被动式微流体混合器的通道拓扑优化
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摘要
微流体混合器是微流控芯片的重要组成部分,其作用是实现生物试样与试剂的快速混合,可用于化学分析、基因分析和蛋白质分析,对于实现快速和高效的检测分析具有十分重要的意义。被动式微混合器在微流控系统中有着广泛的应用,但其设计方法大多仍采用经验与试凑法。基于拓扑优化的系统性设计方法在2008年由Andreasen等人首次提出。本文在Andreasen等人工作的基础上,进一步讨论了设计区域和制造约束对混合效率的影响,提出了高设计深度、大间距的新型被动式混合单元构型。本文基于连续形式的不可压缩Navier-Stokes流体的控制方程以及对流扩散方程,给出了进行混合分析的有限元离散形式以及数值解法。针对微混合器设计问题给出了优化模型,以GLS稳定方法对目标函数进行了有限元离散,并以Petrov- Galerkin/Compensated稳定方法分析了伴随敏度。采正六面体网格,在Re=10情况下,以进出口的压力差作为约束条件,给出了3D模型下直通道混合器的优化算例,得到了收敛性比较好的优化结果,相比于直通道混合效率最大提高了3倍。针对不同的压差系数β和制造约束条件,分析了约束条件对优化结果的影响。最后,设计了微混合器的混合实验,结果显示,优化结构的混合效果与实验结果较吻合。
Micromixer, which achieves the efficient mixing of reagents, is an important functional part of the microfluidic chips. In the area of biologic reaction, such as chemical analysis, genic analysis and albuminoid analysis, micromixer can help to perform a fast and efficient biologic reaction. However, the design of micro-mixer was mainly based on test-and-error method. A systematical design procedure was first proposed by Andresen et al. in 2008 based on topology optimization method. In this thesis, the effect of design domain and manufacturing constraint which influence the efficiency of mixing is discussed based on work by Andresen et al. A micro-mixer with deep design domain and long space between two block units is proposed. Based on the continuous impressible Navier-Stokes equation and the convection-diffusion equation, the finite element method is used to simulate the mixing problem. For the design of the micromixer, the optimization model is constructed, and the optimization model is analyzed by the GLS and Petrov-Galerkin/Compensated stabilized method. By the adjoint analysis method, the adjoint sensitivity of the optimization model is obtained. The cubic mesh (3D) are used for the discritization of the problem. When the pressure drop between the inlet and outlet of the fluidic channel is set as constraint in the optimization model, the optimized results can at most improve the effect of mixing about three times when compared with a empty pipe with the same length of micro channel. For different values ofβand manufacturing constraint, the influence of the constraint on the results are analyzed. At last, the experiments of the mixing is designed, and the mixing effect for the design micromixer has been verified by experiments.
Micromixer, which achieves the efficient mixing of reagents, is an important functional part of the microfluidic chips. In the area of biologic reaction, such as chemical analysis, genic analysis and albuminoid analysis, micromixer can help to perform a fast and efficient biologic reaction. However, the design of micro-mixer was mainly based on test-and-error method. A systematical design procedure was first proposed by Andresen et al. in 2008 based on topology optimization method. In this thesis, the effect of design domain and manufacturing constraint which influence the efficiency of mixing is discussed based on work by Andresen et al. A micro-mixer with deep design domain and long space between two block units is proposed. Based on the continuous impressible Navier-Stokes equation and the convection-diffusion equation, the finite element method is used to simulate the mixing problem. For the design of the micromixer, the optimization model is constructed, and the optimization model is analyzed by the GLS and Petrov-Galerkin/Compensated stabilized method. By the adjoint analysis method, the adjoint sensitivity of the optimization model is obtained. The cubic mesh (3D) are used for the discritization of the problem. When the pressure drop between the inlet and outlet of the fluidic channel is set as constraint in the optimization model, the optimized results can at most improve the effect of mixing about three times when compared with a empty pipe with the same length of micro channel. For different values ofβand manufacturing constraint, the influence of the constraint on the results are analyzed. At last, the experiments of the mixing is designed, and the mixing effect for the design micromixer has been verified by experiments.
