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Surface Tension Driven and 3-D Vortex Enhanced Rapid Mixing Microchamber I-Da Yang, Yu-Feng Chen, Fan-Gang Tseng, Member, IEEE, Hui-Ting Hsu, and Ching-Chang Chieng
Abstract—This paper proposes a novel passive micromixer design for mixing enhancement by forming a large three-dimensional (3-D) flow vortex in a counterflow microfluidic system. The counterflow fluids are self-driven by surface tension to perform mixing in an open chamber. The chamber design consists of two rectangular bars to house the chamber and to form two opening inlets from opposite directions. The best design is selected from various versions of mixing chambers. The mixing effectiveness is tremendously increased by folds of contacting surface between two fluids induced and enhanced due to the stretching of two fluid contacting interfaces by the formation of a 3-D large size vortex structure inside the mixing chamber itself with unaccountable numbers of fluid layers. Both numerical simulations and experiments are performed and compared to identify the design parameters for maximum utilization in this microfluidic system, such as the length of rectangular bar, microchannel wall height, and mixing chamber size. Compared to traditional micromixers operated by two-dimensional (2-D) vortex, this passive mixer can greatly enhance mixing efficiency and reduce mixing time by tenfold from around 10 s to less than 10 ms by 3-D effective chaotic flow structures in a more compact size. This mixing chamber is also suitable for an H-shape digital fluidic system for parallel mixing process in different mixing ratio simultaneously as a lab-on-a-chip system. [1509] Index Terms—Microfluidics, mixing, surface tension, vortex.
NOMENCLATURE AR
Aspect ratio of mixing chamber. Depth of the main parallel incoming channels. Percentage of Reaction_Product_C occupied in the mixing chamber. Volumetric surface tension force. Pressure. Mixing reaction ratio: time. Velocity of the liquid-gas mixture. Width of the main parallel incoming channels. Width opening for the square mixing chamber. Entrance opening for the square mixing chamber. Surface tension per unit interfacial area. Mixture fraction for the th mixture. Unit normal vector. Opening ratio of mixing chamber. Surface area delta function. Diffusion coefficient.
Manuscript received January 20, 2005; revised August 3, 2005. This work was supported by the National Science Council, Taiwan, R.O.C., under Contract NSC 92-2323-B-007-003. Subject Editor S. Shoji. The authors are with the Department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan 30043, R.O.C. (e-mail:
[email protected]). Digital Object Identifier 10.1109/JMEMS.2006.872228
Curvature of interface. Viscosity of the liquid-gas mixture. Specific density of tracing particles Density of the liquid-gas mixture. Surface tension coefficient.
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I. INTRODUCTION
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APID and efficient mixing with passive or active means is an issue in biomedical and chemical diagnosis with microfluidic systems. For fluid flow system in micrometer dimension, the Reynolds number is low and implies laminar flow with small convective effect, and thus the molecular diffusion is the basic mechanism of laminar mixing process with slow rate. In the previous literature, laminar mixing has been promoted by the extraordinary increase in one dimension of the mixing structure and the tremendous increase of interfacial surface area of the two streams via solid structure designs through stretching and folding of fluid interface, such as formation of numerous plumes from micronozzles by injecting reagent into the samples [1], multistage multilayer lamination of two liquid stream [2], spiral architecture designs of various flow paths [3], or enhancement of chaotic flow characteristics using repeating “C-shaped” unit in three-dimensional (3-D) serpentine microchannels [4], introducing the unsteadiness in the flow or periodic/oscillatory flow systems [5], adding geometric complexity with helical microchannel [6], or placing ridges on floor of the channel at an oblique angle with respect to the long axis [7]. These systems mainly increased the interfacial area in one dimension for the two fluids flows in the same direction. Very rare approaches attempted to alter the major flow patterns inside the simple configuration of the mixing region, except the idea of T-type microfluidic mixer [8] that changes the mixing length of gas flow characteristics. Therefore, the mixing times for the above mixers are usually limited to a few seconds or even to minutes; few of them can be reduced into millisecond range. As a result, this paper proposes a novel design of a surface tension driven passive mixer, in which a 3-D vortex can be generated by optimized structure design; thus the mixer can greatly reduce mixing time and increase mixing efficiency by ten- to 100-fold over a traditional mixing device with two-dimensional (2-D) flow structure. The major chamber size and shape are unchanged in this paper, but fluid–fluid interface areas are tremendously increased by flow structure inside the mixing chamber with different extents of mixing by minor entrance structure modifications. The basic structure of the mixer, as illustrated in Fig. 1(a), allows counterflows (Fluid _A and Fluid_B in the figure) to meet at the mixing area (the central stroke of H) from the opposite
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Fig. 2. Schematic diagram of fluid injecting system.
