micro mixer with fast diffusion

8/14/2019 Micro Mixer With Fast Diffusion

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Micro Mixer with Fast DiffusionRyoMiyakel , The0 S.J. Lammer inkz, Miko Elwenspoek2

JanH.J. Fluitman21 Mechanical Engineering Research Laboratory, Hitachi, Ltd.

502, Kandatsu, Tsuchiura 300 Japan2. MESA Research Institute, UniversRyof Twente,P.O. Box 217,7500 E Enschede, The Netherlands

ABSTRACTA new concept for micro-mixing of liquid s introduced and fea-sibility is demonstrated. The mixer allows fast mixing of smallamounts of two liquids and it is applicable o micro-liquid handlingsystems [l ]. The mixer has a channel for the liquid, an inlet portfor the reagent, and a 2.2 m m x 2 mm x 330 pm m ixing area, andits bottom has 400micro-nozzles 15 pm x 15 pm). Through these

nozzles, a reagent is injected nto he sample liquid, making manymicro-plumes. These plumes increase the contact surface be-tween the two liquids drastically, and hasten the speed of the mix-ing by diffusion. The nozzle holes and channel are etched usingKOH into a 3-inch (100)-Si wafer from bo th sides. The fabricationprocess is extremely simple. Flow visualization by microscopeshows the mixing is complete within a few seconds, andabsorptiometry using a pair of optical fibers showed that a homo -geneous state of mixing is reach ed in 1.2 seconds, when the totalvolume injected is 0.5 pIand the injection flow rate is 0.75 pus.

A micro-liquid dosing system with micropump and flowmeterhas been presented [6],which is able to transport a small amount(- lp l) of liquid accurately at a flow rate of less than 1 p k . Micro-liquid handling systems require micro mixers that can b e easilyintegrated with this dos ing system on a single chip. The proper-ties necessa ry for the m icro mixer are1) the abilitytomix smallamounts of jquids(- 1 l)2) a simple m ethod or mixing quickly and uniformly3) a simpfe fabrication process or integrationon a single chipIn general, mixing is performed by a com bination of convectionand molecular diffusion. However, when sm all amount of liquidsare mixed, the Reyno lds number is very small, and it is, therefore,difficult to generate sufficient convection for the m ixing.We propose a new concept for mixing liquids when theReynolds number is small, and demons trate a mixer which allowsfast mixing of small am ounts of two liquids, which is also appli-cable in micro-llquidhandling systems.

PRINCIPLEINTRODUCTIONVarious sorts of micro mechan ical devices have been devel-oped using micro-technolog ies. Micro-liquid handling devicessuch as micropu mps [2], active [3] and pas sive [4] icrovalveshas rece ived considerable attension, and current studies are try-ing to integrate them as m icro-liquid handling systems 111.The basic concep t of micro-liquid handling systems has beenproposed as illustrated in Fig. 1. It consists of micro-liquid dosingsystems, a m icro-mixer and reactor, a detector, and m icro-chan-nels connecting h e devices. A sample liquid s introduced nto hemicro mixer by the dosing system, mixed with a reag ent and mea -sured by the detector. Compared to an ordinary automatic chemi-cal analyzer, this system has the advantages of superior portabil-ity, high accuracy, low consumption of reagents, and the ability ohandle small amounts of sample [SI.

Reagent Micro-LiquidI

Micro-Liquid Micio MixerDoaing System S] and RoactorFig. 1 Basic Concept ofMicro-Liquid Han dling System [ l

2

Molecular diffusion plays a more imp ortant role in a flow with asmall Reynolds number, since it is driven by a c oncentration dif-ference ( Ficks law ). First, we consider the cha racteristics ofmolecular diffusion in the m icrod om ain, and utilize it to create amicro mixer.Diffusion speed increases with the rise of the contact surfaceof two liquids. In an ordinary mixing chamber, the turbulence flowby stirrer provides minu te segregated domains of liquid, whichincrease the contac t surface (71. For quick diffusion , it is requiredto create this segregated state.The time taken when molecules travel is increasing n propor-tion to the squa re value of the distance [8]. For instance, if thedistance is 10 pm, the traveling time in water is around 1 sec., andif 1 mm, the time is on the order of 1000 sec. Therefore, the dis-tance for diffusion should be short enough to reduce he travelingtime.The basic idea of the micro mixer, reflecting the abo ve 2 char-acteristics, s illustrated n Fig. 2. The mixer has an a rea for mixingwhich is very flat and thin with many m icro-nozzles on the bottom.During operation, first, the m ixing area is filled with one liquid, andthe other liquid is injected into the area through the many micronozzles, making many m icro-plumes. These plumes increase thecontact surface. The nozzles are positioned very closely in rows,10-100 pm a pan, in order that the p lumes may quickly diffuse forthis distance. Thus, effective mixing will be performed without anyadditional driving.

