Mec. Ind. (2001) 2, 343–348 2001 Éditions scientifiques et médicales Elsevier SAS. All rights reservedS1296-2139(01)01114-9/FLA

Passive mixing in microchannels:Fabrication and flow experiments

David J. Beebe a,c, Ronald J. Adrian b, Michael G. Olsen a, Mark A. Stremler a, Hassan Aref b,Byung-Ho Jo a

a Beckman Institute for Advanced Science and Technology, 405 North Mathews Avenue, Urbana, IL 61801, USAb Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, 104 South Wright Street,

Urbana, IL 61801, USAc Department of Biomedical Engineering, University of Wisconsin-Madison, 1410 Engineering Drive, Madison, WI 53703-1608, USA

Abstract—Obtaining rapid mixing in microfluidic systems is a problem that must continue to be addressed if microelectromechanicalsystems are to attain their full potential in commercial markets. We present the paradigm of “designing for chaos” as a generalframework for enhancing mixing in microfluidic applications. Designing for chaos is based on a fundamental understanding ofthe kinematics underlying the mixing process, freeing the MEMS researcher to work with design guidelines instead of empiricallydetermined physical configurations. We have applied this strategy in designing a passive in-line micromixer that relies on threedegrees of freedom to create chaos. The mixer design was fabricated using a compression micromolding process to create three-dimensional flow channels in polydimethylsiloxane (PDMS). Computational and experimental analyses demonstrate the effectivenessof the resulting design in generating chaos in the flow and hence enhancing mixing. 2001 Éditions scientifiques et médicalesElsevier SASmixing / microchannels / experiments

Résumé—Mélange passif dans les microcanaux : fabrication et expérience. L’obtention d’un mélange rapide dans les systèmesmicrohydrauliques est un problème dont la solution conditionne le succès commercial de certains MEMS. On présente le paradigme du«dessin pour le chaos» comme le cadre général pour améliorer le mélange de deux fluides dans les applications microhydrauliques. Le«dessin pour le chaos» est basé dans la connaissance de la cinématique déterminant le processus de mélange. Il apporte au chercheurla liberté de travailler avec des critères de dessin au lieu d’être confiné à des configurations établies expérimentalement. Nous avonsutilisé cette strategie pour concevoir un micromélangeur passif « in-line» qui est fondé sur l’utilisation de trois dégrées de liberté pourgénérer le chaos. Le micromelangeur fut fabriqué par un procédé de micromoulage par compression de polydimethylsiloxane (PDMS)permettant de réaliser des microcanaux tridimensionnels. L’analyse des résultats de la modélisation numérique et des expériencesmontrent la capacité du micromélangeur à générer du chaos et donc d’améliorer le melange. 2001 Éditions scientifiques etmédicales Elsevier SASmélange / microcanaux / expériences

1. INTRODUCTION

The difficulty in mixing fluids on the microscale liesin the small size of the devices. Despite the small lengthscales involved, mixing solely by molecular diffusion istoo slow for many applications, as the relevant time scalescan be extremely long. Flows at this scale are predomi-nantly laminar, so the efficient mixing obtained in tur-bulent flows is not practically attainable. Furthermore,fabrication limitations often preclude the use of standardmacroscale mixing techniques such as mechanical stir-ring.

Fortunately, mixing in such flows can be enhancedthrough “chaotic advection” [1–3], in which passive fluidparticles advected by a periodic, laminar velocity fieldexhibit chaotic trajectories. Relative to integrable (non-

chaotic) advection, chaotic advection enhances stretchingand folding of material interfaces. This deformationof fluid–fluid boundaries increases the interfacial areaacross which diffusion occurs, which increases the meanvalues of the gradients driving diffusion and leads tomore rapid mixing.