引文
[1] Harrison D J, Fluri K, Seiler K. Fan Z et al. Micromachining a Miniaturized Capillary Electrophoresis-Based Chemical Analysis System on a Chip[J]. Science 1993; 261, 895-897.
[2]林炳承,秦建华.图解微流控芯片实验室[M].北京:科学出版社,2008. 12-14.
[3] McDonald J C, Duffy D C, Anderson J R et al. Fabrication of microfluidic systems in poly(dimethylsiloxane)[J]. Electrophoresis 2000; 21, 27-40.
[4] Thorsen T, Maerkl S J, Quake S R. Microfluidic Large-Scale Integration[J]. Science 2002; 298, 580-584.
[5] Whitesides G M. The origins and the future of microfluidics[J]. Nature 2006; 442, 368-373.
[6] Janasek D, Franzke J, Manz A. Scaling and the design of miniaturized chemical-analysis systems[J]. Nature 2006; 442, 374-380.
[7] Psaltis D, Quake S R, Yang C. Developing optofluidic technology through the fusion of microfluidics and optics[J]. Nature 2006; 442, 381-386.
[8] Craighead H. Future lab-on-a-chip technologies for interrogating individual molecules[J]. Nature 2006; 442, 387-393.
[9] Mello A J. Control and detection of chemical reactions in microfluidic systems[J]. Nature 2006; 442, 394-402.
[10] EI-Ali J, Sorger P K, Jensen K F. Cells on chips[J]. Nature 2006; 442, 403-411.
[11] Yager P, Edwards T, Fu E et al. Microfluidic diagnostic technologies for global public health[J]. Nature 2006; 442, 412-418.
[12]林炳承,秦建华.图解微流控芯片实验室[M].北京:科学出版社,2008. 147-158.
[13] Bessoth F G, de Mello A J, Manz A. Microstructure for efficient continuous flow mixing[J]. Alalytical Communication, 1999, 36(6):213-215.
[14] Jensen K. Chemical kinetics-Smaller, faster chemistry[J]. Nature, 1998,393(6687): 735-737.
[15] Buchegger W, Wagner C, Lendl B et al. A highly uniform lamination micromixer with wedge shaped inlet channels for time resolved infrared spectroscopy[J]. Microfluid Nanofluid 2011; 10, 889-897.
[16] Gray B L et al. Novel interconnection technologies for integrated microfluidic systems[J]. Sensors Actuators A 1999; 77, 57–65.
[17] Munson M S, Yager P. Simple quantitative optical method for monitoring the extent of mixing applied to a novel microfluidic mixer[J]. Anal. Chim. Acta 2004; 507 63–71.
[18] Lim T W, Son Y, Jeong Y J et al. Three-dimensionally crossing manifold micro-mixer for fast mixing in a short channel length[J]. Lab on a Chip 2011; 11,100.
[19] Lin Y, Gerfen G J, Rousseau D L et al. Ultrafast microfluidic mixer and freeze-quenching device[J]. Analytical Chemistry, 2002,74(16): 4279-4286.
[20] [20] Mengeaud V, Josserand J, Girault H H. Mixing processes in a zigzag microchannel: Finite element simulations and optical study[J]. Analycal Chemistry, 2002, 74(16): 4279-4286.
[21] Sudarsan A P, Ugaz V M. Multivortex micromixing[J]. PNAS http://www.pnas.org/cgi 2006; 103(19), 7228-7233.
[22] Hong C C, Choi J W, Ahh C H. A novel in-plane passive microfluidic mixer with modified Tesla structures[J]. Lab on a Chip, 2004; 4(2): 109-113.
[23] Liu R H, Sremler M A, Sharp K V et al. Passive mixing in a three-dimensional serpentine microchannel[J]. Journal of Microelectro- mechanical Systems, 2000; 9(2): 190-197.
[24] Kang T G, Singh M K, Anderson P D et al. A chaotic serpentine mixer efficient in the creeping flow regime: from design concept to optimization[J]. Microfluidic Nanofluidic 2009; 7, 783-794.
[25] Bokenkamp D, Desai A, Yang X et al. Microfabricated silicon mixers for submillisecond quench-flow analysis[J]. Analytical Chemistry,1998;70(2): 232-236.
