Polymer-based device for efficient mixing of viscoelastic fluidsHiong Yap Gan, Yee Cheong Lam, and Nam-Trung Nguyen

Citation: Applied Physics Letters 88, 224103 (2006); doi: 10.1063/1.2206682 View online: http://dx.doi.org/10.1063/1.2206682 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/88/22?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Flow-induced demixing of polymer-colloid mixtures in microfluidic channels J. Chem. Phys. 140, 094903 (2014); 10.1063/1.4866762 Jeans instability in a viscoelastic fluid Phys. Plasmas 18, 012901 (2011); 10.1063/1.3526685 Dynamics of viscoelastic fluid filaments in microfluidic devices Phys. Fluids 19, 073103 (2007); 10.1063/1.2747660 Collision of viscoelastic jets and the formation of fluid webs Appl. Phys. Lett. 87, 014101 (2005); 10.1063/1.1984099 Mixing of viscous polymer liquids Phys. Fluids 12, 1411 (2000); 10.1063/1.870392

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APPLIED PHYSICS LETTERS 88, 224103 �2006�

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Polymer-based device for efficient mixing of viscoelastic fluidsHiong Yap Gan, Yee Cheong Lam,a� and Nam-Trung NguyenSchool of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue,Singapore 639798, Republic of Singapore

�Received 18 January 2006; accepted 5 April 2006; published online 2 June 2006�

We demonstrated rapid mixing of viscoelastic fluids in microchannels constructed based onpolymethyl methacrylate. Viscoelastic mixing without diffusion was achieved with an effectivemixing length of less than 5 mm and a relatively fast flow rate. With an abrupt contractionmicrogeometry �8:1 contraction ratio�, we mixed two different viscoelastic fluids experimentally atvery low Reynolds numbers, but enormous Peclet and elasticity numbers. This special geometricalconfiguration triggers flow instability, leading to turbulent and efficient mixing. This flow regimehas negligible inertia effects but significant elastic effects. © 2006 American Institute of Physics.�DOI: 10.1063/1.2206682�

Microscale characteristic dimensions lead to low Rey-

nolds number, Re=�V̄do /�o, where V̄, do, �, and �o are themean velocity, the characteristic length, the fluid density, andthe viscosity, respectively. Flows of a Newtonian fluid in amicrochannel are therefore well confined within the laminarflow regime. Mixing of multiple streams is normallyachieved by molecular diffusion, and not by the more effec-tive mechanism of flow instability. Numerous mixing mecha-nisms for micromixers had been proposed1,2 without over-coming the constraints and limitations of a low Re. Theselimitations result in the requirement of external actuators orlong and complicated channel structures, and the associatedcomplex and expensive fabrication processes. Consequently,these micromixers are not attractive from a practical point ofview. As such, a different mechanism that introduces anotherdominant force and bypasses the Re limitation will bevaluable.

It is known that trace amount of deformable polymers ina solution can introduce an elastic stress in addition to theviscous stress,3–9 i.e., from a viscoelastic fluid. Chaotic flowinstability with negligible Re but enormous Peclet number�Pe� has been illustrated clearly. The effect of fluid elasticityand the relative dominance of elastic to inertial effects can becharacterized by Deborah number, De, and the elasticitynumber, El=De/Re.10 However, the unique characteristics ofviscoelastic fluids have not been exploited yet for efficientmixing of two dissimilar fluids in microdevices.

A variety of fabrication methods is available for micro-fluidic devices, including wet etching, reactive ion etching,photolithography, soft lithography, in situ construction, andplasma etching. However, most of the methods have utilizedglass or silica as substrates in fabrication. Recently the use ofpolymeric microstructures has gained immense interestsfrom microfluidic fraternity. The polymeric substrates intro-duce an alternative for the production of microfluidic sys-tems because they are less expensive and easier to manipu-late than silica-based substrates. It introduces a fast andsimple fabrication method that allows direct-writing fabrica-tion for a channel by utilizing a CO2 laser. The inherentnonreactive hydrophilic nature of the polymethyl methacry-late �PMMA� substrate allows direct application of the chan-

a�

Electronic mail: myclam@ntu.edu.sg

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nel for clinical analyses of biomolecules without the need forsurface modifications to reduce wall adsorption. However,analytical assays on these devices need to be explored beforetheir usefulness can be fully assessed.