A number of tools are available for detecting chaoticadvection and measuring its extent, making it possiblefor a microscale mixer to be “designed for chaos”. First,a general configuration is chosen based on design guide-lines suggested by the theory of chaotic advection. Forexample, the active mixer of Evans, Liepmann and Pisano[4] is derived from the pulsed source-sink system inves-tigated by Jones and Aref [5]. A mixer is then designedfrom the general configuration by taking into account thespecific application and the fabrication constraints. The

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Figure 1. One segment of the “3D serpentine” mixer. Thefabricated mixer consists of 11 segments placed end-to-end,and the channel cross-section is 300 × 300 µm2.

resulting device is modeled numerically, and diagnosticsare computed to verify the occurrence of chaotic advec-tion. Iterations can then be made on the design to opti-mize the amount of chaos present. Finally, the device istested experimentally to verify that mixing is enhanced.The use of this paradigm for designing a passive mixer isillustrated in the following sections.

2. DEVICE DESIGN

Passive mixing in a single microchannel is attractivefor a number of reasons. First of all, a passive mixingscheme, which relies solely on a constant flow source,is generally more robust and easier to implement thanan active mixing scheme, which relies on exerting someform of control over the flow field through such meansas moving parts or varying pressure gradients. Secondly,a single channel maintains a relatively constant cross-section, which results in lower strain rates than if theflow is split into multiple smaller streams or forcedthrough small orifices. Thus the existing work on chaoticadvection is investigated to determine the guidelines fordesigning such a mixer.

It has been shown with a simple analytical model thatflow in a “twisted pipe” can contain significant amountsof chaotic advection [6]. The basic configuration consistsof a sequence of pipe bends, with successive bendsoriented along different planes. This result has beenapplied successfully to heat transfer enhancement on themacroscale [7–9], and the goal is to now implement thisdesign on the microscale.

Previous studies of the “twisted pipe” have only con-sidered flow in circular pipes arranged in curved three-dimensional configurations. Fabrication limitations leadus to consider instead the related orthogonal geometryshown in figure 1, which can be constructed using a vari-ety of techniques. The channels used in this study are fab-ricated of polydimethylsiloxane (PDMS) using a micro-molding and layered manufacturing technique [10]; avariation on the design in figure 1 has also been fabri-cated and tested in silicon [11].

Figure 2. One segment of the “square-wave” mixer. Thefabricated mixer consists of 14 segments placed end-to-end,and the channel cross-section is again 300 × 300 µm2.

An alternative configuration is the “zig-zag” channelinvestigated by Branebjerg, Fabius, and Gravesen [12].However, theoretical results for the “twisted pipe” sug-gest that this channel design will generate little or nochaotic advection. We investigate the similar “square-wave” geometry shown in figure 2 and compare its mix-ing capabilities with the 3D serpentine channel to illus-trate the effectiveness of producing chaos in the flow.

3. DEVICE FABRICATION

The micromixer designs were constructed of PDMSusing a micromolding and layered manufacturing tech-nique developed by Jo et al. [10]. The technique con-sists of molding microchannels into PDMS and thenbonding two (or more) layers of PDMS to create three-dimensional structures.

The layout for each layer of the structure was drawnusing a computer-aided drafting program, and these lay-outs were printed onto transparency films using a high-resolution laser printer. These transparencies were thenused as masks in a photolithography technique to gen-erate molds made from a negative-tone UV photoresist.The process for forming the thin layers of the device isdepicted in figure 3, and the process for forming the thick,bottom layer is shown in figure 4.

Figure 3(a) shows a master formed on a siliconwafer using photolithography, while figures 3(b)–(e) il-lustrate schematically a sandwich molding procedurefor producing thin layers. First, the PDMS prepoly-mer mixture was poured onto the master, and then atransparency film was placed over the prepolymer mix-ture. The master/prepolymer/transparency stack was thenclamped within a sandwich and cured for 3 hours at100 ◦C on a hot plate. After curing, the thin PDMS layerswere peeled from the masters.

Figure 4 shows the molding of a thick bottom layerand the coring procedure that was used to connect thefluidic device to an external fluid network with the inletand outlet tubes. The master for the bottom layer wasplaced in a petri dish and then the prepolymer waspoured onto the master to make a bottom layer thickenough so that inlet/outlet channels could be cored in it.