[26] Stroock A D, Dertinger S K W, Ajdari A et al. Chaotic mixer for microchannels[J]. Science, 2002; 295(5555): 647-651.
[27] Tofteberg T, Skolimowski M, Andreassen E et al. A novel passive micromixer: lamination in a planar channel system[J]. Microfluid Nanofluid 2010; 8, 209-215.
[28] He B, Burke B J, Zhang X et al. A picoliter-volume mixer for microfluidic analytical systems[J]. Analytical Chemistry, 2001; 73(9): 1942-1947.
[29] Ryu K S, Shaikh K, Goluch E et al. Micro magnetic stir-bar mixer integrated with parylene microfluidic channels[J]. Lab on a Chip, 2004; 4(6): 680-613.
[30] Liu R H, Yang J N, Pindera M Z et al. Bubble-induced acoustic micromixing[J]. Lab on a Chip, 2002; 2(3): 151-157.
[31] Yang Z, Goto H, Matsumoto M et al. Active micromixer for microfluidic systems using lead-zicronate-titanate(PZT)-generated ultrasonic vibration[J]. Electrophoresis, 2000; 21(1): 116- 119.
[32] Lin C H, Fu L M, Chien Y S. Microfluidic T-form mixer utilizing switching electroosmotic flow[J]. Analytical Chemistry, 2004; 76(18): 5265-5272.
[33]张兆顺,崔桂香.流体力学[M].北京:清华大学出版社,1998.46-81.
[34]景思睿,张鸣远.流体力学[M].西安:西安交通大学出版社,2001.55-83.
[35]朱自强,吴子牛,李建.应用计算流体力学[M].北京:北京航空航天大学出版社,1998.8
[36] Golub G H. Greegbaum A. Stuart A M. Finite Elements and Fast Iterative Solvers[M].Oxford University press. 2005.
[37] Bends?e M P, Sigmund O. Topology Optimization—Theory, Methods and Applications[M]. Springer.2003.
[38] Bends?e M P, Kikuchi N. Generating topologies in structural design using a homogenization method[J]. Computer Methods in Applied Mechanics and Engineering 1988; 71:197–224.
[39] Borrvall T, Petersson J. Topology optimization of fluids in Stokes flow[J]. International Journal for Numerical Methods in Fluids 2003; 41(1):77–107.
[40] Gersborg-Hansen A, Sigmund O, Haber R. Topology optimization of channel flow problems[J]. Structural and Multidisciplinary Optimization 2005; 30:181–192.
[41] Olesen LH, Okkels F, Bruus H. A high-level programming language implementation of topology optimization applied to steady-state Navier–Stokes flow[J]. International Journal for Numerical Methods in Engineering 2006; 65(7):975–1001.
[42] Nocedal J, Wright S J, Numerical Optimization[M], Springer. 1999.
[43] Okkels F, Bruus H. Scaling behavior of optimally structured catalytic microfluidic reactors[J]. Physical Review E 2007; 75(1):016301.
[44] Evgrafov A. The limits of porous materials in the topology optimization of Stokes flows[J]. Applied Mathematics and Optimization 2005; 52(3):263–277.
[45] Andreasen C S, Gersborg A R, Sigmund O. Topology optimization of microfluidic mixers[J]. International Journal for Numerical Method in Fluids. 2009; 61:198-513.
[46] Svanberg K. The method of moving asymptotes—a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering. 1987; 24:359–373.
[47] Hughes TJR, Franca LP. A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: symmetric formulations that converge for all velocity/pressure spaces[J]. Computer Methods in Applied Mechanics and Engineering 1987; 65(1):85–96.
[48] Donea J, Hureta A. Finite Element Methods for Flow Problems[M]. Wiley: West Sussex, 2003.
[49] Brooks A N, Hughes T J. Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32(1–3):199–259. DOI: 10.1016/0045-7825(82)90071-8.
[50] Codina R. Comparison of some finite element methods for solving the diffusion–convection– reaction equation[J]. Computer Methods in Applied Mechanics and Engineering 1998; 156:185–210.
[51]林炳承,秦建华.图解微流控芯片实验室[M].科学出版社,2008,32-35.
[52]张平,胡亮红,刘永顺.主辅通道型微混合器的设计与制作.光学精密工程, 2010; 18(4), 872-879.
