Mixing of Liquids Using Obstacles in Y-Type Microchannels

Transcription

1 Tamkang Journal of Science and Engineering, Vol. 13, No.?, pp. 0 0 (2010) 1 Mixing of Liquids Using Obstacles in Y-Type Microchannels C. T. Wang* and Z. Y. Hu Department of Mechanical and Electro-Mechanical Engineering, National I-Lan University, I-Lan, Taiwan 260, R.O.C. Abstract Mixing of binary or multi-component fluid streams is difficult in microchannels because they rely on diffusion during a limited mixing length. Therefore, obstacles applied and placed in the microchannel need to be used to try to disrupt the flow and reduce the diffusion path. In this study, finding a better layout for such obstacles embedded in Y-type microchannel is important to enhance flow mixing and will be executed at Reynolds numbers ranging from 0.5 to 60. These parameters of layout, such as number, horizontal spacing distance and angle of arrangement for cylinders embedded in the channel, as well as an inlet Reynolds number ratio, are worthy of study because they directly influence mixing and have rarely been previously addressed. The useful numerical results confirmed by our experiment will be addressed in this paper. Generally speaking, a larger number of cylinders, and a smaller horizontal spacing distance between them, normally correspond to a stronger flow mixing. In the case studied herein, five cylinders, arranged in a V with an angle of 90 at the base of the V, and the horizontal spacing distance between pairs of cylinders of 100 m, is a better choice for providing enhanced flow mixing. In addition, the Reynolds number ratio of ten is suggested because it induces a more intensive lateral convection and produces enhanced flow mixing. Placing obstacles or textures in the microchannel is a significant method for mixing in microfluidic devices because of its simple prototype and ease of fabrication, and the results could provide useful information for future optimal design of these devices. Key Words: Y-Type Microchannel, Obstacle, Flow Mixing, Optimal Design 1. Introduction *Corresponding author. ctwang@niu.edu.tw Micromixers are crucial in many bio-applications, such as the analysis and synthesis of RNA/DNA, and PCR amplification. Recently, the field of microfluidics has addressed physical phenomena of fluids and particle flows in microchannels at the micro scale. Bio-samples in a miniaturized device must be transmitted by passing through microchannels on a chip [1]. As a result, such a device is commonly called a microfluidic chip. The multi-functionality that is required for a complete analytical procedure will be integrated onto a single microfluidic chip, and called a Lab-on-a-Chip or a micro Total Analysis System [2 4]. MEMS technology is often utilized to fabricate microfluidic chips [5]. The microfluidic chip has many advantages over conventional biochemical methods of analysis because it can automate the process of analysis and reduce the consumption and contamination of bio-samples, as well as the analysis time [6]. Among the various functions, rapid mixing is crucial because biological analyses, such as enzyme reactions, protein folding and cell activation, depend on a rapid reaction process that can be controlled by the mixing of reactants. Unfortunately, flow mixing, which depends mainly on molecular diffusion, is a slow process and a long microchannel is needed for complete mixing