We employed a PMMA microchannel of 200 �m indepth with an abrupt contraction of 1600 �m: 200 �m:1600 �m to introduce convergent/divergent flows. The mi-crochannel was fabricated using two 1 mm thick PMMA lay-ers, with the channels machined by CO2 laser onto the toplayer, and sealed by the bottom layer. The length of the con-traction is 800 �m. Side streams were introduced into thecentral main stream through two side channels, each at eitherside of the main channel. The side channels were 800 �m inwidth and 3400 �m upstream from the centerline of the con-traction. Mixing of two dissimilar fluids was investigated asthe mixing of two streams of the same fluid has little practi-cal value. The main stream, which has higher viscosity andelasticity, consists of 1 wt % poly�ethylene oxide� �PEO� in55 wt % glycerol water �1%PGW for brevity� with greenfluorescent dye �C20H10Na2O5�. The side streams, consistingof 0.1 wt % PEO in water �0.1%PW for brevity� with 3 �mred fluorescent microsphere solution �Duke Scientific Co.�,enter the main microchannel through the two side channels.The molecular weight �Mw� of PEO employed is approxi-mately 2�106 g/mol. The trace amounts of fluorescent dyeand microspheres have negligible effects on the fluids’ prop-erties. In any case, the fluids’ properties tabulated in Table Iwere determined with the additives. The sample liquids weredelivered by a precision microsyringe pump �Lomir Bio-

medical Inc.�. The main stream flow rate was Q̇. The flow

rate of the two side streams was the same, each having 0.5Q̇.

TABLE I. Fluid properties at 25 °C. GW: glycerol in water solution; PW:PEO in water; PGW: PEO in glycerol water.

Fluid

Zero-shearviscosity�o �Pa s�

Density� �kg/m3�

Relaxationtime� �s�

0.1%PW withmicroparticle 1.79�10−3 997 1.5�10−3

1%PGW withfluorescence dye 423�10−3 1134 50�10−3

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224103-2 Gan, Lam, and Nguyen Appl. Phys. Lett. 88, 224103 �2006�

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Thus, the total flow rate in the device was 2Q̇.With reference to the main stream fluid properties, the

characteristic shear rate �̇char, De, Re, Pe, and El are esti-

mated as �̇char= �2Q̇ /wcd� / �wc /2�= �4Q̇ /wc2d�, De

=��4Q̇ /wc2d�=4�Q̇ /wc

2d, Re=4�Q̇ /�o�wc+d�, Pe

=2Q̇Lchar / �Ddwc�, and El=De/Re, where the contractionwidth wc is the same as the channel depth d, � is the relax-ation time measured in shear, Lchar is the upstream channelwidth and D is the diffusion coefficient, estimated to be D

=4.2�10−12 m2/s for 1%PGW. For 1%PGW at Q̇=20 ml/h, Pe=106�106, Re=0.149, De=139, and El=932,approximately. Pe values for all these experiments were large

�Pe�26.5�106 for Q̇=5 ml/h�, and thus diffusive mixingwas negligible. Mixing experiments were carried out at room

temperature and the investigated Q̇ were 5, 10, 15, and20 ml/h. For each flow rate, flow field images in the sameexperiment identified by green fluorescent dye �main stream�or red fluorescent microsphere solution �side stream� werecaptured at a different time by changing the epifluorescentfilter sets.

Figure 1 shows the flow fields for Q̇=5 ml/h �Re

=0.037, Pe=26.5�106, De=34.7, and El=932� and for Q̇=20 ml/h �Re=0.149, Pe=106�106, De=139, and

El=932�. At Q̇=5 ml/h, small viscoelastic vortices formedat the corners of the upstream contraction in a symmetricalfashion �see Figs. 1�a� and 1�b��. Flow instability and pulsa-tion induced by viscoelastic effects were observed in theflow field. When the flow approached the contraction en-trance, more and more fluorescent creeks �initially containedwithin the central main stream� were directed to the sidesinstead of flowing through the contraction �see Fig. 1�a��.The diverted “creeks” were then circulated within the vortex�swirling stream� and then blended back into the central mainstream. Competition between the main and the side streamswas taking place at the entrance region next to the contrac-tion. This competition increased with an increase in flow

FIG. 1. Viscoelastic fluids at Q̇=5 ml/h. Experimental results were col-lected at different time intervals in the same experiment. For both upstreamand downstream, flow instability with some mixing �indicated by the over-lapping of the fluorescent dye �main stream� and microspheres �sidestreams�� was observed. Mixing was not uniform and did not extend acrossthe entire cross section.

