摘要

本研究探討具有對齊入口流道與分合流道模組的微混合器，將比較三種模組，分別為三維彎曲不對齊匯流流道模組、平面彎曲不對齊匯流流道模組及平面彎曲對齊匯流流道模組。由於網格法在高培克萊特數下會產生數值擴散問題而高估混合度，因此本研究以反向粒子追跡結合近似擴散模式及蒙地卡羅法模擬，並以前者之模擬結果分析不同雷諾數下流體的流動與混合情形。為了驗證數值模擬，使用微影技術製作微混合器，並利用共軛焦顯微鏡觀察流體的混合結果。研究結果顯示，在較低雷諾數下流體的混合以擴散為主，若以圓弧轉彎的方式分割流體可將流體保持其進入模組子流道之前的濃度分佈形態，經過平面彎曲對齊匯流流道模組的對齊接頭匯流後兩不同流體會以相間的方式匯合，使其接觸面積大幅增加，而促進混合。在較高雷諾數下流體經過蜿蜒流道將產生離心力，引起狄恩渦流，這些渦流使流體交界面產生拉伸折疊效應，而提升混合效率。若匯流處再以不對齊接頭進行匯流，流體注入主流道將產生一渦流，此渦流對流體的混合幫助很大。在雷諾數100時，使用4組三維彎曲不對齊匯流流道模組，壓降可在合理範圍內，且流道出口的混合度大於0.9。

關鍵字：流體混合，引發渦流，分合流道模組，粒子反向追跡，蒙地卡羅法

SUMMARY
This study explores micromixers with aligned inlet channels and split-and-recombination mixing modules. We compare the mixing performance of three modules, including three-dimensional curved unaligned recombination channel module (3DCURCM), planar curved unaligned recombination channel module (PCURCM) and planar curved aligned recombination channel module (PCARCM) by using a grid method, the particle-tracking simulation with approximate diffusion model (ADM) and the Monte Carlo simulation. Because of balance between precision and efficiency, we mainly use the particle-tracking simulation with ADM to analyze the flow and mixing of fluids at different Reynolds numbers. To verify numerical simulation, we used lithography to make a micromixer and use confocal microscopy to acquire the image for the mixing and flow in the micromixer. The simulation results show that the mixing of fluids at the lower Reynolds number is dominated by diffusion. If the fluid is divided by circular turn, the fluid can maintain its concentration distribution before entering the sub-channel of the module. After flowing through a PCARCM, the two different fluids will merge in phase, which greatly increases the contact area and promotes mixing. At higher Reynolds numbers, the fluid will generate centrifugal force and Dean vortex through curved channel, which improves mixing efficiency. If the confluence is achieved by an unaligned joint, the fluid will create a vortex in the main mixing channel, which will improve the mixing of the fluid. When the Reynolds number is 100, using four 3DCURCM’s, the pressure drop can be within a reasonable range and the mixing degree of the flow at outlet is greater than 0.9.

Key words: mixing, induced eddy, split-and-recombination modules, particle tracking, Monte Carlo simulation