2 2 C. T. Wang and Z. Y. Hu because of its laminar flow. Many micromixers have been developed to enhance and control mixing. The two broad categories of micromixers are passive and active. An active mixer depends on external energy to perturb the flow. Active mixers generally mix better than passive mixers, but they require complicated fabrication procedures and sophisticated operating process [7]. An active micromixer uses oscillation of a flow-driving source, such as by a pressure field [8,9] or an electric field [10,11], acoustic wave generation [12 14] or magnetic field variation [15]. Some passive micromixers have special geometries that include grooves, rivets, obstacles, textures or posts that are embedded in microchannels, to increase vorticity and cause a chaotic advection in mixing [16 23]. Another passive mixer is the lamination mixer, which reduces the diffusion length and increases the contact area of fluids by splitting incoming flow and laminating it into a stream [24 28]. Passive mixers are often adapted to apply in the development of integrated microfluidic chips because of their simplicity and ease of fabrication. A model that was developed by Maeng et al., predicts mixing in microchannels in terms of a vortex index [29]. The vortex index was defined for 2-D planar mixers and the concept must be modified to predict 3D mixing performance under various inlet flow conditions. Despite numerous studies of passive micromixers, the finding of a better layout, such as number, distance and arrangement of obstacles, specifies any associated property or quantity of the number of cylinders embedded in the channel. And the inlet Reynolds number ratio was seldom addressed but is worthy of study because it directly influences mixing. In this work, a simple and short Y-type microchannel, shown in Figure 1, will be applied at flow conditions ranging from Re = 0.5 to Re = 60 to bring up an improved arrangement of obstacles. and the results are presented. To improve mixing, obstacles have been placed in the channel to try to disrupt flow and reduce the lamella width. In this study, pure water at room temperature is used as the flow. The equations that govern the mixing process are obtained by solving the continuity, momentum and diffusion equations: (1) (2) (3) where Re is the Reynolds number and defined as RE = VD 0 h ; Sc is the Schmidt number, and Sc. D h is D ij A the Hydraulic diameter and Dh 4, V is the velocity P vector; t is time; p denotes pressure; C i represents mole concentration, V 0 is the characteristic velocity, is the fluid viscosity, is the density of fluid and D ij is the mass diffusivity. 2. Numerical Method In general, the Reynolds number is low in microfluidic channels. This means that the viscous force plays a dominant role. As a result, the flow is most likely to be laminar under normal conditions, especially for liquids. Therefore, diffusion, rather than turbulence, affects the mixing. In this work, the commercial computational fluid dynamics tool for microfluidics, known as CFD-ACE+, is used to study the mixing of two liquids in a Y channel Figure 1. Prototype of passive micromixer with one cylinder embedded in Y-type microchannel. X denotes the distance of the center of the cylinder to the point of intersection between the two middle lines of the inlet channel. D is the diameter of the cylinder and is set to 30 m. The width of the two inlet channels is set to 200 m and the width of outlet channel is 300 m. The total length of the channel from the intersection point of the two inlet sidewalls to the outlet is 1000 m.

3 Mixing of Liquids Using Obstacles in Y-Type Microchannels 3 The mixing performance is numerically simulated using a commercial package, CFD-ACE+ software. A multi-physics package based on the Finite-Volume method will be executed. The program was run on a 2.4 Ghz Pentium IV processor with 1 GB of RAM memory. Mesh-independent tests have been performed before the studies. The numerical results will satisfy the grid independent required by using CFD-ACE+. An upwind method for solver and a multi-block unstructured grid with 20,000 to 30,000 cells were used as the computational domain inside the micromixer. The convergent condition was assumed to be for the numerical simulations. On the boundary condition of the simulation process, a constant inlet velocity calculated from a given Reynolds number, whose values are from 0.5 to 60, will be used for steady analysis. In this study, a simple Y-type microchannel with embedded cylinders, as shown in Figure 1, is used as a prototype passive micromixer because it has the advantages of not damaging a bio-cell in the transmission and eases fabrication. The width of two inlet channels selected as 200 m and 300 m used for the outlet width of the channel will be applied to investigate mixing related to embedded obstacles. Here, we shall note that although increasing the mixing length will increase the mixing performance, the total length of the microchannel selected was 1000 m, which is less than that of other known passive micromixers because the mixing length is not the main object of this work. In addition, obstacles were placed in the microchannel to disrupt flow and increase mixing. The importance of the optimal design of a passive micromixer has seldom been addressed, and optimal parameters such as the number, distance between, and arrangement of cylinders embedded in the channel, as well as the inlet Reynolds number ratio are worthy of study because they directly affect mixing. In this work, a shear stress flow was produced from cylinders in a Y-type microchannel at Reynolds numbers ranging from 0.5 to 60. The disruption of the flow velocity field changes the flow direction from one fluid to another. In this way, convection may occur and result in enhanced mixing. A mixing index mixing is employed to optimize the layout. It is defined as follows: (4) where X Amax is the maximum mole fraction of fluid A and the value is unity. X Ax, outlet is the mole fraction of fluid A at the outlet location and L denotes the outlet width of the channel. As mixing approaches 1, the mixing efficiency increases. Here, some cases of experimental verification will be made by way of disposable apparatus for the numerical results in this study. The experimental framework is shown in Figure 2. The constant flow velocity of the inlet channel ranging from Re = 1 to 60 was be pushed by an injector (KDS 220). The dye flow visualization was made and a gray-scale was used and applied for the quantitative mixing coefficient of the outlet channel. These experimental data are added in the section on results and discussion. Figure 2. Experimental framework.