:48 0-7803-0957-2/93 3.00 0 993 EEE


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Micro-Plumes Upper GlassSurfaceBottom withMlcro-Nozzles

Fig.2 Basic idea of Micro-MixerFeasibility est

Numerical analysis of the diffusion flow was employed tocheck the feas ibility of the concept. Figure 3 is a comparison ofdiffusio n efficien cy between a large single plume (a) and in themany m icro-plumes from the 400 micro-nozzles (b). The formercase (a) ma y be considered as a simple junction of two liquids.Here it should be n oted that the latter case (b) was simulated foronly one plume, since the flow pattern rom each nozzle is similar.The diffu sion coefficient D = 1.O mm2/s was used to repre-sent mo lecular diffusion in water. Please note that this value of Dis used for all calculations in this paper. The parameter for esti-mating the degree of mixing is given by a percentage of the totalmass injected where concentration decreases less than 50YO.

jvQdvDegreeof Mixing =- 100 OO)i v c dvc d = c < 0.5

DegreeofMixing (oh )

Here, the value of 50% is used as an index of the degree of mix-ing. c and Cd is standardized by the in itial concentration CO. Thetotal liquid njected is 1pl, and the flow rate is 4 pus. Therefore, itstops at 0.25 sec. This result indicates that mixing in the micro-mixer is 100 times faster than in case (a), com paring the time toreach a value of 40%. A 3-D diagram of concentration distributionindicates hat all portions of the micro-plume s diffused in 1.Osec.Hence, this analysis predicts that this mixer has a property to fin-ish mix ing within a few seconds.

DESIGN OF MICRO MIXERThe main parameters for designing a micro mixer are thenumber of micro-nozzles and the distance between each nozzle,which determines the area of mixer, the height of the mixing area(h), the size of the micro-nozzles (d), and the injection flow ra te ofthe m icro-plumes (9).The distance between each nozzle is set to be 100pm due tothe fabrication process ; orientation dependent etching with KOHsolution). The area for mixing was determined to be 2 mm x 2mm, which provides enough volume to mi x a microliter of liquid,and allows space for 400 micro-nozzles.Height (h), size of nozzle (d), and injection flow rate (q) arediscussed using numerical analysis, since they are directly re-lated to the diffusion flow. A finite differential method is used tosimulate changes in the micro-plume over time [9].Figure 4de-

picts the mod el of the flow passage, which is symmetrical aroundthe axis of the micro-nozzle n order to simplify to a 2-dimensionalanalysis (see Appendix). Here, a flow with a m icro-plume comesout through the m icro-nozzle and expands radially.Upper surface.

Height (h)

Fig. 4 Model of Flow Passage40122The diffusion Row is well estimated using he center of gravity

56 sec,kter zg and the variance of ma ss diffused U [lo].00 0.01 0.1 1 10 100

Concentrationdi?nbution

CIC 01 o0.80.60.40.20a

Flow rate : 4 VSInletFig.3 Feasibility Test of Micro Mixer

249


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where c(t,v) means the mass concentration at the unit volume v,at timet , and z(v) is the height in the position of the volum e v. Theconcentration was standardized by the initial concentration CO.s(t) represe nts he va riance of mass diffused. The larger the valueof %(t), the higher the micro-plume is injected, which results inwell mixure n the ax ial direction. Likewise, when the va lue of o(t)becomes larger, the micro-plume is dispersing more and be-comes well mixed.

SimulationresultsFirst, we checked the influence on the diffusion flow of thenozzle diameter d, which relates to the injection velocity. Figure 5shows a comparison of d = 10,20 , and 30 pm when the flow rateis 4 pl/s, giving mean values for injection velocity of 12 7 mm/s (d=10 pm), 32 mm/s (d = 20 pm), and 14 mm/s (d = 30pm). All resultsshow similar curves for both %(t) and s(t) for this large velocityrange. The injection flow from the nozzle was found to be a lami-nar jet, since the Reynolds number (taking the diame ter d as therepresentative ength) is of the order of 1. It s therefore assumedthat a viscous force moderates the injection flow immediately af-ter it comes out the nozzle. Here, we chose d = 20 pm as thediameter for the following analysis.Next, we discuss the influence of the injection low rate, usingq = 1.O~ l / s , .0 pVs, and 8.0 pVs, and a total injection volume of

