Design of passive mixers utilizing microfluidic self-circulation inthe mixing chamber

Yung-Chiang Chung,a Yuh-Lih Hsu,b Chun-Ping Jen,c Ming-Chang Lud and Yu-ChengLin*c

a Electronics Research & Service Organization, Industrial Technology Research Institute,Chutung, Hsinchu, Taiwan, R.O.C

b Department of Life Science, National Tsing Hua University, Hsinchu, Taiwan, R.O.Cc Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan, R.O.Cd Energy and Resources Laboratories, Industrial Technology Research Institute, Chutung,

Hsinchu, Taiwan, R.O.C

Received 5th September 2003, Accepted 5th November 2003First published as an Advance Article on the web 4th December 2003

This paper proposes the design of a passive micromixer that utilizes the self-circulation of the fluid in the mixingchamber for applications in the Micro Total Analysis Systems (mTAS). The micromixer with a total volume of about 20mL and consisting of an inlet port, a circular mixing chamber and an outlet port was designed. The device was actuatedby a pneumatic pump to induce self-circulation of the fluid. The self-circulation phenomenon in the micromixer waspredicted by the computational simulation of the microfluidic dynamics. Flow visualization with fluorescence tracer wasused to verify the numerical simulations and indicated that the simulated and the experimental results were in goodagreement. Besides, an index for quantifying the mixing performance was employed to compare different situations andto demonstrate the advantages of the self-circulation mixer. The mixing efficiencies in the mixer under differentReynolds numbers (Re) were evaluated numerically. The numerical results revealed that the mixing efficiency of themixer with self-circulation was 1.7 to 2 times higher than that of the straight channel without a mixing chamber at Re =150. When Re was as low as 50, the mixing efficiency of the mixer with self-circulation in the mixing chamber wasimproved approximately 30% higher than that in the straight channel. The results indicated that the self-circulation in themixer could enhance the mixing even at low Re. The features of simple mixing method and fabrication process makethis micromixer ideally suitable for mTAS applications.

1 Introduction

The Micro Total Analysis Systems (mTAS) research, which isaimed at miniaturization and integration of biochemical analysis,has recently made explosive progress.1,2 However, there is stillconsiderable technical challenge in integrating these proceduresinto a multi-stage system.3 The microfluid management devices,such as micropumps, microvalves, microsensors and micromixers,have been rapidly developed over the past few years.4 Rapid andeffective mixing is essential for biochemical analysis. mTAS canreduce the analyzing time by rapid mixing and improve procedurecontrol. Numerous microfluidic devices designed to improvemixing on the microscale have been reported in the literature.Mixing in these devices generally involves two steps: first, aheterogeneous mixture of substantially homogeneous domains ofthe two fluids is created by convection; second, diffusion betweenadjacent domains causes a homogeneous mixture at the molecularlevel.5 While examining the mixing efficiencies of various channelshapes for mini and micro channels, Branebjerg et al.6 noticed thatsharp corners in the zigzag channel caused complete mixing due toturbulent flow in the case of mini channels while turbulence did notoccur in the case of micro channels and the mixing was caused bydiffusion only. However, the mixing procedures on the macro-scopic scale, such as stirring or creation of turbulent flow cannot bescaled down to fit into the miniaturized systems (whose dimensionsare so small to obtain Re over 2000, the critical value for turbulentflow). At the microscale, rapid mixing is not produced byturbulence due to the extremely weak inertial forces. Therefore,alternative mechanisms must be employed to improve mixing inmicrofluidic systems.