B. Fabrication of Microfluidic System
Fig. 1. Schematic of (a) H-type microchannel systems and the reaction/mixing regions and (b) fabrication process.
ends of the H-shape microchannel system. There are at least four advantages by this design. 1) Flow driving and vortex structure formation are fully operated by surface tension effect, thus no extra pumping or actuating mechanisms are needed in this passive system. 2) A continuous 3-D vortex generated in this system can dramatically shorten the mixing time less than 10 ms, which is at least 10 to 100 times faster than most of the micromixers by effective chaotic flow structures during mixing. 3) The mixing chamber requires only a compact size owing to the 3-D vortex structures folding all the mixing interfaces three-dimensionally. 4) This mixing system can be employed into an H-shape digital fluidic network system [9], allowing fixed amount fluid mixing with different mixing ratio simultaneously in parallel. The procedure for optimizing mixer chamber is illustrated both by experiments and first principle simulations in three steps: 1) selection from various versions of additional structures at inlets of mixing chamber, and the enhancements of mixing with different versions of additional structures are compared using the experimental [10] and numerical approaches, so that the base design for mixing chamber can be determined; 2) characterization of the base design by its flow characteristics, which plays the major role of mixing mechanism; and 3) identifications of design parameters for mixing chamber with maximum performance. Before the analysis, methodologies of experiments and numerical simulations are briefly described. A. Experimental Methodology Experiments include the manufacture of microfluidic systems, visualization of the mixing phenomenon, and characterization of detailed flow field inside the mixing chamber.
The micromixer systems are manufactured by microelectromechanical systems technologies by thick photoresistor process and polymer molding technique. Fig. 1(b) illustrates the detailed manufacturing process of the flow network. A 4-in Piranha-cleaned and 120 C dehydration baked glass wafer is prepared as the substrate of the thick photoresistor SU-8 mold. SU-8 (Microchem) is spun onto the wafer with two spinning steps (500 rpm for 10 s and 1500 rpm for 20 s) to form a 60- m-thick layer. The patterns of the flow networks are defined by Mask#1 with designed dimensions. PDMS (DowCorning) is the structural material of the network in this experiment. The prepolymer of PDMS is made of the mixture of 20 ml base resin and 2 ml curing agent. The prepolymer mixture is placed in a vacuum chamber for one hour to remove air bubbles entrapped before it is poured over the wafer. The wafer is then placed in the vacuum chamber for an additional hour to remove the air bubbles trapped between the mold and prepolymer. After the air-evacuation process, the wafer is cured in an oven at 60 C for four hours. The flow network is obtained by peeling the cast from the SU8 mold and the cleaning by isopropylalcohol (IPA) after the curing. The rectangular bar structures around and at the entrance of the mixing chamber are the key installations to promote mixing. The size of the mixing chamber is defined as 250 250 m and the geometry of the m Width 170 m Length in the experiintrusions is ment. For the flow network purely constructed by PDMS, the solid/liquid contact angle in the experiments is 20 measured by surface tension measuring instrument (First Ten Angstroms 200, Cole-Parmer Instrument Co.). II. OPERATION OF MIXING EXPERIMENTS Mixing experiments are performed by injecting two fluids to the flow inlets at the same time and recording the concentration of reaction_product_C by mixing Fluid_A and Fluid_B or measuring the flowfield inside the mixing chamber using microparticle tracking velocimetry. Both liquids A and B enter into the reservoirs from opposite inlets and precisely timed by the single syringe pump with two branches of same length. The schematic diagram of the experimental setup is shown in Fig. 2. The operational procedure is described as follows. Syringe-1 and Syringe-2 are filled with Liquid_A and Liquid_B and positioned on the tops of Inlets A and B, respectively. The air-pumping syringe connected with Syringe-1 and
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-2 by tubes provides the pumping force to eject the liquid drops into both inlets of the microchip. Then the reagents A and B flow into the mixing chamber by the surface tension to conduct the mixing experiments. A. Flow Visualization The flow visualization system records the gray levels and color brightness due to the presence of reaction products after mixing by the microscopic high-speed camera system so that the moving and mixing processes of two fluids from different directions can be analyzed qualitatively or quantitatively. In the mixing experiments, two indicators are employed to illustrate the mixing effectiveness: 1) color change and 2) intensity increment. In the first method, pH indicator bromthymol blue is injected from the top right inlet and the 6.2 M KOH solution is the second fluid injected from the bottom left inlet. The pH level makes the color change as the two liquids meet and mix and then the mixing process can be illustrated qualitatively. However, the qualitative illustrations are not satisfactory for providing good design guidelines but limited physics only. In the second method, the intensity increment of florescence is used as the indicator of mixing effectiveness. The production and increment of florescence is observed after the mix solution consists of dimethyl phthalate) of Fluid_A (the and Fluid_B (Cppo solution consists of DI-Phenyl oxalic dibutyl phthalate; China-Japan Illuminate, Inc., Taiwan). The changes of fluorescence intensities are indicated by the brightness level and analyzed by Image-PRO plus (Media Cybernetic, Inc.). In order to quantify the mixing effectiveness, a mixing reacis defined as tion ratio (1) where is the intensity of fluorescence after mixing started and is the average intensity as mixing reaches maximum. B. Detailed Flow-Field Measurements Due to the small size and less number of seeding particles of the mixing chamber, microparticle tracking velocimetry PTV is chosen for flow-field measurements. The use of PTV has been applied in small-scale flow-fields, such as vector velocities of droplets (with size of 150 m) dispersing in turbulent pipe (50.8 mm) [11]. This paper extends PTV with embedded color time code for the studies of velocity field measurements during the mixing process. The major challenges of flow visualization are the requirements of high resolutions m and temporally ( ms) in microscale both spatially flow region (less than 250 250 m ) and the elimination of optical noise by high reflectivity at the curvature of liquid’s surface for the open channel designs of present flow networks. The operational procedures for the embedded color time code PTV are described briefly as follows. 1) Record sequential images of particles inside flow fields using high speed camera. 2) Identify the particles by the image pixel values. The particle is recognized by pixel values lower than the low cut pixel value, i.e., the pixel value is artificially
Fig. 3. Postprocess of images: (a) the original (left column) and binary (right column) of images and (b) a set of combined images selection of particles.