1BI. The flow stops at 1.O sec (1.O pl/s), 0.25 sec (4 p k ) , and0.125 sec. (8 plls . Fi ure 6shows the variance of q = 1.Opl/s at42 x 102 ( ~ 1 ~ ) .quick injection causes the mass to dispersefaster. We see tha t convective flow accelerates the d ispersionmore. However, t must be noted hat even when the flow rate q =1.O~ l / s ,he mixing s done quickly. Hence, we used q = 4 pl/s asthe flow rate for the following simulation.Figure7 is the change of variance depending on the height (h),from 11OHm to 440Hm. He re, the injection stops after 0.25 sec.This shows o(t) reaches a maximum around 300 pm.In sum, a diameter of around 20pm, and a he ight of 300 pm issuggested, and a flow ra te more than 4 pl/s is best, but the lastdepends on the performance of the pump.

1 Osec. is 34x 103 81.11 ), relativelysmall compared to the value of


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Ci(t) are equal. Therefore, it is deduced that, when the output lightpower takes a minimum value, the concentration becomes uni-form in the direction perpendicular o the light beam. On the otherhand, the concentration in the beam direction also becom es uni-form, since the flow from e ach micro nozzle is symmetrical. In thisoptical setup, it is possible to mea sure the time to com plete mix-ing by checking the output light power absorbed.

Measurement resultsThis optical setup is calibrated with regard to the stability of thebaseline in the blank state (no dye in the optical path) and thefeasib ility to work as an absorptiometer. For the stab ility, thechange of the output pow er is within 1.5 TOof the total value for 1min. The stability is therefore enough to check the time taken formixing.For the feasibility, the correlation between the co ncentration ofliquid and the output power is checked. I f it works as anabsorptiometer, he next relation is given from the equ ation (6).

- In(P/Po )= k-c k = q . I (10)The m ixing area is filled with dyes a t several concentrations inturns. The Rhodamine concentration used in this experiment isabout 10'-5W/O. s depicted in Fig. 13, a linear correlation was

obtained. 1.2 I I I I I I1 .o0.8$? 0.6

S 0.40.20

h

v

0 0.2 0.4 0.6 0.8 1Concentration(standardized)

Fig. 13 Feasibilityof Optical SetupUsin g his setup, the time to complete mixing is investigated.Figure 14shows the results of measurem ents when the injectionflow rate is 0.75 plls, the total volume injected is 0.5pl, and theinjection stops after 0.67 sec. The output signal continuously de-creases after the injection stops, and an equilibrium state isreached in 1.2 sec. later. Thus, as seen in the flow visualization,this measu rement reveals the mixing is comp leted within a fewseconds.

DISCUSSIONThe concept of the micro-liquid handling system was illus-trated in Figure 1.The liquid has to be transported to the detectorafter the mix ing completes. Here, we discuss the application ofthe the m icro-mixer o this detector components with regard o therelative position in the system .As mentioned earlier, the mixing area can be treated as a mi-cro reaction beaker. lt is feasible to set the detector in the m ixingarea and measure directly (Fig. 15(a) ). This method has the ad-

vantage of making it possible to measure the early stages of mix -ing and reaction, and the system is simply integrated with the de-tector.

Ftr ector(a) Detection at Mixer (b) Detection at Downstream

22mmI' - 1l l m m J a b c d

I 1. ./FmOpticalRefledorP

Center of Mixing area(measuringwidth 1mm)

Fig. 15 Application to DetectorThe setup shown in Fig.15 (b), with the detector set down-stream from the mixer, has the advantages that a more compli-cated detector can be used, and that the number of measure-ments per unit time may be increased by performing mixing anddetection of successive samples simultaneously. However, asthe mixed fluid s conveyed o the detector location, its concentra-tion profile is deformed by convection. We observed this deforma-tion and then checked the feasibility of this metho d.As depicted in Fig. 10,the pair of optical fibers are positionedalong the flow channel with an xyz-positioner.Figure 15 illustratesthe mea surement positions, which are the center of the mixingarea, 3 mm from the cen ter, 5 mm, and 7 mm. The timedep en-dent signal from each po sition is shown in Figure 16 for a trans-portation low rate of about 0.3 pl/s. Thus, the deformation of con-centration occurs quickly only in the first few millimeters down-stream. Figure 17gives the reproducibility of the co ncentrationprofile observed at 5mm and 7 mm downstream. This shows that

0 2 4 6 8 10Time ( sec.)