The micromixers are classified into two categories: active andpassive mixers. Active mixers employ external forces or forms ofactive control on the flow field by moving parts or varying

gradients.7–10 Conversely, passive mixers5,11–17 exert no energyinput except for the mechanism used to cause the microfluid flowat a constant rate. Liu et al.12 proposed a three-dimensionalserpentine microchannel design with a C-shaped repeating unit as ameans of implementing chaotic advection to enhance passivemixing. Their micromixer was fabricated in a silicon wafer using adouble-sided KOH wet-etching technique. A plastic 3D L-shapedserpentine micromixer was subsequently developed to enhance themixing of biological sample preparation.13 Three-dimensionalpolydimethylsiloxane (PDMS) microfabrication and plastic micro-molding technique were employed to fabricate the L-shapedmicromixers. Hong et al.14 designed an in-plane passive micro-mixer which employed the “Coanda effect” to improve mixing. T-type micromixers with constant and varying sizes of channels havebeen developed and their mixing performances have been stud-ied.15 Stroock et al.16 proposed the staggered herringbone mixer toenhance mixing by chaotic advection. Jen et al.17 investigated amicromixer with twisted microchannels to enhance the mixingperformance. Volpert et al.18 developed an active micromixer forimproving the mixing of two fluids in a microchannel. The flowthrough the main channel of the micromixer was unsteadilyperturbed by three sets of secondary flow channels, wherebyenhancing the mixing. Lee et al.19 designed a micromixer, whichemploys unsteady pressure perturbations superimposed to a meanstream to enhance the mixing. The channels of the mixer wereetched into silicon wafer using the deep reactive ion etching (DRIE)technique and anodically bonded to Pyrex plates. Although activemixers may effectively provide rapid mixing, the actuators used inthese mixers need extra energy and are difficult to fabricate.Additionally, the electrical field and heat generated by the activecontrol of these mixers may damage the biological samples. Theoperation and integration of active mixers onto a biochemicalsystem are problems that need to be overcome. Passive mixers have

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the potential to be an attractive solution due to their simplicity andeasy operation.

Most of the passive mixers are usually suitable for mixing twofluids in two channels, afterwards they will be mixed in the thirdchannel. Consider that two or more fluids (or reagents) are injectedinto the same channel on a microfluidic chip simultaneously. Thefluids are totally unmixed initially when they contact each other. Inthis case, it is difficult to highly improve the mixing performance ifone uses these conventional passive mixers. In the present study, anovel passive mixer that utilizes microfluidic self-circulation in themixing chamber is proposed to improve the mixing performance.The self-circulation of microfluid in the mixing chamber isachieved by the forward and backward pumping of the workingfluids. The mixing performance of the passive micromixer atdifferent Re was investigated by numerical simulations. Thesimulated results were verified by flow visualization usingfluorescence tracer. This micromixer is suitable for mTAS since itdoes not require microfabricated electrodes or heaters and thereforehas minimal effect on the biochemical process. It is, therefore,particularly suited to micro devices for biochemical analysis, suchas polymerase chain reaction (PCR) and DNA hybridization.

2 Device design and experimental setupThe development of microfluidic self-circulation in the mixingchamber can be described in terms of Re, which is a measure ofinertia to viscous effect. When the fluid flowing into the mixingchamber is starting to be separated into a main flow region (M) anda circulation region (S), as shown in Fig. 1a, the minimum Re isdefined as the critical Re, Rec. The velocity of region M is higherthan that of region S. In region S, the circulating velocity is higherthan the central velocity, thus forming a free vortex that increasesthe contact area and improves the mixing.

The phenomenon of microfluidic self-circulation in the micro-mixer is illustrated in Fig. 1b. Fluid volume in the chamber and thechannels is divided into nine parts, denoted by A–I. The fluid isinjected into the channels and the mixing chamber. The flow isactuated back and forth by a pump. Initially, the fluid moves forth,parts E and F are shifted downstream and replaced by parts B andC. Parts G and H are stationary (or they become a circulation).