set to zero (i.e., black) or is set to 255 (i.e., white) if it is below or above the low cut value (50 in this paper). Selection of the low cut pixel value depends on the intensities of the illumination light, particle scattering, and noise level in the flow system. 3) Embed the time code with pseudocolors. The colored binary images represent the images at different time. In the experiments, four sequential images are grouped in a set. The images are colored in red, green, as yellow, and black sequentially at , , , and shown in the second column of Fig. 3(a). 4) Combine the sequential images [Fig. 3(b)] to trace the particle trajectories and to conduct the analysis by selfdeveloped program:
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at interface. With two-phase homogenous flow model and the interface tracking technique, the volume-of-fluid method in cooperation with piecewise linear interface calculation [14], [15] is selected to obtain robust solutions for the interface determination. The simulations are performed on the platform based on first principle equations by a commercial finite-volume computer code from CFD Research Corporation (CFD-ACE+). Conservative laws of mass and momentum equations, and general transport equation are formulated as follows. 1) Continuity equation Fig. 4. Diagram of micro-flow-field visualization system.
(2) The streak images by connecting color particles are the bases resolving the velocity field using the self-developed program.
where m and m are the velocity and density of the liquid–gas mixture. represents time. 2) Momentum equation
C. Selection of Particles In order to eliminate the disturbance by particles to the microflow-field during visualization, the tracing particles must be 1) small enough to follow the fluid flow faithfully and 2) large enough to restrain the effect of Brownian motion and to produce sufficient signals. Polystyrene fluorescence tagged partiare cles with diameter 7 m and specific gravity of used in this paper. The volumetric density of particles in the experiment is chosen as 0.5%.
(3) where is the pressure and is the viscosity of the is the volumetric surface tension liquid–gas mixture. force, which can be represented by continuum surface force model, i.e., (4)
D. Optical System Setup Because of the flow region is in microscale, it is not easy to define the measurement spot applying the optical light sheet. Meinhart et al. [12] have proposed a methodology to define the thickness of the interrogation spot of micro-PIV system based on the depth of focus (DOF) of the objective lens. The image intensity of particles in DOF is naturally 10 times greater than that out of focus. As a result, the out-of-focus images are considered as the background noise and are filtered out during the digitalization process by applying the low cut pixel value. In this paper, a microscope (Optem-Zoom70) incorporated with an ultra-2X magnification lens is selected to obtain images with spatial resolution of 2 m and the DOF of the system is about 20 m (Fig. 4). The calibration is conducted by adjusting the focal plane on the middle plane ( 40 m up from bottom) and by the manual optical stage with resolution of 1 m. The temporal resolution is determined by the frame rate of the highspeed camera, i.e., FastCam-Ultima APX (Photron Inc., Japan) with frame rate of 250 fps with full-scale resolution of 1024 1024 pixels corresponding to the measurement domain size of 1400 1400 m . The sequential images are recorded with time steps of 4 ms for quantitative analysis. III. THEORY AND MATHEMATICAL FORMULATION The formulations of mathematical modeling for the flow system consist of equations of mass conservation, momentum conservation, volume fraction, and general transport equation. For a fluidic system in microscale, surface tension force is the major driven force applying at the liquid/gas interface that is also a part of the solution for the equation set. A continuum surface force model [13] is chosen to calculate the surface force
is the surface tension per unit In the above equation, interfacial area, is the surface area delta function, is is the curvature the surface tension coefficient, of interface, and is the unit normal vector. 3) General transport equation: The mixing is tracked with a mixture fraction variable , which is governed by the general transport equation (5) represents the mixture fraction for the mixture. Note that this equation contains no source terms due is to chemical reaction. The diffusion coefficient assumed the same for all mixture fractions. Two mixture fluids flow from the opposed ends of the H-shape microfluidic system and perform chemical reactions as they are mixed inside the micromixer chamber. Fluid_A and Fluid_B are the solvents with species_A and species_B from the microchannels of opposite ends. Reaction_Product_C is produced as Fluid_A and Fluid_B are mixed. In order to obtain the effect of the geometry parameters, a constant forward reaction rate of very high value (10 kmol/s) is set in the present computations with the assumption of excellent reaction. The concentration of Fluid_A and B is set as 1 (mol ), so the concentration of Reaction_Product_C is 0.5 mol in perfect mixing. IV. RESULTS AND DISCUSSIONS The effectiveness of the mixing chamber is illustrated by experiments and/or first principle simulations in following steps:
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Fig. 5. Schematic diagrams of mixing chambers for mixing from opposing flows: (a) plane rectangular mixing chamber, (b) rectangular chamber with sharp intrusion structure at inlets, and (c) chamber with housing rectangular bars at inlets.
