Topology optimization of microfluidic mixers

International Journal for Numerical Methods in Fluids

Volumn 61, Issue 5, 2009, Pages 498-513

  Andreasen, Casper Schousboe ^a   Gersborg, Allan Roulund ^a   Sigmund, Ole ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Convection dominated transport; Finite element methods; Incompressible flow; Laminar flow; Micro fluids; Microfluidic mixing; Navier Stokes; Optimization; Porous media; Sensitivity analysis; Stabilized FEM; Topology optimization; Transport

Indexed keywords

CONVECTION DOMINATED TRANSPORT; CONVECTION-DOMINATED; MICROFLUIDIC MIXING; NAVIER STOKES; POROUS MEDIA; STABILIZED FEM; TOPOLOGY OPTIMIZATION;

FINITE ELEMENT METHOD; FLUIDIC DEVICES; INCOMPRESSIBLE FLOW; INLET FLOW; LAMINAR FLOW; MICROFLUIDICS; MIXERS (MACHINERY); MIXING; NAVIER STOKES EQUATIONS; PIPE; POROUS MATERIALS; PRESSURE DROP; REYNOLDS NUMBER; SENSITIVITY ANALYSIS; STRUCTURAL OPTIMIZATION; TOPOLOGY;

TRANSPORT PROPERTIES;

EID: 75649121815     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1964     Document Type: Article

References (38)