Then, the fluid moves back, parts G and H are shifted upstream, andparts B and C are stationary. After that, the fluid moves forwardagain, parts B and C arrive at the right channel, and parts E and Fare stationary. Finally, the fluid moves back again, parts E and Farrive at the left channel, and parts G and H are stationary. Based onthese steps, the fluid can be transported from one channel to theother. It is worth noticing that the two pump cycles can perform onefluid-transporting cycle. If the volumes of parts A and I could bemade to approach zero by a servo system, there would always be nofluid volume in one of the channels and the fluid in the chamber andchannels could be alternately transported to any channel. Thisdesign can be integrated with a bi-directional pumping de-vice.20,21

Based on the above concept, two micromixers (M1 and M2) weredesigned as shown in Fig. 2. The mixer M1 (Fig. 2a) had a chamberof diameter 4 mm and channels that are symmetrical about thecentral point with a width of 500 mm. The mixer M2 was identicalto M1 except that there was a circular pillar of diameter 1 mm in thecenter of the chamber, as depicted in Fig. 2b. The directions offlows in both cases are also indicated in Fig. 2.

The device was constructed with two PMMA (poly-methylmethacrylate) layers. The upper PMMA layer was blank. Thestructures of the components were built on the lower PMMA layerusing a CNC high-speed engraving and milling machine. Thedevice consisted of a mixing chamber (4 mm in diameter and 500mm in depth) and two channels (500 3 500 mm in cross-section),and the total volume was about 20 mL. After bonding the twoPMMA layers and drilling two 1.5 mm diameter holes to formliquid inlets and outlets, a complete PMMA block 50 mm long, 50mm wide and 15 mm high was fabricated. The flow pattern in themicromixer was traced by injecting a solution of yellow-greenpolystyrene fluorescent particles (15 mm diameter) through an inletport. The flow field was visualized by a LEICA-MZFLIIIfluorescence stereomicroscope (McBain Instruments, Chatsworth,CA, USA). The bi-directional motion of the fluid was generated bythe push/pull action of a syringe injector. The switching time,which was defined as the time period of a complete cycle of onepush and pull action, was determined based on the length of thechannel and the longitudinal velocity of the fluid. The switchingtime was 2 s in experiments.

3 Numerical simulationThe Navier–Stokes equations and the continuity equation,22 whichare given below, can be solved numerically to predict the flow fieldwithin an arbitrary device.

Fig. 1 Schematic diagram of the two regions in the chamber: (a) main flow(M) and circulation (S); (b) the self-circulation process in the micro-mixer.

Fig. 2 Schematic diagram of the two types of mixers. (a) M1: mixer witha circular chamber; (b) M2: mixer with an annular chamber.

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(1)

(2)

where m and r are the viscosity and the density of the fluid. P is thepressure, and V is the velocity vector. Here, it was assumed that thefluid is incompressible and the flow is in transient state.

Fluid dynamic simulations based on Finite Volume Method andthree-dimensional structured grids as implemented in the CFD-ACE™ software (CFD Research Corporation, Alabama, USA)were employed to predict the flow fields under typical operatingconditions. The Algebraic MultiGrid (AMG) solver was used forvelocity and pressure correction, and Conjugates Gradient Squared(CGS) and Preconditioning (Pre) solver were used for species. Theinlet fluid velocity was kept constant, so that the flow field at somemoment was considered as in quasi-steady state. The boundaryconditions at the outlet were set at a fixed-pressure. The totalnumber of cells in the mixer case and straight channel case wereapproximately 17 000 and 9000, respectively. The details of thenumerical method were: the maximum iteration was 250, theconvergence critical was 1025 and minimum residual was 10215. Inthe initial state, the fluid in the inlet channel and left-half mixingchamber was ethanol and in the other parts water. The Re values,which are the ratios of the inertial forces to the viscous forces, werein the range of 5 to 400, which are less than 2000 (the limit forturbulent flow). Therefore the flows in these cases can beconsidered as laminar.