1) selection of the base design for mixing chamber, 2) characterization of the flow pattern during mixing, and 3) identifications of design parameters for maximum performance. A. Selection of the Base Design for the Mixing Chamber In order to select the base design of the mixing chamber, designs of minor modifications at inlets of the central stroke of H-shape system are compared in terms of the mixing effectiveness for the mixing chamber of same size. The designs can be categorized into three groups: the original rectangular chamber [Fig. 5(a)], chamber with sharp intrusion structure at inlets [Fig. 5(b)], or chamber with rectangular shape bar housing at entrances [Fig. 5(c)]. The first column of Fig. 6 shows the photomasks of mixer chambers manufactured; the second column shows the gray levels of the titration images by charge-coupled device camera as two fluids encounter each other. The mixing occurs at dark gray regions. The third and fourth columns of Fig. 6 show the corresponding velocity vectors and the concentration of Reaction_Product_C obtained from first principle numerical simulations. Velocity vectors with magnitudes and directions for Fluid_A and Fluid_B are colored in red and blue, respectively, and the Reaction_Product_C vectors are colored in green. Computed velocity distributions inside the mixing chambers reveal the detailed flow characteristic and thus explain the mixing mechanism. The fourth column shows the computed concentration contours of Reaction_Product_C and indicates the mixed region with bright gray. For the top row figures, reactions of Fluids A and B are observed only at contact line of two fluids, which implies no or poor mixing except at locations near diagonal line and inlet corners [Fig. 6(a)]. The sharp intrusion structure [second row, Fig. 6(b)] intends to perturb the laminated flow before entering the mixing chamber, but the mixing zone is slightly enlarged by curving the two fluid interfaces only. Both experimental observation and numerical simulation [Fig. 6(b)] show that lamination is retained and limited mixing is enhanced even with the implementation of sharp intrusion structure. For the third row configuration [Fig. 6(c)], rectangular bars at chamber entrances guide the incoming flow to circulate inside the mixing chamber before leaving the chamber and a much larger region undergoing mixing is obtained. For the same design as the third row, for fluids entering the chamber with opposite directions as Fig. 6(d) shows [comparing Fig. 6(c) and (d)], the rectangular bars at opposite corners enforce the inflow to circulate with different directions and form a single flow vortex of larger size in Fig. 6(c) and two flow vortices of smaller
Fig. 6. Comparisons of mixing performance for five mixing chamber designs by experimental visualization and numerical simulations. Column 1) photomasks of mixing chambers. Column 2) Mixing products in dark gray level. Column 3) Velocity vectors inside chamber. Fluid A in red, fluid_B in blue, and Reaction_Product_C in changed colors. Column 4) Concentration contours of mixing products in bright gray level (at z = 100 m plane from the channel bottom).
size in Fig. 6(d). Different flow patterns shown both by observations and simulations indicate different mixing efficiencies. As the lengths of the rectangular bars are increased [fifth row, Fig. 6(e)], a single and larger sized [but smaller than in Fig. 6(c)] flow vortex circulates in opposite direction from that in Fig. 6(c). Therefore, the design of mixer chamber with rectangular bars is selected as the base design [Fig. 5(c)] and the flow directions designated as Fig. 6(c) indicates are preferred. The design parameters will be discussed in the next sections. B. Characterization of the Flow Pattern During Mixing 1) Measured Flow Fields Inside Mixing Chamber: For the flow case in Fig. 5(c) with ratio of height to width of incoming channel as 0.125, the particle streak plots with embedded color time code are registered [shown in the left column of Fig. 7(a)] and the velocity vectors are obtained accordingly [shown in
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Fig. 7. (a) Particle streaks with embedded color time code. (b) Analyzed velocity vector (AR = 0:125).