[2]林炳承,秦建华.图解微流控芯片实验室[M].北京:科学出版社,2008. 12-14.
[3] McDonald J C, Duffy D C, Anderson J R et al. Fabrication of microfluidic systems in poly(dimethylsiloxane)[J]. Electrophoresis 2000; 21, 27-40.
[4] Thorsen T, Maerkl S J, Quake S R. Microfluidic Large-Scale Integration[J]. Science 2002; 298, 580-584.
[5] Whitesides G M. The origins and the future of microfluidics[J]. Nature 2006; 442, 368-373.
[6] Janasek D, Franzke J, Manz A. Scaling and the design of miniaturized chemical-analysis systems[J]. Nature 2006; 442, 374-380.
[7] Psaltis D, Quake S R, Yang C. Developing optofluidic technology through the fusion of microfluidics and optics[J]. Nature 2006; 442, 381-386.
[8] Craighead H. Future lab-on-a-chip technologies for interrogating individual molecules[J]. Nature 2006; 442, 387-393.
[9] Mello A J. Control and detection of chemical reactions in microfluidic systems[J]. Nature 2006; 442, 394-402.
[10] EI-Ali J, Sorger P K, Jensen K F. Cells on chips[J]. Nature 2006; 442, 403-411.
[11] Yager P, Edwards T, Fu E et al. Microfluidic diagnostic technologies for global public health[J]. Nature 2006; 442, 412-418.
[12]林炳承,秦建华.图解微流控芯片实验室[M].北京:科学出版社,2008. 147-158.
[13] Bessoth F G, de Mello A J, Manz A. Microstructure for efficient continuous flow mixing[J]. Alalytical Communication, 1999, 36(6):213-215.
[14] Jensen K. Chemical kinetics-Smaller, faster chemistry[J]. Nature, 1998,393(6687): 735-737.
[15] Buchegger W, Wagner C, Lendl B et al. A highly uniform lamination micromixer with wedge shaped inlet channels for time resolved infrared spectroscopy[J]. Microfluid Nanofluid 2011; 10, 889-897.
[16] Gray B L et al. Novel interconnection technologies for integrated microfluidic systems[J]. Sensors Actuators A 1999; 77, 57–65.
[17] Munson M S, Yager P. Simple quantitative optical method for monitoring the extent of mixing applied to a novel microfluidic mixer[J]. Anal. Chim. Acta 2004; 507 63–71.
[18] Lim T W, Son Y, Jeong Y J et al. Three-dimensionally crossing manifold micro-mixer for fast mixing in a short channel length[J]. Lab on a Chip 2011; 11,100.
[19] Lin Y, Gerfen G J, Rousseau D L et al. Ultrafast microfluidic mixer and freeze-quenching device[J]. Analytical Chemistry, 2002,74(16): 4279-4286.
[20] [20] Mengeaud V, Josserand J, Girault H H. Mixing processes in a zigzag microchannel: Finite element simulations and optical study[J]. Analycal Chemistry, 2002, 74(16): 4279-4286.
[21] Sudarsan A P, Ugaz V M. Multivortex micromixing[J]. PNAS http://www.pnas.org/cgi 2006; 103(19), 7228-7233.
[22] Hong C C, Choi J W, Ahh C H. A novel in-plane passive microfluidic mixer with modified Tesla structures[J]. Lab on a Chip, 2004; 4(2): 109-113.
[23] Liu R H, Sremler M A, Sharp K V et al. Passive mixing in a three-dimensional serpentine microchannel[J]. Journal of Microelectro- mechanical Systems, 2000; 9(2): 190-197.
[24] Kang T G, Singh M K, Anderson P D et al. A chaotic serpentine mixer efficient in the creeping flow regime: from design concept to optimization[J]. Microfluidic Nanofluidic 2009; 7, 783-794.
[25] Bokenkamp D, Desai A, Yang X et al. Microfabricated silicon mixers for submillisecond quench-flow analysis[J]. Analytical Chemistry,1998;70(2): 232-236.
[26] Stroock A D, Dertinger S K W, Ajdari A et al. Chaotic mixer for microchannels[J]. Science, 2002; 295(5555): 647-651.