To evaluate the mixing efficiency of the micromixer, quantifica-tion of percentage of mixing, which was modified from a previouswork,23 was used as an index in the present study. Here, the molefraction difference is considered as the fluidic mixing index, and theboundary conditions are assumed to be isolated. The mole fractiondistribution in the mixer after each cycle was simulated. Initially,

the mole fraction of ethanol at the entire inlet channel and half ofthe chamber were set at 1.0 and the remaining part of the mixer wasfull of water (the mole fraction of water was 1.0). As the time of thefluid moving back and forth periodically increases, the percentageof mixing increases and the mole fraction distribution in the mixerbecame more uniform. The percentage of mixing, f, after eachcycle was determined by the following equation:

(3)

where Ni is the mole fraction of ethanol (or water) at the samplingpoints in the mixer and N is the equilibrium mole fraction of ethanol(or water) in the mixer. Vi is the volume at the sampling points, n isthe number of sampling points and the subscript o represented theinitial state in the mixer.

The fluids were forced to move back and forth periodically in thethree-dimensional CFD simulations. In all cases, the flow wassimulated to proceed forwards to the middle of the inlet channel atwhich it inverted its direction and then moved backwards.Therefore, the sampling points located between the middle of theinlet channel and the middle of the outlet channel were chosen toguarantee that the sampling points were always those that initiallyexisted in the channel. The switching times for Re = 150 and 50were calculated to be 0.166 and 0.5 s, respectively. A similarapproach was applied when the sizes of the sampling cells werechanged. The cross section of the channel was 500 3 500 mm as Reis larger than 50, and becomes 50 3 50 mm as Re gets smaller than50. When the mixing performances (including the streamlines,velocity distribution and mixing percentage) of different channel(and chamber) sizes (50 3 50, 100 3 100 and 500 3 500 mm) ofthe devices but at the same Re (from 5 to 300) were compared, theywere still similar (data not shown).

Fig. 3 Calculated velocity field in the mixer with the circular chamber (M1) at Re equals (a) 300, (b) 150, (c) 50 and (d) 10.

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4 Results and discussion

The velocity and pressure distributions in the mixer M1 werecalculated and the results are depicted in Figs 3 and 4. As the Rewas gradually reduced from 300 to 50, the maximum velocity of themain flow region was shifted to the central zone as shown in Fig. 3.The self-circulation in the mixing chamber still existed, but thecenter of the circulation was shifted upstream, and the area ofcirculation region became smaller. Not only the area of thecirculation region decreased, but the path of the main fluid alsomoved towards the central zone of the chamber. The area ofcirculation was nearly equal to one quarter of the chamber at Re =50. At Re = 10, the circulation almost disappeared, and the flowwas similar to the symmetrical creeping flow. The pressure dropfrom upstream to downstream was larger for higher Re as illustratedin Fig. 4. For Re = 300, the pressure drop after the mixing chamberwas about 300 Pa. The pressure drop was 100, 20 and 4 Pa at Re =150, 50 and 10, respectively. There were sharp pressure drops in thecorners of the downstream channels, and this phenomenon wasmore obvious when Re was increased. Pressure drop in the mainflow region was larger than that in the circulation region as Re >50. The pressure contour for Re = 10 (Fig. 4d) indicated that thepressure distribution was almost symmetrical about the centralpoint of the chamber.

The velocity and pressure distributions in the mixer M2 fordifferent Re are plotted in Figs 5 and 6. At Re = 300 (Fig. 5a), theflow phenomenon was similar to that of M1 at the same Re, exceptthat the center of the vortex was slightly shifted and the circulationarea was smaller. At Re = 150 (Fig. 5b) and 50 (Fig. 5c), thecirculation regions were relatively smaller than those in the mixerM1 (Figs 3b and 3c). At Re = 10, the circulation region in themixing chamber totally disappeared (Fig. 5d). The pressuredistributions in the mixer M2 (Fig. 6) were similar to those in themixer M1 at the same Re, except that the distributions near the pillarwere different. Similar to the pressure contour in the mixer M1, the

pressure distribution in the mixing chamber of the mixer M2 whenRe = 10 was symmetrical about the central point of the chamber(Fig. 6d).