參考文獻
[1] A. Manz, N. Graber, and H. M. Widmer, “Miniaturized total chemical analysis systems: a novel concept for chemical sensing,” Sensors and Actuators B: Chemical, vol. 1, no. 1-6, pp. 244-248, 1990.
[2] N.-T. Nguyen and Z. Wu, “Micromixers - a review,” Journal of Micromechanics and Microengineering, vol. 15, no. 2, R1-R16, 2005.
[3] C.-Y. Lee, W.-T. Wang, C.-C. Liu, and L.-M. Fu, “Passive mixers in microfluidic systems: A review,” Chemical Engineering Journal, vol. 288, pp. 146-160, 2016.
[4] N. Kockmann, C. Föll, and P. Woias, “Flow regimes and mass transfer characteristics in static micro mixers,” Proceedings of International Society for Optics and Photonics, vol. 4982, pp. 319-330, 2003.
[5] D. Bothe, C. Stemich, and H.-J. Warnecke, “Fluid mixing in a T-shaped micro-mixer,” Chemical Engineering Science, vol. 61, no. 9, pp. 2950-2958, 2006.
[6] M. A. Ansari, K.-Y. Kim, K. Anwar, and S. M. Kim, “Vortex micro T-mixer with non-aligned inputs,” Chemical Engineering Journal, vol. 181-182, pp. 846- 850, no. 2, 2012.
[7] C. A. Cortes-Quiroz, A. Azarbadegan, and M. Zangeneh, “Effect of channel aspect ratio of 3-D T-mixer on flow patterns and convective mixing for a wide range of Reynolds number,” Sensors and Actuators B: Chemical, vol. 239, no. 2, pp. 1153-1176, 2017.
[8] W. R. Dean, “Note on the motion of a fluid in a curved pipe,” Philosophical Magazine, vol. 4, no. 20, pp. 208-223, 1927.
[9] F. Jiang, K. S. Drese, S. Hardt, M. Küpper, and F. Schöfeld, “Helical flows and chaotic mixing in curved micro channel,” AIChE Journal, vol. 50, no. 9, pp. 2297-2305, 2004.
[10] N. Kockmann, M. Engler, D. Haller, and P. Woias, “Fluid dynamics and transfer processes in bended microchannels,” Heat Transfer Engineering, vol. 26, no. 3, pp. 71-78, 2005.
[11] C. Nonino, S. Savino, and S. D. Giudice, “Numerical assessment of the mixing performance of different serpentine microchannels,” Heat Transfer Engineering, vol. 30, no. 1-2, pp. 101-112, 2009.
[12] C.-Y. Wu, and R.-T. Tsai, “Fluid mixing via multidirectional vortices in converging–diverging meandering microchannels with semi-elliptical side walls,” Chemical Engineering Journal, vol. 217, pp. 320-328, 2013.
[13] F. Garofalo, A. Adrover, S. Cerbelli, and M. Giona, “Spectral Characterization of Static Mixers. The S-Shaped Micromixer as a Case Study.” AIChE Journal, vol. 56, no.2, pp. 318-335,2010.
[14] W. Ruijin, L. Beiqi, S. Dongdong, and Z. Zefei “Investigation on the splitting-merging passive micromixer based on Baker's transformation,” Sensors and Actuators B: Chemical, vol. 249, pp. 395-404, 2017.
[15] T. Matsunaga, H. J. Lee, and K. Nishino, “An approach for accurate simulation of liquid mixing in a T-shape micromixer,” Lab on a Chip, vol. 13, no. 8, pp. 1515-1521, 2013.
[16] V. Özceyhan, M. Sen, “Particle-tracking random-walk computation of high-Peclet-number convection,” Numerical Heat Transfer, Part A: Applications, vol. 50, no. 7, pp. 607-622, 2006.
[17] Z.-W. Liu, “Micromixer with non-aligned inlets and split-and-recombination module junctions,” Master's Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, 2018.
[18] C. Galletti, M. Roudgar, E. Brunazzi, and R. Mauri, “Effect of inlet conditions on the engulfment pattern in a T-shaped micro-mixer,” Chemical Engineering
Science, vol. 185-186, no. 3, pp. 300-313, 2012.
[19] T. Matsunaga, K. Shibata, K. Murotani, and S. Koshizuka, “Hybrid grid-particle method for fluid mixing simulation,” Computational Particle Mechanics, vol. 2, no. 3, pp. 233-246, 2015.
[20] S.-C. Lin, “Numerical simulation of fluid mixing in micromixers with quasi-omega-shaped modules based on zigzag channels,” Master's Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, 2018.
[21] H. Bockhorn, D. Mewes, W. Peukert, and H. J. Warnecke, Micro and Macro Mixing, Berlin, Germany: Springer, 2010.
[22] C. Nonino, S. Savino, and S. D. Giudice, “Numerical assessment of the mixing performance of different serpentine microchannels,” Heat Transfer Engineering, vol. 30, no. 1-2, pp. 101-112, 2009.
[23] A. Nealen, “An as-short-as-possible introduction to the least squares, weighted least squares and moving least squares methods for scattered data approximation and interpolation,” Technische Universität Darmstadt, Tech. Rep., 2004, URL:http://www.nealen.com/projects.
[24] J. L. Bentley, “Multidimensional binary search trees used for associative Searching,” Communications of the Association for Computing Machinery, vol. 18, no. 9, pp. 509-517, 1975.
[25] S. Arya, D. M. Mount, N. S. Netanyahu, R. Silverman, and A. Y. Wu, “An optimal algorithm for approximate nearest neighbor searching in fixed dimensions,” Journal of the Association for Computing Machinery, vol. 45, no. 6, pp. 891-923, 1998.
[26] T. Most and C. Bucher, “A moving least squares weighting function for the element-free Galerkin method which almost fulfills essential boundary conditions,” Structural Engineering and Mechanics, vol. 21, no. 3, pp. 315-332, 2005.
[27] Y.-C. Chien, “Micromixers with double T-junction and split-and-and recombine sub-channels,” Master's Thesis, Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, 2016.
[28] T. Most and C. Bucher, “A moving least squares weighting function for the element-free Galerkin method which almost fulfills essential boundary conditions,” Structural Engineering and Mechanics, vol. 21, no. 3, pp. 315-332, 2005.
[29] Z. Wu, N.-T. Nguyen, and X. Huang, “Nonlinear diffusive mixing in microchannels: theory and experiments,” Journal of Micromechanics and Microengineering, vol. 14, no. 4, pp. 604-611, 2004.