4 4 C. T. Wang and Z. Y. Hu 3. Results and Discussion I. Location of One Cylinder versus Flow Mixing The nature of microfluidics limits its ability to generate sufficient mixing which is critical in the development of microfluidic devices. This study uses various geometric parameters to enhance mixing on a microscopic scale, and is compatible with normal micromachining technology. Therefore, the role of obstacles, cylinders used in this study, applied to the flow mixing would first need to be clarified before a next series of studies. Here, flow mixing in cases of one obstacle placed at different locations in a Y-type microchannel, as displayed in Figure 1 with Reynolds numbers from 0.5 to 60, are investigated and compared with cases without obstacles. Figure 3 plots the mixing efficiency and pressure drop at various distances from a cylinder with a diameter of 30 m, embedded in the channel at X/D = 0, 1, 2 to the intersection point of two center lines of inlet channel. Comparing the results of Figure 3 under these flow conditions indicates that an embedded cylinder will be promoted with about 20% of mixing in relation to the case of that without a cylinder, despite the associated increase in the pressure drop. This evidence reveals that the flow convection would be enhanced by the shear stress flow that is induced by an embedded cylinder. Therefore the flow mixing would be enhanced. In addition, Figure 3 indicates that the mixing efficiency at a further location of the cylinder will be smaller during the same Reynolds number flow, i.e., the mixing efficiency at X/D = 2 is smaller than that at X/D = 1. This reason could be the result of an inadequate mixing length between the cylinder and outlet of the microchannel. Similar results X/D = 0 and X/D = 2 shown in Figure 3 have been obtained by experiments at Re = 1, 10 and 60. The symbol of X and + indicated in Figure 3 refers to experimental mixing data. The flow mixing executed by the experiment seems to be a little larger than that of the simulation because the inevitable appearance of channel roughness and a longer length of inlet channel will result in a higher flow mixing performance. These verifications show a similar tendency between the experiment and simulation. Generally speaking, concerning the mixing performance and pressure drop effect that occur simultaneously under the condition of the placing of a micro cylinder, the lower Reynolds number and shorter location of the obstacle seem to be suitable and possess a greater mixing performance. Figure 3. Mixing efficiency and pressure drop versus Reynolds number for X/D = 0, 1 and 2 for one cylinder and 2D original case (without cylinder). The symbol of X and + indicated means an experimental data.

5 Mixing of Liquids Using Obstacles in Y-Type Microchannels 5 II. Variations of Angle at Base of V Arrangement versus Flow Mixing When two or more obstacles are placed in a microchannel, the angle of arrangement of cylinders as obstacles in the microchannel needs to be studied. In this investigation, three angles, 45, 60 and 90 are taken, and are used in the V arrangement of the three cylinders at flow Reynolds ranging from 1 to 60, as displayed in Figure 4. The results shown in Figure 5 reveal that changing the angle of the V of the cylinders would be useful in flow mixing because the interaction between the flow and the cylinder would be strengthened. This would produce a positive result for a flow mixing reaction by changing the angle of the V of cylinders. The flow mixing in the case of the angle of the V in the cylinders set at 90 and confirmed by experiment, (the symbols of X and +, are indicated in Figure 5), is larger than others in previously studied cases. In addition, the flow images shown in Figure 6 are taken at Reynolds number Re = 10 and indicate that there is a more significant interaction between the inlet flow and cylinders in the case of the 90 degrees than those of 45 and 60 de- Figure 4. Angles of V arrangement are set to 45,60 and 90 for three cylinders. Horizontal distance between the cylinders is 100 m.the scale unit of this framework and Figure 1 are the same. Figure 6. Flow images taken at Re = 10 versus the angle of the V arrangement with 45 and 90 for three cylinders respectively. Figure 5. Mixing efficiency and pressure drop against angle of V arrangement for three cylinders at different Reynolds numbers.