The tendency for the main flow region to completely occupy themixing chamber could be easily understood from the ratio of thearea of circulation region to the area of the chamber (Rc). The areaof circulation region was calculated from the streamline andvelocity distributions. The variation of Rc with Re was computedand is shown in Fig. 7. The ratio of the circulation area to the totalmixing chamber, Rc, was equal to zero at Re = 20 for the mixer M1and at Re = 40 for the mixer M2. However, the values of Rc for themixer M1 and M2 increased asymptotically when Re was increasedfurther. The asymptotic values of the mixer M1 and M2 were foundto be 0.7 and 0.6 respectively. From Fig. 7, the Re corresponding tothe same Rc values in the mixer M1 were always found to be smallerthan those in the mixer M2. Therefore, the mixer M1 was moresuitable for operating at Re varying from 20 to 400 than the mixerM2. Further studies were conducted by using this (M1) mixerdesign.

The streamlines of flow in M1 at different Re are shown in Fig.8. The self-circulation area was the largest at Re = 300, and itgradually became small as the Re decreased. As mentioned above,the self-circulation area totally disappeared at Re = 10. The flowpattern obtained from the fluorescence images are shown in Fig. 9.The particles in the channel followed a tangential path in the mixingchamber (Fig. 9a) in which the fluid was moving forward and theRe was equal to 150. Nevertheless, the particles in the opposite sideof the chamber were self-circulated or nearly stationary. Thevelocity field for the fluid moving backward (Fig. 9b) at Re = 50was of less magnitude than that in Fig. 9a. As a result, thecirculation zone became smaller, and the moving path of theparticles was less noticeable. A comparison between the simulatedand experimental results (Figs 7 and 9) indicated that theexperimental results were quite close to the simulated results.However, the circulation region in the experiments was larger than

Fig. 4 Calculated pressure distributions in the mixer with a circular chamber (M1) at Re equals (a) 300, (b) 150, (c) 50 and (d) 10.

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Fig. 5 Calculated velocity field in the mixer with an annular chamber (M2) at Re equals (a) 300, (b) 150, (c) 50 and (d) 10.

Fig. 6 Calculated pressure distributions in the mixer with an annular chamber (M2) at Re equals (a) 300, (b) 150, (c) 50 and (d) 10.

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that predicted by the simulated results. The deviations in thenumerical results could be due to the non-incorporation of thesurface roughness factor in the numerical simulation. The fabrica-tion error might be another possible reason that caused thedifferences between the numerical and experimental results. Thesesituations will influence the accuracy of the predicted results. Thelarger circulation area could result in an improved self-circulationleading to a better mixing performance. The experimental resultsdemonstrated the occurrence of the self-circulation in the mixingchamber.

The performance of the mixer with the self-circulation wasevaluated using the percentage of mixing calculated according toeqn. (3). If the boundary conditions were isolated, the average molefraction at any time would be the same. In the present case, theaverage difference was smaller than 0.1%, which corresponded tothe isolation assumption. The percentage of mixing in the mixer M1and the straight channel without the mixing chamber at different Rewere calculated and compared as shown in Fig. 10. Fig. 10aindicated the numerical results of the fluid moving back and forth

Fig. 7 The ratios of circulation region in the mixing chambers of M1 andM2 at different Re.

Fig. 8 Streamlines of flow in M1 at Re equals (a) 300, (b) 150, (c) 50 and (d) 10.

Fig. 9 Fluorescence stereomicroscopic image of the self-circulationmixer: (a) fluid moving from left to right at Re = 150; (b) fluid moving fromright to left at Re = 50.