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Figure 3. Schematic illustration of the sandwich molding process for thin upper layers. (a) A master for each layer was formed ona silicon wafer using photoresist and standard photolithography procedures. (b) Next, the PDMS prepolymer mixture was pouredonto the master. (c) A transparency film was placed over the poured prepolymer mixture. (d) A multilayer stack of aluminum plates,the mold master, the PDMS prepolymer mixture, a transparency film, a rigid Pyrex wafer, and a rubber sheet is used to form acompression mold. (e) Finally, all the layers are clamped tightly during the cure.

(a)

(b)

(c) (d)

Figure 4. Scheme for fabricating a thick bottom layer and off-chip connection via the bottom layer. (a) A master for the bottom layer.(b) Molding a thick bottom layer in a Petri dish. (c) A bottom layer containing L-shaped microtunnels and tube connections. (d) Thefinished micromixer.

Figure 4(c) shows a completed bottom layer that includesthe L-shaped inlet and outlet and tubes connecting toan external fluid network. The completed micromixer isshown in figure 4(d).

After the various layers were made, they were alignedand bonded into a single device. This was done byfirst activating the layer surfaces with a reactive ionetching (RIE) system. Two such activated surfaces will

permanently bond when placed into contact with eachother.

After the surfaces were activated, aligning was per-formed using a surface-tension technique. Each of thelayers contained alignment holes in addition to the chan-nel geometry. The layers were stacked with methanolused as a surfactant between each layer. The surfacetension of the methanol at the holes acted to self-align

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Figure 5. Generation of a Poincré section in a spatially periodicsystem. (a) A passive particle is advected by the periodicvelocity field and passes through a series of periodic planesin the system. For the mixers considered here the planesare located at the exit (or entrance) of each mixing segment.The position at which the particle passes through each planeis recordered. (b) All of the positions are transferred to asingle plane, which is the Poincaré section. Regular patterns inthe Poincaré section indicate integrable (non-chaotic) behavior,while random patterns indicate chaotic behavior.

Figure 6. Poincaré maps in the square-wave mixer at (a) Re =10, (b) Re = 20, (c) Re = 30, and (d) Re = 50. Each closed curveshown is generated by tracing a single particle. Those curvespassing very close to the boundary are not shown as closeddue to numerical error that occurs in following particles nearthe wall of the channel. While the complexity of the advectiondoes increase with increasing Reynolds number, no chaos ispresent.

the layers. The accuracy of alignment achieved with thismethod was within 15 µm. After the PDMS layers werestacked and aligned, a #1 microscope cover glass (about150 µm thick) was used as the topmost layer. The en-tire device was then heated on a hot plate to 85 ◦C toevaporate the methanol and thus complete the bondingprocess.

4. NUMERICAL MODELING

While theory can suggest or predict the occurrenceof chaotic advection, the amount of chaos present can

Figure 7. Particle traces in the square-wave mixer at a Reynoldsnumber of 10. The lower tube corresponds to initial conditionslying on the lower left “circle” in figure 4(a), and the upper tubeto the upper right “circle” in figure 4(a).

only be determined for specific examples. A standardtool for detecting chaos in spatially or temporally pe-riodic systems is the Poincaré section [3]. A schematicof how this section is generated for spatially periodicsystems is shown in figure 5. The Poincaré section con-sists of patterns of points formed by passive particles ad-vected through the periodic flow field. Chaotic advectionis present in those portions of the section where the re-sulting pattern is random.