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rate, and the entire flow field became increasingly unstable

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and with increasing size of the vortices �Q̇=10–20 ml/hwith De=69.4–139 and El=932�. As shown in Figs. 2�a� and

2�b�, at Q̇=20 ml/h, salient and large corner vortices wereformed, and “whipping” or repeated swinging of the fluores-cent main central stream across 70% of the channel widthwas observed. This whipping effect resulted in the fluores-cent mainstream “encapsulating” the fluid of the sidestreams. The main stream with the encapsulated fluid swungtogether continuously as the flow was progressing. As shownin Fig. 2�a�, a lower level of fluorescent intensity was ob-served at the proximity of the “swinging” mainstream, indi-cating some degree of mixing at upstream. By comparingFigs. 2�a� and 2�b�, we observed significant overlapping oc-curring between the main and the side streams, indicatingmixing. The occurrence of upstream mixing and whipping ofthe main stream is depicted schematically in Fig. 3.

Viscoelastic flow instability was more significant down-stream of the contraction, subsequent to the main and sidestreams competing and gushing through the contraction at

high speed. At Q̇=5 ml/h, there was expansion flow for the

FIG. 2. Viscoelastic fluids at Q̇=20 ml/h. Experimental results were col-lected at different time intervals in the same experiment. Both flow expan-sion and chaotic instability contributed effectively to mixing. Mixing wasobserved extensively almost across the entire cross section, except for thinlayers next to the channel walls.

FIG. 3. Pictorial images of viscoelastic flow field of low-viscosity PEOfluids at two different flow conditions. The light-color lines represent main

stream and dark-thick arrow lines represent side streams. �a� Q̇=5 ml/h

showing corner vortices and some mixing downstream, and �b� Q̇=20 ml/h highlighting the viscoelastic instability �whipping� upstream andct to the terms at: http://scitation.aip.org/termsconditions. Downloade

turbulence and chaotic flow behavior downstream.9 May 2014 02:36:21

224103-3 Gan, Lam, and Nguyen Appl. Phys. Lett. 88, 224103 �2006�

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main stream immediately downstream of the contraction �seeFig. 1�c��. However, as shown in Fig. 1�d�, there was obviouspenetration of the side stream fluid into the central portion ofthe channel, overlapping with the main stream fluid. Thispenetrated stream fluctuated in location and was intermittent,indicating flow instability. Similarly, by comparing Figs. 1�c�and 1�d�, there was overlapping between the main and theside streams, indicating mixing, but not fully extended across

the whole channel width downstream. At Q̇=20 ml/h, as dis-cussed previously, there was a significant viscoelastic whip-ping of the mainstream at upstream. This caused flow fluc-tuation of the main stream through the contraction, andfluctuation of flow resistance to the two side streams. Indeed,this whipping of the main stream facilitated the side streamspenetrating deeply into the central portion downstream �seeFig. 2�d��. These fluctuations resulted in chaotic flow �andpossibly turbulence� downstream of the contraction. Thischaotic flow, together with the expansion flow of the mainstream, promoted effective mixing. As illustrated in Figs.2�c� and 2�d�, other than a thin layer next to the edge of thechannel wall, significant mixing had occurred over the entirecross section. The above flow behaviors are depicted picto-rially in Fig. 3.

In summary, we had developed and characterized a low-cost, disposable PMMA microdevice for an efficient mixingof two different fluids by viscoelastic flow instability. Thisflow regime has negligible Re and high De, thus a large El.

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The proposed device is simple in fabrication yet effective formixing over a short distance, with a relatively fast flow rate.

The authors would like to thank the Agency of Science,Technology and Research, Singapore �A*Star� for its finan-cial support �SERC Grant No. 0521010013�. One of the au-thors �H.Y.G.� gratefully acknowledges A*Star for providinghim an A*Star Graduate Scholarship and for supports re-ceived from its affiliated institution, the Singapore Instituteof Manufacturing Technology �SIMTech�. PEO powder wasprovided by The Dow Chemical Company. This research isprotected by US provisional patent application No. 67/701,078.

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