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in the mixer M1 and the straight channel with a width of 500 mm (Re= 150). The results showed that the percentage of mixing increasedas the number of cycles (forward and backward) increased in M1and in the straight channel. However, the mixer M1 exhibited bettermixing performance and the percentages of mixing were about 1.7to 2 times larger compared to those in the straight channel. Whenthe fluids were stationary in the mixer M1, the fluids could hardlymix even after the same time corresponding to eight cycles. Themixer with self-circulation in the mixing chamber did improve themixing of the fluids. As Re was decreased to 50, the variation of thepercentage of mixing in the mixer M1 and the straight channel withthe number of cycles is as depicted in Fig. 10b. The fluids in themixer M1 still showed a better mixing than that in the straightchannel. The percentages of mixing in the mixer M1 at differentcycles were approximately 1.3 times higher than those in the

straight channel. When the size of the mixers was scaled down, forexample, the width of the inlet channel became 50 mm, which isone-tenth of the aforementioned mixer, the calculated percentage ofmixing in the mixer M1 and the straight channel at Re = 5 afterdifferent cycles were as plotted in Fig. 10c. The percentages ofmixing in the mixer M1 at different cycles were only about 1.1times larger than those in the straight channel. When the fluids werestationary in the mixer M1, mixing occurred due to the smaller sizeand the effect of diffusion became more obvious. These resultsrevealed that the mixing chamber design in the mixer M1 couldslightly enhance the mixing at low Re. It was possibly due to thesudden increase in the contact area of the fluid when the fluidflowed from the channel into the chamber.

5 Conclusion

We have outlined the design of a micromixer utilizing the self-circulation approach, and verified its principle of operation usingnumerical modeling. The mixer demonstrated the ability to mixfluid utilizing self-circulation within the device of the mixingchamber. When the Re was higher than a critical value, Rec (Rec =20 by simulation), the fluid would be separated into two regions:main flow region and circulation region. Two pumping cyclesperformed one fluid-transporting cycle in the device, and the fluidin the chamber and channels could be alternately transported to anychannel. Two types of mixers, one having a hollow mixing chamberand the other having a pillar in the center of the mixing chamber,were investigated and compared. The simulation results demon-strated that the one with a hollow mixing chamber exhibited bettermixing performance, especially at Re ranged from 20 to 400. Theexperimental results agreed with the simulation results. However,the circulation region in the experiments was larger than thatpredicted by the simulation results presumably due to the wallroughness and the fabrication errors. The proposed novel design ofpassive mixers can be applied in the field of mTAS.

References

1 A. Manz, N. Graber and H. M. Widmer, Miniaturized total chemicalanalysis systems: a novel concept for chemical sensing, Sens. Actuators,B, 1990, 1, 244–248.

2 Y. Baba, S. Shoji and A. van den Berg (Eds.), Micro Total AnalysisSystems 2002: Proceedings of the mTAS 2001 Symposium held in Nara,Japan, November 2002, Kluwer Academic Publishers.

3 M. A. Burns, B. N. Johnson, S. N. Brahmasandra, K. Handique, J. R.Webster, M. Krishnan, T. S. Sammarco and P. D. T. Burke, Anintegrated nanoliter DNA-analysis device, Science, 1998, 1, 484–487.

4 S. Shoji and M. Esashi, Micro flow devices and systems, J. Micromech.Microeng., 1994, 4, 157–171.

5 J. Branebjerg, P. Gravesen, J. P. Krog and C. R. Nielsen, Fast mixing bylamination, in Proceedings of the IEEE Micro Electro MechanicalSystems, San Diego, USA, February 1996, pp. 441–446.

6 J. Branebjerg, B. Fabius and P. Gravesen, Application of MiniatureAnalyzers: from Microfluidic Components to mTAS, in Proceedings ofMicro Total Analysis Systems Conference, Twente, Netherlands,November 1994, pp. 141–151.

7 J. Evans, D. Liepmann and A. P. Pisano, Planar laminar mixer, inProceedings of the IEEE Micro Electro Mechanical Systems, Nagoya,Japan, January 1997, pp. 96–101.

