smallest width of liquid streams under external pressures to regulate liquid flow. These pressuresensitive microfluidic gates are expected to find applications in microfluidic devices for applications in micrototal analysis systems, bioassays, and microreactors. In addition, we have analytically found that the initial rate of liquid flow in surface-patterned channels is proportional to cos θp and (-1/w). Experimental results are generally in agreement with analytical results. Acknowledgment. This work was supported by grants from DARPA F30602-00-2-0570. We thank David Quirk for his data on the use of protein solutions. LA026294E