the right column of Fig. 7(b)] by the analysis from the particle streaks at different time span, i.e., the particle streaks confined by red and black dots provide the information of the particle tracing history and give the velocity vectors. From the first row plot [Fig. 7(b)], Fluid_A and Fluid_B flow in opposing directions downwardly and upwardly aligned with 45 , and insignificant change is observed at time 0.048–0.060 s [second row of Fig. 7(b)]. However, the flow directions are significantly changed at time at 0.056–0.068 s and flow vortex is formed
[third row of Fig. 7(b)]. The strength of the vortex is much reduced at 0.072–0.084 s [fourth row of Fig. 7(b)] and eliminated further at 0.10 s. The flow process indicates the existence of 3-D flow structure in the mixing chamber and the vortices can contribute the mixing efficiency by 3-D structures with continuous and chaotic motion. Due to the limitation of the visualization experiments in 3-D transient flow, the CFD simulation provides the detail investigations of the 3-D flow structures and the related physics.
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Fig. 9. The mixing factor (E ) versus time by different grid systems: Grid1, Grid2, and Grid3 with node numbers of 18160, 27002, and 36 384.
Fig. 8. (a) The top view of the computational grid system for the H-shaped microchannel system. The green regions represent the occupancies of liquid fluids before entering the mixing chamber. The width (W ) of main channel is 500 m for the base case. (b) Total dimension (W ) of the mixing chamber is 250 m with entrance width (W ) of 80 m.
V. MIXING EFFECTIVENESS The mixing effectiveness are analyzed and characterized in terms of the detailed flow fields obtained by first principle simulations. Parameters as channel size, aspect ratio of the open channel, and the opening width of the mixing chamber are parameters changing flow pattern and enhancing mixing. In this paper, the configuration of the base design [Fig. 8(a) and (b)] is set with AR of 1 and opening ratio of 1/6. The AR and opening ratio of mixing chamber are defined as AR
(6) (7)
where and represent the width and depth of the main parand repallel incoming channels [Fig. 8(a) and (b)]. resent the width and entrance opening for the square mixing chamber [Fig. 8(b)]. The mixing factor is defined as percent of Reaction_Product_C occupied in the mixing chamber, i.e., (8) For this system, capillary force is the only driving force, which is closely correlated to the contact angle of solid/liquid/gas and the contact angle is chosen as 20 (measured by First Ten Angstroms 200, Cole-Parmer Instrument Co.). Three computational grids [Fig. 8(a)] are illustrated for the selected designs of the flow system in the computations. Total grid numbers for these grids are 18160, 27002, and 36 384. An increasing number of computational nodes leads to the proof of grid-independence and implies higher resolution and accuracy for validation of numerical results. Computed mixing factors in different grid systems agree with each other with difference
less than 5% (Fig. 9). The grid independence study confirms the computation reliability and indicates the efficient accuracy of numerical simulations using Grid_1 of 18 160 nodes. The process of flow pattern changes is illustrated in Fig. 10, which includes the 3-D flow-field with velocity vectors (in black color), the patterns of particle traces (band in gray color), and the concentration distributions of Reaction_Product_C (which is an indicator of mixing) for the base design of mixing and ) at three cutting-planes (i.e., chamber (AR m from the bottom of channel). Fluids_A and B are filled up from the bottom of the chamber in circulating patterns and the liquid level inside mixing chamber (shown in red color) is rolling up higher than the liquid level of incoming open channel flow, i.e., the liquid level in the mixing chamber climbs up faster than the liquid level in main channel. After the mixing chamber is filled up with the liquid mixtures and retains the same liquid levels of incoming and outgoing channels, mass contained inside the parallel channels will not be changed. From the velocity vector [Fig. 10(a)] and the particle trace [Fig. 10(b)], a clear picture of 3-D rolling-up vortex is observed. The transient process of the flow pattern indicates that two mixtures are in contact by unaccountable number of layers within a large circulating vortex, which is major mechanism promoting mixing dramatically. 1) Identifications of Design Parameters by Systematic Studies: In order to achieve most optimal design, the systematic studies of the design parameters as the size of parallel channel with respect to channel size, aspect ratio of the channel system, and opening size of the chamber entrance (i.e., the length of the intrusion bar) are performed. a) Aspect ratio of open channel: Different channel heights with the same width of the open microchannel represent different aspect ratios of the open channel. The liquid level (or liquid front) histories [Fig. 11(a)] at the center of mixing chamber for microchannels of different channel heights (aspect ratios) indicate the up and down or oscillatory fashion of liquid level when the aspect ratio is larger than or equal to one. The lift velocity of the liquid level is also higher for higher wall height (aspect ratio) of the open channel [Fig. 11(b)]. Similar
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Fig. 11. (a) Liquid level histories and (b) average lift velocity of liquid front for microchannels with different aspect ratios.