In order to generate Poincaré sections in these chan-nels, the velocity fields are first computed on a grid usingCFD-ACE, a commercial finite-volume code from CFDResearch Corporation. The channels are modeled as in-finitely long by enforcing periodic boundary conditionsat the inlet and exit of a single mixer segment. An im-portant parameter in these flows is the Reynolds number,Re = UL/ν, which gives the relative importance of iner-tia and viscosity in the system in terms of the mean chan-nel velocity U , the kinematic viscosity ν of the fluid, andthe width L of the channel cross-section. For water-basedflows in these channels, Re = 10 corresponds to a flowrate of approximately 0.2 mL·min−1. Velocity fields arecomputed at various Reynolds numbers by varying thespecified pressure drop across one segment of the mixer.Particle traces and the corresponding Poincaré sectionare then generated by integrating numerically throughthe discrete velocity field using an adaptive Runge–Kuttascheme. The velocity at any point within the channel isdetermined by polynomial interpolation.

Poincaré sections in the 3D serpentine channel forReynolds numbers from 1 to 20 are shown in figure 8. Incontrast to the square-wave mixer, chaotic advection doesoccur in the flow for the Reynolds numbers considered,with significant amounts of chaos present already at Re =10. Thus it is expected that the 3D serpentine mixer will

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Figure 8. Poincaré maps in the 3D serpentine mixer at(a) Re = 1, (b) Re = 5, (c) Re = 10, and (d) Re = 20. At lowReynolds numbers the Poincaré sections are dominated byregular closed curves, and the advection is predominantly non-chaotic. However, for Re ≥ 10 the Poincaré sections containlarge regions of chaos. In (c) and (d) the particle patternsforming the chaotic regions are generated by following only1 or 2 particles.

perform significantly better than the square-wave mixerfor moderate Reynolds numbers (roughly for Re ≥ 10).

5. EXPERIMENTAL COMPARISONS

Mixing in the channels is evaluated experimentallyby observing the color change of a pH indicator as itflows through the channel. Two separate fluid streamsflow into each channel through a T-junction. One streamcontains phenolphthalein dissolved in a mix of 50% ethylalcohol and 50% de-ionized water with a concentrationof 0.016 M. The second stream contains 98.3% sodiumhydroxide pellets also dissolved in a 50/50 mix of alcoholand water, giving a pH of approximately 13.

The phenolphthalein and sodium hydroxide streamsare introduced into the mixer from two water columns.After the two colorless streams come in contact, bothsodium hydroxide and phenolphthalein begin to diffuse.The reaction time of the phenolphthalein is negligible, al-though the ratio of reacted to unreacted phenolphthaleinat any point within the device depends on the local pHvalue in a non-trivial way [13]. Thus, the amount of re-acted phenolphthalein produced depends on the diffusiv-ities and initial concentrations of both phenolphthaleinand sodium hydroxide.

Figure 9. (a) Experimental results and (b) computational resultsfor diffusion in the first two segments of the square-wavemixer at a Reynolds number of approximately 10. Flow isfrom left to right. The view is from the front of the mixeras oriented in figure 2. At the mixer inlet the top half of thechannel contains the NaOH stream and the bottom half thephenolphthalein stream. The reacted phenolphthalein appearsas a dark product.

The mixing ability of the device is determined quali-tatively by observing the color change of the phenolph-thalein during the mixing process. Images of the reactedphenolphthalein are captured through an Olympus BX60microscope at 4× magnification with a Sony 8-bit CCDcamera. The microscope objective used has a depth-of-focus of 175 µm. Although by this definition the entirechannel depth is not in perfect focus, blurring of fea-tures in the flow is negligible. Illumination comes from ahalogen light source mounted behind the mixer. Since thehalogen lamp produces incoherent light, the light wavesscattered by two molecules are assumed to have addi-tive intensities when the images of the molecules over-lap. Thus, the intensity of red observed in the channelis proportional to the amount of reacted phenolphthaleinpresent.

As shown in figures 9 and 10, there is good qualitativeagreement between the experimental results and a simplecomputational diffusion model, which demonstrates thevalidity of the numerical model and lends credibility tothe numerical diagnosis of chaos presented in figures 6and 8.

The mixing capabilities of these two channels arecompared experimentally in figure 11. In the square-wavemixer product is observed only in the bottom half of thechannel, and much of the product is concentrated at thecenterline. In contrast, the 3D serpentine mixer producesmore product, and this product is distributed throughoutthe channel cross-section. Thus, designing for chaos hasresulted in a mixer that performs better than one that doesnot produce chaotic advection.