8 R. M. Moroney, R. M. White and R. T. Howe, Ultrasonic inducedmicrotransport, in Proceedings of the IEEE Micro Electro MechanicalSystems, Nara, Japan, January 1991, pp. 277–282.

9 S. Böhm, K. Greiner, S. Schlautmann, S. de Vries and A. van den Berg,A rapid vortex micromixer for studying high-speed chemical reactions,in Proceedings of the mTAS 2001 Symposium, California, USA, October2001, pp. 25–27.

10 M. H. Oddy, J. G. Santiago and J. C. Mikkelsen, Electrokineticinstability micromixers, in Proceedings of the mTAS 2001 Symposium,California, USA, October 2001, pp. 34–36.

Fig. 10 The calculated mixing percentages in the mixer with the circularmixing chamber (M1) and in the straight channel without the mixingchamber for different numbers of cycles or dimensionless time (time/periodtime in the flowing case, for the stationary cases compared to the flowingcases at the same time) at (a) Re = 150; (b) Re = 50 and (c) Re = 5.

L a b C h i p , 2 0 0 4 , 4 , 7 0 – 7 77 6

11 R. Miyake, T. S. J. Lammerink, M. Elwenspoek and J. H. J. Fluitman,Micro mixer with fast diffusion, in Proceedings of the IEEE MicroElectro Mechanical Systems, Fort Lauderdale, USA, February 1993, pp.248–253.

12 R. H. Liu, M. A. Stremler, K. V. Sharp, M. G. Olsen, J. G. Santiago, R.J. Adrian, H. Aref and D. J. Beebe, Passive mixing in a three-dimensional Serpentine microchannel, J. MEMS, 2000, 9, 190–197.

13 R. H. Liu, M. Ward, J. Bonanno, D. Ganser, M. Athavale and P.Grodzinski, Plastic in-line chaotic micromixer for biological applica-tions, in Proceedings of the mTAS 2001 Symposium, California, USA,October 2001, pp. 163–164.

14 C. C. Hong, J. W. Choi and C. H. Ahn, kA novel in-plane passivemicromixer using Coanda effect, in Proceedings of the mTAS 2001Symposium, California, USA, October 2001, 3133.

15 D. Gobby and P. Angeli and A. Gavriilidis, Mixing characteristics of T-type microfluidic mixers, J. Micromech. Microeng., 2001, 11,126–132.

16 A. D. Stroock, S. K. W. Dertinger, A. Ajdari, I. Mezic, H. A. Stone andG. M. Whitesides, Chaotic mixer for microchannels, Science, 2002, 295,647–651.

17 C. P. Jen, C. Y. Wu, Y. C. Lin and C. Y. Wu, Design and simulation ofthe gaseous micromixer with chaotic advection in twisted micro-channels, Lab Chip, 2003, 3, 77–81.

18 M. Volpert, C. D. Meinhart, I. Mezic and M. Dahelh, An activelycontrolled micromixer, in: Proceedings of MEMS ASME IMECE,Nashville, Tennessee, November 1999, 483487.

19 Y. K. Lee, J. Deval, P. Tabeling and C. M. Ho, Chaotic mixing inelectrokinetically and pressure driven micro flows, in Proceedings ofthe IEEE Micro Electro Mechanical Systems, Interlaken, Switzerland,January 2001, pp. 483–486.

20 C. P. Jen and Y. C. Lin, Design and simulation of bi-directionalmicrofluid driving systems, J. Micromech. Microeng., 2002, 17,115–121.

21 C. P. Jen, W. D. Wu, C. Y. Wu, Y. C. Lin, G. G. Wu and C. C. Chang,Improved design and experimental demonstration of the bi-directionalmicrofluidic driving system, Sens. Actuators, B, 2003, 96, 701–708.

22 R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Phenomena,Wiley, New York, USA, 1960.

23 T. J. Johnson, D. Ross and L. E. Locascio, Rapid microfluidic mixing,Anal. Chem., 2002, 1, 45–51.

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