Microelectronic Engineering 88 (2011) 959–963

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Microelectronic Engineering

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Realization of planar mixing by chaotic velocity in microfluidics

Kai Zhang a, Shishang Guo a,b, Libo Zhao a,b, Xingzhong Zhao b, Helen L.W. Chan a, Yu Wang a,⇑a Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University, Hong Kong, People’s Republic of Chinab Department of Physics, Key Laboratory of Acoustic and Photonic Materials and Devices of Ministry of Education, Wuhan University, Hubei 430072, People’s Republic of China

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 June 2010Received in revised form 24 October 2010Accepted 16 December 2010Available online 30 December 2010

Keywords:MicrofluidicsPassive micromixerChaotic velocityMicromixer system

0167-9317/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.mee.2010.12.029

⇑ Corresponding author. Tel.: +86 27665668; fax: +E-mail address: apywang@inet.polyu.edu.hk (Y. W

We present the design, fabrication and characterization of an effective planar passive micromixer withrelatively simple construction for microfluidic applications. This micromixer consists of a zigzag micro-channel in which realization of fluid mixing is expected because the variation of the flow velocity direc-tion and magnitude in the channels may cause the laminar flow to become chaotic. Simulations weremade to study the influence of geometry of the microchannel on the mixing effect and it has been foundthat the turning angle plays a very important role in the mixing process. Prototype devices were fabri-cated using polydimethylsioxane soft lithography technology. Mixing efficiency of the micromixer wasexamined by tracing the color uniformity of de-ionized water and red ink travelling through the micro-channel. It was found that, for these two flows with a wide range of flow rates, the resulted fluid at theoutlet of the micromixer would always show good color uniformity, indicating a high mixing efficiency. Aprototype micromixer system for future fast chemical and biological analysis was proposed and fabri-cated based on this design. Easy to fabricate and use, we believe that our micromixer can be used as ageneral-purpose component for microfluidic systems.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

There has been increasing interest to develop microfluidic sys-tems for chemical and biological applications [1,2]. Because ofspace constraint, a physical and/or chemical process within amicrofluidic system could be different from what is observed ina macrosystem [3–5]. The mixing of fluid flows in a macrosys-tem, for example, is a simple process that has been well under-stood. However, in a microfluidic system with a flow channelof several or tens of micrometers wide, the mixing of fluid flowswould become quite different. The flows tend to form a laminatestructure instead of a uniform mixture mainly due to the smallReynolds number (Re = Ul/m, where U is the average flow rate, lis the length scale – typically the channel height, and m is thekinematic viscosity) [6,7]. For instance, for a system with flowrate = 10 mm/s, length scale = 100 lm, water viscosity = 1 mm2/s,then Re � 1 (as for comparison, the value of Re for a macroscopicfluidic system is typically >2000) [7]. To enhance the mixingefficiency, two types of micromixers (or microfluidic mixers)have been developed. The first type involves the use of externalstimulation (e.g. electrical, magnetic field, or ultrasonic force) toenhance the mixing effect [8–15]. The microchannel in such amicromixer is usually small and has a simple structure yet the

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86 23337629.ang).

entire micromixer system could be complex as it has to be asso-ciated with devices for energy transfer, control and etc. The othertype of micromixer, which is often called passive micromixer,does not require external stimulation and the enhancementof mixing efficiency is realized by modifying the shape of themicrochannels so that the contact area of fluidic layers can beincreased or advections between solutions can be induced[16–23]. Micromixers with complex three-dimensional (3-D)microchannels have been developed [19–23]. However, such 3-D structures often face the problem of poor compatibility withplanar lab-on-chip systems whereas micromixers with two-dimensional (2-D) microchannels are fully compatible with pla-nar lab-on-chip systems and can be fabricated much more easily.In recent years, a large number of 2-D micromixers with differentmixing styles have been reported. Nevertheless, how the mixingefficiency can be enhanced through microchannel design remainsa key issue in the field [24–28].