6. CONCLUSIONS

The paradigm of designing for chaos in microfluidicsystems gives the MEMS researcher the freedom to work

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Figure 10. (a) Experimental results and (b) computationalresults for diffusion in the first segment of the 3D serpentinemixer at a Reynolds number of approximately 10. Flow is fromleft to right. The view is from the front of the mixer as orientedin figure 1.

Figure 11. Comparison of the mixing results at the last mixingsegment in (a) the square-wave mixer and (b) the 3D serpentinemixer. The fluid has traveled approximately the same distancein each mixer at the segments shown. Stretching anf folding ofthe material interface is apparent in (b).

within a flexible design framework instead of relyingsolely on the use of empirically determined devices. Thevalidity of this approach has been demonstrated in the

design of a passive, in-line micromixer. The resultingdevice enhances mixing significantly relative to a similarin-line mixer that does not produce chaotic advectionin the flow. This approach of “designing for chaos” isnot limited to passive in-line devices. Indeed, there area variety of mixers that can be developed using thisframework. The development of rapid three dimensionalprototyping methods, such as those described here, allowfor rapid design iterations making the “designing forchaos” approach practical.

Acknowledgements

This work was supported under a grant from DARPA-MTO (# F33615-98-1-2853,Program manager: Dr. Abra-ham Lee).

REFERENCES

[1] Aref H., Stirring by chaotic advection, J. Fluid Mech. 143(1984) 1–21.

[2] Aref H., Chaotic advection of fluid particles, Phil. Tran. Roy.Soc. London Ser. A 333 (1990) 273–288.

[3] Ottino J.M., The Kinematics of Mixing: Stretching, Chaos,and Transport, Cambridge University Press, 1989.

[4] Evans J., Liepmann D., Pisano A.P., Planar laminar mixer, in:Proc. IEEE Workshop Micro Electro Mech. Sys. (MEMS ’97),Nagoya, Japan, 1997, pp. 96–101.

[5] Jones S.W., Aref H., Chaotic advection in pulsed source-sinksystems, Phys. Fluids 31 (1988) 469–485.

[6] Jones S.W., Thomas O.M., Aref H., Chaotic advection bylaminar flow in a twisted pipe, J. Fluid Mech. 209 (1989) 335–357.

[7] Acharya N., Sen M., Chang H.-C., Heat transfer enhancementin coiled tubes by chaotic mixing, Int. J. Heat Mass Tran. 35(1992) 2475–2489.

[8] Sawyers D., Sen M., Chang H.-C., Effect of chaotic interfacialstretching on bimolecular chemical reaction in helical-coilreactors, Chem. Engrg. J. 64 (1996) 129–139.

[9] Mokrani A., Castelain C., Peerhossaini H., The effect ofchaotic advection on heat transfer, Int. J. Heat Mass Tran. 40(1997) 3089–3104.

[10] Jo B.H., Van Lerberghe L.M., Motsegood K.M., BeebeD.J., Three-dimensional micro-channel fabrication in Poly-dimethylsiloxane (PDMS) elastomer, J. Microelectromech.Sys. 9 (1) (2000) 76–81.

[11] Liu R.H., Sharp K.V., Olsen M.G., Stremler M., Santiago J.G.,Adrian R.J., Aref H., Beebe D.J., A passive three-dimensional‘C-shape’ helical micromixer, J. Microelectromech. Sys. 9 (2)(2000) 190–198.

[12] Branebjerg J., Fabius B., Gravesen P., Application of minia-ture analyzers: from microfluidic components to µTAS, in:Proc. Micro Total Anal. Sys. Workshop (µTAS ’94), Enschede,The Netherlands, 1994, pp. 141–151.

[13] Zhang S., Schneider S.P., Collicott S.H., Quantitativemolecular-mixing measurments using digital processing of ad-sorption images, Exp. Fluids 19 (1995) 319–327.

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