[27] Tofteberg T, Skolimowski M, Andreassen E et al. A novel passive micromixer: lamination in a planar channel system[J]. Microfluid Nanofluid 2010; 8, 209-215.
[28] He B, Burke B J, Zhang X et al. A picoliter-volume mixer for microfluidic analytical systems[J]. Analytical Chemistry, 2001; 73(9): 1942-1947.
[29] Ryu K S, Shaikh K, Goluch E et al. Micro magnetic stir-bar mixer integrated with parylene microfluidic channels[J]. Lab on a Chip, 2004; 4(6): 680-613.
[30] Liu R H, Yang J N, Pindera M Z et al. Bubble-induced acoustic micromixing[J]. Lab on a Chip, 2002; 2(3): 151-157.
[31] Yang Z, Goto H, Matsumoto M et al. Active micromixer for microfluidic systems using lead-zicronate-titanate(PZT)-generated ultrasonic vibration[J]. Electrophoresis, 2000; 21(1): 116- 119.
[32] Lin C H, Fu L M, Chien Y S. Microfluidic T-form mixer utilizing switching electroosmotic flow[J]. Analytical Chemistry, 2004; 76(18): 5265-5272.
[33]张兆顺,崔桂香.流体力学[M].北京:清华大学出版社,1998.46-81.
[34]景思睿,张鸣远.流体力学[M].西安:西安交通大学出版社,2001.55-83.
[35]朱自强,吴子牛,李建.应用计算流体力学[M].北京:北京航空航天大学出版社,1998.8
[36] Golub G H. Greegbaum A. Stuart A M. Finite Elements and Fast Iterative Solvers[M].Oxford University press. 2005.
[37] Bends?e M P, Sigmund O. Topology Optimization—Theory, Methods and Applications[M]. Springer.2003.
[38] Bends?e M P, Kikuchi N. Generating topologies in structural design using a homogenization method[J]. Computer Methods in Applied Mechanics and Engineering 1988; 71:197–224.
[39] Borrvall T, Petersson J. Topology optimization of fluids in Stokes flow[J]. International Journal for Numerical Methods in Fluids 2003; 41(1):77–107.
[40] Gersborg-Hansen A, Sigmund O, Haber R. Topology optimization of channel flow problems[J]. Structural and Multidisciplinary Optimization 2005; 30:181–192.
[41] Olesen LH, Okkels F, Bruus H. A high-level programming language implementation of topology optimization applied to steady-state Navier–Stokes flow[J]. International Journal for Numerical Methods in Engineering 2006; 65(7):975–1001.
[42] Nocedal J, Wright S J, Numerical Optimization[M], Springer. 1999.
[43] Okkels F, Bruus H. Scaling behavior of optimally structured catalytic microfluidic reactors[J]. Physical Review E 2007; 75(1):016301.
[44] Evgrafov A. The limits of porous materials in the topology optimization of Stokes flows[J]. Applied Mathematics and Optimization 2005; 52(3):263–277.
[45] Andreasen C S, Gersborg A R, Sigmund O. Topology optimization of microfluidic mixers[J]. International Journal for Numerical Method in Fluids. 2009; 61:198-513.
[46] Svanberg K. The method of moving asymptotes—a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering. 1987; 24:359–373.
[47] Hughes TJR, Franca LP. A new finite element formulation for computational fluid dynamics: VII. The Stokes problem with various well-posed boundary conditions: symmetric formulations that converge for all velocity/pressure spaces[J]. Computer Methods in Applied Mechanics and Engineering 1987; 65(1):85–96.
[48] Donea J, Hureta A. Finite Element Methods for Flow Problems[M]. Wiley: West Sussex, 2003.
[49] Brooks A N, Hughes T J. Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982; 32(1–3):199–259. DOI: 10.1016/0045-7825(82)90071-8.
[50] Codina R. Comparison of some finite element methods for solving the diffusion–convection– reaction equation[J]. Computer Methods in Applied Mechanics and Engineering 1998; 156:185–210.
[51]林炳承,秦建华.图解微流控芯片实验室[M].科学出版社,2008,32-35.
[52]张平,胡亮红,刘永顺.主辅通道型微混合器的设计与制作.光学精密工程, 2010; 18(4), 872-879.