Fig. 10. Flowfields inside mixing chamber during mixing process. (a) Velocity vectors at different heights. (b) Particle traces and Reaction_Product_C concentrations. Left column figures show regions occupied by liquid (red); vectors (black) indicate velocity magnitudes and directions. Right column figures show the corresponding patterns of particle traces (gray) and Reaction_Product_C distribution at z -plane cut at 100, 250, and 400 m distance from the channel bottom at different time steps. Level of liquid inside 3 s (first row). The level is mixing chamber is shallow at t = 3:0096E raised with higher concentration of Reaction_Product_C at t = 3:4210E 3 s (second row), which implies higher degree of mixing and further increase of liquid level, Reaction_Product_C concentration, and rolling flow patterns are observed at t = 3:8379E 3 s (third row). In the right column, the color distribution from red to blue indicates the different degrees of mixing from high to low.
0
0
0
patterns of flow vectors with 3-D vortex structures inside the mixing chamber are observed in the plots of Fig. 12 for mixing chambers of different wall height (aspect ratio). Higher velocity magnitude of flow patterns and higher upward flowing flows are obtained for higher channel wall with higher aspect ratio. Vorticity contours representing the vortex structure at planes of 1/3 depth from the bottom are plotted in two dimensions. Comparisons of these colored vorticity contours indicate higher
Fig. 12. Vorticity strengths (1/s) (in colors) and flow vector (in black arrows) plots with different channel heights (AR = D=W ). (a) AR = 0:25, (b) AR = 0:5, (c) AR = 1, and (d) AR = 1:5.
strength of vorticity of the flow vortex for higher channel walls of higher aspect ratio.
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Fig. 13.
The mixing factor histories for different channel heights (aspect ratio).
Fig. 13 indicates that faster mixing rate can be achieved for higher AR and confirms that the channel wall height with higher aspect ratio is an important parameter for mixing chamber design, especially with aspect ratio larger than one. Furthermore, further increase of the aspect ratio from one does not significant increase the mixing rate and the effectiveness. It is also noted that a subpeak is observed at the early history and the peak is obvious for aspect ratio greater than one. Comparing the height of liquid front history in mixing chamber [Fig. 11(a)], it is found that the subpeak occurs at the same time as the liquid front arrives the highest level. With the oscillation process of liquid level, Reaction_Product_C as mixing indicator is moved out of the mixing chamber and flows along with the main channels. As the aspect ratio decreases (less than 0.5), the peaking or the oscillatory of liquid level is not observed with poor mixing efficiency. Fig. 14 shows good agreement of measured and computed histories of mixing reaction ratio [defined in (1)] for AR of 0.25 and confirms that the mixing rate increases as the aspect ratio increases. b) The entrance opening ratio of mixing chamber: The entrance opening width of mixing chamber restricts the entrance of the main channel flow into the mixing chamber and the mixing efficiency is thus affected. In this section, mixing performance is studied for various opening widths but the aspect ratio for channel wall height is set to one. Fig. 15 shows the flow characteristic in terms of velocity vector field and Reaction_Product_C distribution for different opening widths and m from at four different planes ( the channel bottom). For the shortest house bar with open ratio of 1/3, flow vectors inside the mixing chamber indicate a larger fraction of fluid directing to incoming/outgoing channels. The vortex structure is not complete and slightly opened at higher levels of the mixing chamber so that a larger fraction of mixture C is carried out of the mixing chamber [Fig. 15(a)]. As the opening is decreased and the incoming flow is restricted with
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Fig. 14. Comparisons of the measured and computed histories of mixing reaction ratio for different channel heights (aspect ratio).
opening ratio decreased to 1/6, the vortex structures formed are nearly complete at all levels and the incoming/outgoing flows are laminated. Therefore, most of the reaction products as mixture C can be trapped inside the chamber [Fig. 15(b)] with higher mixing performance. However, as the opening is further restricted to opening ratio of 1/12, the incoming flow becomes more laminate with smaller vortex structure although the vortex is still complete and closed. Therefore, the mixing zone becomes smaller with slightly slower mixing rate and lower mixing efficiency [Fig. 15(c)]. The mixing factor histories for different opening ratios (Fig. 16) show the increase of mixing effectiveness from opening ratio of 1/3 to 1/6 but the decrease of mixing form opening ratio of 1/6 to 1/12. The analyses indicate that the opening ratio is a parameter that needs to be taken into consideration. c) Size effect of mixing chamber: Size effect is usually an issue in microfluidic systems. Mixing characteristics with different sizes of the “house” mixing chambers are compared in this section. Sizes of chambers for comparison are 125 125 m (Case A), 250 250 m (Case B), and 500 500 m (Case C) with channel widths of 500 and 250 m and aspect ratio of one. For the cases of channel size of 250 m, better mixing performance for smaller size of the mixing chamber and poor mixing for chamber size larger than the channel width are observed (Fig. 17). It results from the best flow mechanism driving the microfluidic system, i.e., microchannel flows are induced by surface tension that is stronger for smaller size flow channels. For the case of channel size of 500 m with chamber size of 250 m, similar mixing factor is observed as compared to the case of channel size of 250 m with chamber size of 125 m. This observation implies that the same mixing effectiveness can be obtained for the same ratio of the size of channel width and chamber size and for the open channel systems in microscale.