Fig. 14 Experimental Result252


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the profiles are quite similar. It may be possible to use thismethod, even though the profile changes drastically due to thetransporting flow.Thus, both of the above methods for detection are feasible.One must be selected on the basis of usage and their advan-tages, and further de tailed investigation, both experimental andnumerical, on matching in actual systems is n ecessary.

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0.80.60.40.2

00

Time ( sec.)Fig. 16 Deformation of Concentration

Time ( sec.)- 1o 07 5 P.asi&.:.d ................ ! ..................... 1 ,.......... ......,..-

m .0.25 I I I I0 50 loo 15 0 m 250Time ( sec.)

Fig. 17 Reproducibilityof Co ncentration Profile

CONCLUSIONA new concept for micro mixin g utilizing he effect of mo leculardiffusion is introduced and its feasibility is demonstrated numeri-cally and experimentally. The mixing process using the micromixer is faster by a factor of -1 00 as than that of a single plume,according to the n umerical simulation.Flow visualization by microscope revealed that mixin g s com-plete within a few seconds, and an absorptiometry using a pa ir ofoptical fibers showed that a homogeneous state of mixing isachieved in 1.2 seconds, when the total volume injected is 0.5 HIand the injection flow rate is 0.75 J.II/s.This m icro mixer is app licable to micro-liquid handling systemsdue to its simple mixing method and fabrication process.

REFFERENCES[ l ] Frans C.M. van de Po l,"Micro Fluid Handling Systems," 5th Int.Conf. on Advanced Robotics, June 19-22, 1991, Pisa, Italy,121 F.C.M.Van de Pol, H.T.G.Van de L intel, M. Elwenspoek andJ. H. J. Fluitman, "Thermopneumatic Micropump Based onMicro-engineering Techniques," S ensors and Actuators,[3] T. Ohnstein, Fukida, T., J. R idley, and U. Bonne, "Micro

Machined Silicon Microvalve ," Proc. of MEMS'SO, pp.95-98,1990Microvalve and Micropump Fabricated on a S ilicon Wafer,"Sensors and Ac tuators, 20, pp. 163-169, 1990[5] A. Manz, N. Graber, and H. M. Widmer,."Miniaturized TotalChemical Analysis Systems: A Nov el Concept for ChemicalSensing," Sensors and Actuators, B1, pp.244-248, 1990161 The 0 S.J. Lammerink, Miko Elwenspoek, andJan H. J. F1uitmam"lntegratedMicro-Liquid D osing System,"Proc. of MEM S'93, 1993[7] R.S. Brodkey, 'Turblence in M ixing Operations,"AcademicPress, Inc., New York, 19 75[8] E. L. Cussler, "Diffusion Mass Transfe r in Fuid Systems,"Cambridge Univ. Press , New York, pp.52-53, 1984191 E. S. Oran, and J. P. Boris, 'Numerical S imulation of Re activeFlow," Elsevior, New York, 1987[ l o ] J. C. Sternberg,"Advances in ChromatographyVol. 2,"Marcel Dekker, New York, pp.205-270, 19661111 Miyake, R., Ohki, H., amazaki, I. , andYabe, R.,"Development of Micro Sheath Flow Chamber,"Proc. of MEMS'91(1991), pp265-270[12]0. H.Wheeler, A. A. Kaplan, et a1,"Organic ElectronicSpectral Data vol. 3," Inter Science Publisher, New York,pplO25

pp.281-290, 1991

VOl.A21 -A23, pp. 198-202 , 1990

[4] Esashi, M., Sho ji, S., and Nakan o, A., "Normally Closed

APPENDIXThe b asic equations of this finite differential analysis are a vor-tex transport equation and a diffusion equation [$I. The boundaryconditions for the wall are g iven as follows:

u = o (1)In the outlet, we suppose the change of velocity in the r-directionis moderate enough and the flow in the axial direction is smallenough as compared to that in the rdirectio n. For the diffusion,we suppose the change of flu x s mode rate enough. Threfore, we

In the center, since the flow and diffusion are symm etrical, thecondition is given byau, acU r = O , -=o,t- - = or

ACKNOWLEDGEMENTS In the inlet, we suppose a Poiseuilli flow profile.(3)

The author would lik e to thank those involved from the staff ofthe MESA Re search Institute of the University of Twente, particu-lar ly Dr. H. Gardeniers, Dr. C. Eykel, C. van Mullen, D.Ekkelkamp, E. Berenschot, and H. van. Vossen for their valuablecooperation, and U.Lindberg for h is useful suggestions.253

micro mixer with fast diffusion

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