In this paper we report the development of a planar micromixerthat possesses a zigzag-like microchannel with relatively simplyconstruction produced through standard soft-lithography tech-nique. The mixing mechanism of chaotic velocity is analyzed inthe channel geometry design. Experimental results are presentedto demonstrate the high mixing efficiency of this device. A proto-type micromixer system in large-scale integrations based on thisdevice design is proposed for future fast chemical and biologicalanalysis.

960 K. Zhang et al. / Microelectronic Engineering 88 (2011) 959–963

2. Theoretical analysis and simulations

2.1. Theoretical analysis

According to Fick’s law, convective diffusion is a key factor thatinfluences the mass transfer in a multi-fluid system. The equationof convective diffusion can be described as follows [29]:

dCA

dtþ ðU!A � U

!BÞ � rCA ¼ DABr2CA ð1Þ

where CA is the molar concentration, U!

A and U!

B are the velocityvector of the components A and B (hence U

!A � U!

B is the relativevelocity), and DAB is the inter diffusion coefficient for them. WhenU!

A � U!

B ¼ 0, laminar flow is formed where only molecular diffu-sion between the fluids occurs. When U

!A � U!

B – 0, there will bemore efficient convective diffusion. If chaotic advection takes place,mixing in the microchannel will become more efficient [6,8,16,17].The chaotic advection is usually related to a chaotic response froman Eulerian velocity field [16].

Based on the analysis above, we have designed a microchannelwith the hope that convective diffusion and chaotic advectionwould lead to more effective mixing in the system. As shown inFig. 1, the microchannel for mixing has a zigzag type of configura-tion with a width of 50 lm and length of 10 mm (Fig. 1a). Fig. 1bschematically shows how the mixing would occur. Passing throughthe corner, the flow of both Fluid 1 and Fluid 2 will change theirvelocity direction and magnitude due to the velocity slip at thewall [30]. Hence, the relative velocity ðDU – 0Þ along the x axis be-tween the two fluids (marked as zone (1) in Fig. 1b) will cause con-vective diffusion according to Eq. (1) while in the outlet of the turncorner cell, the unparallel velocity ðDu – 0Þ of the fluids will gen-erate advection between them (as can be seen in zone (2) inFig. 1b).

Fig. 1. Schematic configuration of the planar passive micromixer: (a) the overall topview of the micromixer and (b) enlarged structure of a basic mixing cell with a turncorner in angle h. The arrows in the figure show the velocity of the fluid flows. Zone(1) in the mixing cell marks the relative velocity DU/U of the fluids at their interface,while zone (2) depicting transversal advection with relative angle Du between thevelocities of the fluids at outlet of the mixing cell.

2.2. Simulation results and discussions

Fluid dynamic simulation on velocity distribution was per-formed with the Star-CD software based on finite volume method[31]. In the simulation, the geometry information of the channelwas input using three-dimensional structured grids. The low Rey-nolds number K-Epsilon model was used for the mixing cell, whichwas constructed by �2200 meshes. Apart from Eq. (1), the follow-ing two equations were also employed as governing equations inthe simulation [28]:

Continuity equation :@q@t¼ �r � ðqV

!Þ ð2Þ

Momentum conservation equation : qd V!

dt¼ �r P

!þ lr2 V!

ð3Þ

where l and q are the viscosity and density of the fluid, P!

and V!

are the pressure and velocity vectors, respectively. Water and etha-nol were employed as the example fluids in the mixer with a con-stant velocity of 1 mm/s at the inlets. The boundary conditions atthe outlet were set at a fixed pressure without split. The iterationsof the calculation were 100 in the simulation process.

Fig. 2 shows the simulation results of velocity vector distribu-tion in the mixing channels with turning angles h = 0� (180�), 45�,90�, and 135� at Re = 0.05, respectively. In the straight channel(h = 0� (180�)), the flow is developed in a laminar way when theupper and lower fluids carry the same velocity in magnitude(DU = 0) and flow in parallel (Du = 0) along x-axis (Fig. 2a). Inthe channels with h = 45�, 90�, and 135�, it can be seen that thevelocity distributions around the corners have become chaotic.Gradual attenuation velocity fields are formed once the above fluidturns to the outside flow and the one below turns around in the in-ner corner. The magnitude of the velocity responding to the out-side fluid far from the corner can be 1000 times more than thatof the fluid near the wall inside the corner as we can see fromthe marked scale. Near the outlet of the mixing cells, the velocitiesof the fluids appear to be overlapping, which can be explained bythe advection between the fluids. Both the relative velocityðDU – 0Þ at the boundary of the fluids and the advectionðDu – 0Þmay have enhanced the mixing performance in the chan-nels according to the analysis above.