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Fig. 15.
Concentration contours (in colors) of Reaction_Product_C for different opening ratios: (a) q = 1=3, (b) q = 1=6, and (c) q = 1=12.
Fig. 16.
Mixing factor histories for different chamber opening width.
Fig. 17.
The mixing factor versus different size of mixing chamber.
YANG et al.: RAPID MIXING MICROCHAMBER
VI. CONCLUSION This paper introduces a novel passive micromixer design for rapid mixing enhancement by forming a large 3-D flow vortex in a counterflow system. Compared to traditional micromixers operated by 2-D vortex, this passive mixer can greatly enhance mixing efficiency and reduce mixing time from around 10 s to less than 0.01 s by 3-D effective chaotic flow structures in 250 500 m mixing chamber. This a 250 mixing chamber is suitable for an H-shape digital fluidic system for parallel mixing process in different mixing ratio simultaneously as an LOC system. The mixer chamber design with embraced bars is proposed as the base design to enforce mixing due to the formation of a single vortex structure inside the mixing chamber for two parallel microchannel flows from opposite directions. The vortex structure implies the enormous increase of contacting layers of two fluids and thus the mixing is enhanced inside the same chamber with a very simple solid structure of mixing chamber. The mixing mechanism is characterized by numerical simulations using first principle equations, such as the formation process of the vortex with rolling up pattern and the quantification of mixing by the reaction products of two fluids from opposite directions. Flow-field measured by micro particle tracking velocitimetry confirms the formation of a 3-D flow vortex. Mixing experiments performed demonstrate and verify the design in terms of mixing effectiveness qualitatively and quantitatively. Good agreements in mixing_product_C between simulation and experiment are obtained for various chamber design, while very good agreements in mixing reaction ratio are obtained quantitatively for the special design with AR . The design parameters as microchannel wall height, micromixer size, and the opening size of mixer are identified and their effects are studied. The simulation results suggest the channel wall with aspect ratio greater than one, mixing chamber size less than microchannel size (1/2, for example), and relative small size of the opening of the mixing chamber (1/6 of the side of the mixing chamber) to achieve best mixing for this design.
REFERENCES [1] R. Miyake et al., “Micro mixer with fast diffusion,” in Proc. IEEE MEMS, 1993, pp. 248–253. [2] J. Branebjerg, P. Gravesen, J. P. Krog, and C. R. Nielsen, “Fast mixing by lamination,” in Proc. IEEE MEMS, 1996, pp. 441–446. [3] C.-F. Chen, S. C. Kuo, C. C. Chu, and F. G. Tseng, “A power free liquid driven method for micro mixing application,” Proceedings of IEEE MEMS, pp. 100–103, 2003. [4] 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. Microelectromech. Syst., vol. 9, pp. 190–197, 2000. [5] Y. Mizuno and M. Fynakoshi, “Chaotic mixing due to a spatially periodic three-dimensional flow,” Fluid Dyn. Res., vol. 31, pp. 129–149, 2002.
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[6] D. J. Beebe, R. J. Adrian, M. G. Olsen, M. A. Stremler, H. Aref, and B. H. Jo, “Passive mixing in microchannels: fabrication and flow experiments,” Mech. Ind., vol. 2, pp. 343–348, 2001. [7] A. D. Stroock, S. K. W. Dertinger, A. Ajdari, I. Mezic, H. A. Stone, and G. M. Whitesides, “Chaotic Mixer for Microchannels,” Science, vol. 295, pp. 647–651, 2002. [8] D. Gobby, P. Angeli, and A. Gavriilidis, “Mixing characteristic of T-type Microfluidic Mixers,” J. Micromech. Microeng., vol. 11, pp. 126–132, 2001. [9] F. G. Tseng et al., “A surface-tension-driven fluidic network for precise enzyme batch-dispensing and glucose detection,” Sens. Actuators A, vol. 111, no. 1, pp. 107–117, 2004. [10] I. D. Yang, Y. F. Chen, H. T. Hsu, F. G. Tseng, and C. C. Chieng, “Passive Mixing and the flow characteristic of a H-Type microchannel,” in Proc. 7th Int. Conf. Micro-TAS, vol. 2, 2003, pp. 1009–1012. [11] M. M. Lee, T. J. Hanratty, and R. J. Adrian, “An Axial Viewing Photographic Technique to Study Turbulence/characteristics of Particles,” J. Multiphase Flow, vol. 15, pp. 787–802, 1989. [12] C. D. Meinhart et al., “Volume illumination for two-dimensional particle image velocimetry,” Meas. Sci. Technol., vol. 11, pp. 809–814, 2000. [13] J. U. Brackbill, D. B. Kothe, and C. Zemach, “A continuum method for modeling surface tension,” J. Comp. Phys., vol. 100, pp. 335–354, 1992. [14] B. Kothe, W. J. Rider, S. J. Mosso, and J. S. Brock, “Volume tracking of ieterfaces having surface tension in two and three dimension,” in Proc. 34th Aerospace Science Meeting Exhib., 1996, AIAA-96-0859, pp. 1–24. [15] W. J. Rider and D. B. Kothe, “Streching and tearing interface tracing methods,” in Proc. 33rd Aerospace Science Meeting Exhib., 1995, AIAA-95-1717, pp. 1–11.