6 6 C. T. Wang and Z. Y. Hu grees for the V arrangement. Therefore, a much better flow mixing produced in the case of the 90 degrees experiment was expected. From another perspective, changing the angle of obstacles for the V arrangement at a fixed flow Reynolds seems to have only a small effect on the pressure drop. This is because the drag would be connected mainly with the wake region of the cylinders, but increasing the Reynolds number will increase the pressure drop. However, the flow for three cylinders at 90 in the V arrangement yields a better choice for providing a satisfactory arrangement of obstacles. Previous simulation results could be confirmed by experimental flow images because in Figure 6 one can see clearly that there is a more significant interaction between the inlet flows and cylinders, red markings in the circle, under the case of the 90 degrees experiment compared to that of the 45 and 60 degrees for the V arrangement of the cylinders. Therefore, an enhanced mixing produced in the case of the 90 degrees example was to be expected. In addition, the Reynolds number has different effects on mixing according to the angle, but the flow is optimal at approximately Re = 10. III. Horizontal Spacing Distance between Cylinders versus Flow Mixing In this study, five cylinders embedded and the horizontal spacing distance, indicated as S, between them varied from S = 100 m to 200 m, would be investigated at different Reynolds numbers to realize their effect on flow mixing. Figure 7 shows that they were arranged in a V at an angle of 45 because of the constraints of the channel width and the number of cylinders. Figure 8 shows that changing the horizontal spacing distance between the cylinders does not affect the pressure drop because it mainly would be result in the Figure 7. Various horizontal distances for five cylinders in V arrangement with angle of 45. The scale unit of this framework and Figure 1 are the same. Unit of S: m. Figure 8. Mixing efficiency and pressure drop against horizontal distance for five cylinders in V arrangement with 45 angle at various Reynolds numbers.

7 Mixing of Liquids Using Obstacles in Y-Type Microchannels 7 wake region of the cylinders, despite the fact that the latter increases with the differing Reynolds numbers. On the other hand, increasing the Reynolds number reduces the flow mixing ability because the flow convection effect is decreased. The flow imagines in Figure 9 refer to this, in which the standard deviation of the gray-scale, SD, is clarified clearly. Therefore, a horizontal spacing distance between the cylinders of 100 m yields a more thorough mixing for studied cases and could be seen as a better choice to assist in future designs. IV. Effect of Inlet Reynolds Ratio We knew that mixing by diffusion alone was a slow process and a low flow rate was necessary to enable sufficient mixing [30]. In this study, the mixing would still be improved, even at a high Reynolds number, because of the effect of lateral convection. Concerning a significant relationship between lateral convection and shear stress flow, a shear stress flow produced by cylinders, embedded in a Y-type microchannel, was verified to promote mixing. Accordingly, shear stress flows are generated by producing various inlet flows at the inlet of the channel and a series of layouts are examined. To simplify the analysis, one of inlet flows is set as Re = 0.5 and taken as a basis for studying the effect of a Reynolds ratio whose values are set as 1, 10 and 100 for another inlet flow. Figure 10 plots the inlet Reynolds ratio versus mixing efficiency at X/D = 0, 1 and 2 for one cylinder embedded in the microchannel. The result indicates that the inlet Reynolds ratio affects mixing for different X/D s. The flow at an inlet Reynolds ratio of 10 is suggested to cause significant mixing. On other hand, the angle of the V for three cylinders embedded in a microchannel is examined at different inlet Reynolds ratios. Figure 11 demonstrates that a Reynolds ratio of 10 is preferred. A V with five cylinders, embedded in the microchannel and with a base angle of 45, was selected to determine the effect of an inlet Reynolds ratio on the horizontal distance between the cylinders. Figure 12 shows that the shear stress is largest and will occur at an inlet Reynolds ratio of 10, maximizing mixing. According to the results of Figures 10, 11 and 12, the Reynold s ratio of 10 gives a greater mixing performance than that at the ratio of Re 1 and 100, regardless of the layout of the obstacles, because a higher flow mixing results from the appearance of larger shear stress and a more intensive lateral convection at an inlet flow with a Reynolds ratio of 10. More efforts are indeed needed for further clarification in the future. However, these results, as they stand, can provide useful information for the future optimal design of this device. 4. Conclusion In this work, the effects of such parameters as cylinder number, horizontal spacing distance, and angles of the V arrangement between cylinders and the inlet Reynolds number ratio on flow mixing, were investigated. These were all experimented at a flow Reynolds number that ranged from Re = 0.5 to Re = 60 because this has rarely been addressed previously but is of importance in the enhancement of flow mixing. Some useful simulation results confirmed by the experiments are addressed as follows: Figure 9. Flow images were taken at horizontal spacing distance S = 100 m and Re = 10, 60. SD: standard deviation of gray-scale.