The influence of corner angle (h), flow velocity and channelwidth on the mixing performance was further analyzed by simula-tion. Typical simulation results are presented in Fig. 3. Relativevelocity (DU/U) and relative angle (Du) of the fluids are used toevaluate magnitude of convective confusion and advection in thechannels respectively. Fig. 3a shows the values of DU/U and Duas a function of h for a microfluidic system with a velocity of fluidof 1 mm/s and channel width of 200 lm. As h increases, DU/U fluc-tuates with a maximum value achieved at h = 45� and a minimumvalue at h = 90�, while Du reaches its maximum at h = 45�. This re-sult suggests that at h = 45� maximum performance of mixing canbe obtained. Fig. 3b demonstrates the influence of channel widthon the values of DU/U and Du (velocity of fluid = 1 mm/s,h = 45�). Although the simulation results of our design did not in-crease or decrease monotonously with the varying channel widthin 45� corner angle pattern at a flow rate of 1 mm/s, both the mag-nitude of convective diffusion and advection appeared to increasequickly when comparing with thinner channels but decreaseslowly and tend to make minor changes after width of about300 lm. The mixing performance respond to different velocitiesof the inlet fluids was found to be milder by keeping h = 45� andwidth of 200 lm (Fig. 3b). In the simulation, the fluid velocities

Fig. 2. Simulated velocity distribution of flows in various channels: (a) straight channel, (b) 45� corner, (c) 90� corner and (d) 135� corner. Colors in the image represent thevalues of the velocities (decreasing from red to blue). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

Fig. 3. Simulation results of mixing effect with different (a) corner angle h and (b) channel width. The mixing performance was evaluated by the convective diffusion inmagnitude of DU/U and advection in Du as the y axis in the plots.

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were varied from 1 mm/s to 10 mm/s, corresponding to Re with0.05–0.5. The minor change obtained in the results accounts forthat mixing can be steady during low Re in microchannels. It hasbeen confirmed that mixing performance may worsen when thechannel width in the straight channels increases since the diffusionpath between the fluids is increased correspondingly [8].

3. Experiments and results

3.1. Fabrication of the micromixer and experimental setup

Micromixers were fabricated by replica molding and bonded toa glass slide using standard polydimethylsioxane soft-lithographytechnique [32]. Fig. 4a shows a microphotograph of the fabricatedmixing cell with a clear zigzag-type configuration. The enlargedphotograph of the mixing cell (inserted in Fig. 4a, left-hand side)demonstrates that, the mixer has good fidelity to the designeddimension with width of 50 lm and turning angle of 45�. The

AFM (Atomic Force Microscope) characterizing to the mixer sur-face (inserted in Fig. 4a, right-hand side) presents a smooth PDMSchannel with a RMS (Root-Mean-Square) roughness of �6 nm,which would alleviate the worrying from the effect of channelroughness on the mixing results. The performance of the microm-ixer was examined in the setup shown in Fig. 4b. In the experi-ments, fluids (red ink and de-ionized water) were fed into themicromixer by syringe pumps (TS2-60, Longer pump). An invertedfluorescence microscope (Olympus IX71) with a CCD camera(Olympus DP71) was used to monitor the mixing process andcapture the images during the experiment.

3.2. Mixing results with the fabricated passive micromixer

The mixing effect of the designed passive micromixer with theturn corner angle of 45� and channel width of 200 lm were dem-onstrated by de-ionized (DI) water and red ink flowing in the mixercell (Fig. 5). As shown in Fig. 5a, the DI water and red ink forms a

Fig. 4. (a) Optical image of the passive micromixer; (b) setup for observing the mixing process. Inserted photograph in (a) (left) is an enlarged image of the mixing cell, whichgives its detailed dimension with a width of 50 lm and a turning angle of 45�. The inserted AFM image (right) presents a smooth channel surface of the mixer.