I-Da Yang was born in YunLin, Taiwan, R.O.C., in 1974. He received the B.S. degree from the Department of Naval Architecture and Marine Engineering, National Cheng Kung University, Taiwan, in 1996 and the M.S. degree from the Institute of Engineering Science, National Cheng Kung University, Taiwan, in 1999. He is currently pursuing the Ph.D. degree in the Department of Engineering and System Science, National Tsing Hua University, Taiwan. His doctoral work focuses on MEMS technology. His research interests are in the field of microfluidics, especially in microscale two-phase flow system and applications in bio- and optical MEMS. He also addresses his efforts to microscale flow visualization with high-speed photography, microparticle tracing velocimetry, and microparticle image velocimetry.
Yu-Feng Chen was born in Taichung, Taiwan, R.O.C., in 1972. She received the B.S. degree in nuclear engineering and the Ph.D. degree in power mechanical engineering from National Tsing Hua University, Taiwan, in 1994 and 2002, respectively, and the M.S. degree in aeronautics and astronautics engineering from National Cheng Kung University, Taiwan, in 1996. Her Ph.D. dissertation was to develop a numerical algorithm for solving the pressure for various flow configurations of incompressible viscous flows. She is interested in computational fluid dynamics, especially in microfluidics. She was a Postdoctoral Researcher in the Microfluidics Lab, Engineering and System Science Department, National Tsing Hua University. She is now a Senior Engineer in the R&D Division, CoreTech System Co., Ltd. Her major research field is development of the commercial code for the cooling system of microinjection molding.
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Fan-Gang Tseng (M’96) received the B.S. degree in power mechanical engineering from National Tsing Hua University (NTHU), Taiwan, R.O.C., in 1989, the M.S. degree from the Institute of Applied Mechanics, National Taiwan University, Taiwan, in 1991, and the Ph.D. degree in mechanical engineering from the University of California, Los Angeles, in 1998. After one year with the Information Science Institute, University of Southern California, as a Senior Engineer working on a new microfabrication process (EFAB), he became an Assistant Professor with the Engineering and System Science Department, National Tsing Hua University in 1999, and became an Associate Professor there in 2002. His research interests are in the fields of bio-MEMS and nano/microfluidic systems. He has received 14 patents and is the author of two book chapters. He has published more than 40 journal papers and 90 conference technical papers in MEMS, bio-N/MEMS, and micro/nano fluid-mechanics-related fields. Prof. Tseng has received several awards, including the Mr. Wu, Da-Yo Memorial Award from National Science Council, Taiwan (2005), three best paper/poster awards (1991, 2003, and 2004), NTHU New Faculty Research Award (2002), NTHU Outstanding Teaching Award (2002), NTHU Academic Booster Award (2001), and National Science Council Research Award (2000). He has cochaired many technical sessions, including IS M, Hong Kong, in 2000 and IEEE Transducers’01, Munich, Germany, in 2001.
Hui-Ting Hsu, photograph and biography not available at the time of publication.
Ching-Chang Chieng received the Ph.D. degree in aerospace and ocean engineering from Virginia Polytechnic Institute and State University, Blacksburg. She was with the Institute of Nuclear Energy Research, University of California at Davis; and Chung-Yuan Christian University. She has been a Professor in the Department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan, R.O.C., since 1981. She was with the U.S. Department of the Army and IBM Almaden Research Center during her sabbatical years 1987 and 1995, respectively. Her major research emphasis covered advanced nuclear reactor design and turbulence modeling for various applications in earlier years. She switched the focus to microscale heat transfer and fluid flow after her sabbatical year with IBM. She acts as a chief Principal Investigator (PI) of two integrated projects: multipurpose protein microarray chip development and application of MEMS in continuous monitoring of brain functions and as a PI for several independent projects including micro-fuel-cell system development. Her specialties include numerical scheme developments and applications for fluid flow simulations, from macro- and microscale to molecular levels. Prof. Chieng is an Associate Fellow of AIAA and a member of ASME.