8 8 C. T. Wang and Z. Y. Hu Figure 10. Variations of inlet Reynolds number ratio and mixing efficiency at X/D = 0, 1 and 2 for one cylinder embedded in a microchannel. First, the shear stress flow induced by cylinders and different two-inlet flows would enhance the lateral convection and be further helpful to flow mixing. Second, the angle of the V arrangement of the cylinders in the microchannel of 90, and a horizontal spacing distance between the cylinders of 100 m, confirmed that this should be a substantially better choice for increasing the flow mixing. In addition, an inlet Reynolds ratio of around ten was suggested and confirmed to provide a superior flow mixing, regardless of the layout of the obstacles. Finally, an inlet Reynolds number of less than 10 was considered with higher mixing relative to a low pressure drop. These findings would be found to be useful for providing future optimal designs of the device. Acknowledgments The authors would like to acknowledge the kind funding support from NSC Taiwan under the contract #NSC E References Figure 11. Variations of inlet Reynolds number ratio and mixing efficiency at different angles of V for three cylinders embedded in microchannel. Figure 12. Variations of inlet Reynolds number ratio and mixing efficiency for various horizontal distances between cylinders. [1] Yahng, J.-S., Jeoung, S.-C., Choi, D.-S., Cho, D., Kim, J.-H., Choi, H.-M. and Park, J.-S., Fabrication of Microfluidic Devices by Using a Femtosecond Laser Micromachining Technique and -PIV Studies on Its Fluid Dynamics, J Korean Phys Soc., Vol. 47, pp (2005). [2] Auroux, P.-A., Iossifidis, D., Reyes, D.-R. and Manz, A., Micro Total Analysis Systems. 2. Analytical Standard Operations and Applications, Anal Chem., Vol. 74, pp (2002). [3] Reyes, D.-R., Iossifidis, D., Auroux, P.-A. and Manz, A., Micro Total Analysis Systems. 1. Introduction, Theory, and Technology, Anal Chem., Vol. 74, pp (2002). [4] Vilkner, T., Janasek, D. and Manz, A., Micro Total Analysis Systems. Recent Developments, Anal Chem., Vol. 76, pp (2004). [5] Cha, N.-G., Park, C.-H., Lim, H.-W. and Lim, J.-G., J. Korean Phys. Soc., Vol. 47, S530 (2005). [6] Jakeway, S.-C., de Mello, A.-J. and Russell, E.-L., Miniaturized Total Analysis Systems for Biological Analysis, Fresenius J. Anal. Chem., Vol. 366, pp (2000). [7] Nguyen, N.-T. and Wu, Z. J., Micromixers ARe-

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