Fig. 5. Captured video frames to demonstrate the mixing effect of the fabricatedmicromixer: (a) the inlet of the micromixing system. DI water and red ink are usedto trace the mixing procedure; (b) the outlet filled with the mixed solution; (c)evaluation of the mixing effect by comparing color gray value distribution at inletand outlet.

Fig. 6. Captured video frames to demonstrate the dependence of mixing effect onflow rate ratio of fluids: (a, b) the outlet with the mixed solution, flow rate ratio ofink to DI water at inlet are 1:4 and 1:8; (c) evaluation of the mixing results underdifferent flow rate ratio by analyzing color gray value distribution at outlets.

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laminar flow at the inlet. After passing through the mixer cell, thefluid has become uniform in color, indicating that they are wellmixed up (Fig. 5b). Detail color gray value analysis to the fluidsat inlet and outlet of the mixer were illustrated in Fig. 5c. By settingx axis along the channel width and color gray value as y axis, wecan see clearly that big difference of the color gray value betweenseparate fluids at the inlet turned to be uniform without obviousfluctuations at outlet.

Fig. 7. Captured video frames to demonstrate the effect of flow rates on mixingresults: (a, b and c) the outlet with the mixed solution, flow rates of ink to DI waterat inlet are 25:100, 50:200, 100:400, respectively (unit: ll/h); (d) evaluation of themixing results under different flow rates by analyzing color gray value distributionat outlets.

3.3. Compatibility of the micromixer to various flow rates

To confirm the proposed micromixer to be compatible with var-ious microfluidic applications, a few more experiments were con-ducted to examine the influence of flow rate ratio, flow rates ofthe injected fluids on the final mixing effect. Fig. 6 shows the mix-ing results of red ink and DI water at different flow rate ratios of1:4 and 1:8. Both cases can get uniform mixture yet with differentdilute effect (Fig. 6a and b). From the color gray value analysis inFig. 6c, we can see that the results of ink diluted by DI water aftermixing were corresponded to the flow rate ratio set at the inlets. Itenables the ratio of fluids in the final mixture to be easily control-lable by the flow rate ratios. When keeping the flow ratio, we canalso always get a uniform mixture in various injections flow rates.As shown in Fig. 7, nearly same mixing effects can be obtained afterred ink and DI water passing through the micromixers with flowrates of 25:100, 50:200 and 100:400 (unit: ll/h).

3.4. Micromixer system for future chemical and biological analysis

Due to the advantage of simple construction and easy fabricationtechnique of this micromixer device, it can be largely integrated intothe microfluidic systems for various applications. As one examplefor large-scale integration of this smart chip, we proposed a six-cellmicromixer cell for future chemical and biological analysis (as

Fig. 8. (a) Scheme and (b) optical image of prototype device of the proposed micromixer system for chemical and biological analysis.

K. Zhang et al. / Microelectronic Engineering 88 (2011) 959–963 963

schemed in Fig. 8a). The target sample can be effectively mixed withseveral different reagents and analyzed at the outlet, with the con-venience of fast detections and requiring much less samples in sev-eral tens of micro-liters. The prototype device of this proposedmicromixer system was fabricated and illustrated in Fig. 8b.

4. Conclusions

In summary, we have proposed a simple-constructed planarpassive micromixer for microfluidic study. Theoretical analysisand simulation has pointed out that chaotic velocity distributionof fluids in the microchannel can be induced by designing thegeometry of channels, which is critical to improve the mixing effi-ciency. Micromixer chips based on the design were fabricated anddemonstrated to be effective in fast mixing. Results show the com-patibility of this micromixer to various flow rates and its ability ofadjusting fluid ratios in final mixture by fluid flow rate ratios at theinlets. A prototype micromixer system based on this design wasproposed and fabricated showing its possibility for future fastchemical and biological analysis.

Acknowledgments

This research was supported by the Hong Kong Polytechnic Uni-versity (Project Nos.1-ZV46, 1-ZV5K and 1-ZV4W). The authorsalso thank CDAJ-China for their help in the simulation.

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