1. Ottino JM, Wiggins S. Introduction: mixing in microfluidics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2004; 362(1818):923-935. DOI: 10.1098/rsta.2003.1355.
2. Stroock AD, Dertinger SKW, Ajdari A, Mezic I, Stone HA, Whitesides GM. Chaotic mixer for microchannels. Science 2002; 295(5555):647-651. DOI: 10.1126/science.1066238.
3. Bendsøe MP, Kikuchi N. Generating topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering 1988; 71:197-224. DOI: 10.1016/0045-7825(88)90086-2.
4. Bendsøe MP, Sigmund O. Topology Optimization-Theory, Methods and Applications (2nd edn). Springer: Berlin, 2003.
5. Pironneau O. On optimum profiles in Stokes flow. Journal of Fluid Mechanics 1973; 59:117-128.
6. Borrvall T, Petersson J. Topology optimization of fluids in Stokes flow. International Journal for Numerical Methods in Fluids 2003; 41(1):77-107. DOI: 10.1002/fld.426.
7. Evgrafov A. The limits of porous materials in the topology optimization of Stokes flows. Applied Mathematics and Optimization 2005; 52(3):263-277. DOI: 10.1007/s00245-005-0828-z.
8. Guest JK, Prévost JH. Topology optimization of creeping fluid flows using a Darcy-Stokes finite element. International Journal for Numerical Methods in Engineering 2006; 66(3):461-484. DOI: 10.1002/nme.1560.
9. Wiker N, Klarbring A, Borrvall T. Topology optimization of regions of Darcy and Stokes flow. International Journal for Numerical Methods in Engineering 2007; 69(7):1374-1380. DOI: 10.1002/nme.1811.
10. Gersborg-Hansen A, Sigmund O, Haber R. Topology optimization of channel flow problems. Structural and Multidisciplinary Optimization 2005; 30:181-192. DOI: 10.1007/s00158-004-0508-7.
11. Olesen LH, Okkels F, Bruus H. A high-level programming language implementation of topology optimization applied to steady-state Navier-Stokes flow. International Journal for Numerical Methods in Engineering 2006; 65(7):975-1001. DOI: 10.1002/nme.1468.
12. Evgrafov A. Topology optimization of slightly compressible fluids. ZAMM 2006; 86(1):46-62. DOI: 10.1002/ zamm.200410223.
13. Thellner M. Multi-parameter topology optimization in continuum mechanics. Ph.D. Thesis, Department of Mechanical Engineering, Linköping University, 2005. ISBN-10 91-8529-71-2.
14. Gersborg-Hansen A. Topology optimization of flow problems. Ph.D. Thesis, Department of Mathematics and Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, DCAMM Special Report S96, 2007. ISBN-10 87-90416-23-6.
15. Okkels F, Bruus H. Scaling behavior of optimally structured catalytic microfluidic reactors. Physical Review E 2007; 75(1):016301. DOI: 10.1103/PhysRevE.75.016301.
16. Pingen G, Evgrafov A, Maute K. Topology optimization of flow domains using the lattice Boltzmann method. Structural and Multidisciplinary Optimization 2007; 34(6):507-524. DOI: 10.1007/s00158-007-0105-7.
17. Evgrafov A, Pingen G, Maute K. Topology optimization of fluid domains: kinetic theory approach. ZAMM 2008; 88(2):129-141. DOI: 10.1002/zamm.200700122.
18. Aage N, Poulsen TH, Gersborg-Hansen A, Sigmund O. Topology optimization of large scale Stokes flow problems. Structural and Multidisciplinary Optimization 2008; 35:175-180. DOI: 10.1007/s00158-007-0128-0.
19. Guest JK, Prévost JH. Optimizing multifunctional materials: design of microstructures for maximized stiffness and fluid permeability. International Journal of Solids and Structures 2006; 43:7028-7047. DOI: 10.1016/j.ijsolstr.2006.03.001.
20. Othmer C. A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows. International Journal for Numerical Methods in Fluids 2008; Published on-line. DOI: 10.1002/fld.1770.
21. Brooks AN, Hughes TJR. 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.
22. 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. Computer Methods in Applied Mechanics and Engineering 1987; 65(1):85-96. DOI: 10.1016/0045-7825(87)90184-8.
23. Zienkiewicz OC, Taylor RL. The Finite Element Method-Volume 3: Fluid Dynamics. Butterworth Heinemann: London, 2000.
24. Donea J, Hureta A. Finite Element Methods for Flow Problems. Wiley: West Sussex, 2003.
25. Tezduyar TE, Ramakrishnan S, Sathe S. International Journal for Numerical Methods in Fluids 2008; Published on-line. DOI: 10.1002/fld.1743.
26. Masud A, Hughes TJR. A stabilized mixed finite element method for Darcy Flow. Computer Methods in Applied Mechanics and Engineering 2002; 191:4341-4370. DOI: 10.1016/S0045-7825(02)00371-7.
27. Codina R. Comparison of some finite element methods for solving the diffusion-convection-reaction equation. Computer Methods in Applied Mechanics and Engineering 1998; 156:185-210. DOI: 10.1016/S0045- 7825(97)00206-5.
28. Svanberg K. The method of moving asymptotes-a new method for structural optimization. International Journal for Numerical Methods in Engineering 1987; 24:359-373. DOI: 10.1002/nme.1620240207.
29. Vidal CA, Lee HS, Haber RB. The consistent tangent operator for design sensitivity analysis of history-dependent response. Computing Systems Engineering 1991; 2:509-523.
30. Michaleris P, Tortorelli DA, Vidal CA. Tangent operators and design sensitivity formulations for transient non- linear coupled problems with applications to elastoplasticity. International Journal for Numerical Methods in Engineering 1994; 37(14):2471-2499. DOI: 10.1002/nme.1620371408.
31. Choi K, Kim NH. Structural Sensitivity Analysis and Optimization. vols 1 and 2. Springer: Berlin, 2005. ISBN 03872-3336-9.
32. Sigmund O, Petersson J. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural Optimization 1998; 16(1):68-75. DOI: 10.1007/BF01214002.
33. Bruns TE, Tortorelli DA. Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics and Engineering 2001; 190(26-17):3443-3459. DOI: 10.1016/S0045- 7825(00)00278-4.
34. Bourdin B. Filters in topology optimization. International Journal for Numerical Methods in Engineering 2001; 50:2143-2158. DOI: 10.1002/nme.116.
35. Sigmund O. Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 2007; 33:401-424. DOI: 10.1007/s00158-006-0087-x.
36. Liu RH, Stremler MA, Sharp KV, Olsen MG, Santiago JG, Adrian RJ, Aref H, Beebe DJ. Passive mixing in a three-dimensional serpentine microchannel. Journal of Microelectromechanical Systems 2000; 9:190-197. DOI: 10.1109/84.846699.
37. Yang JT, Huang K, Tung KY, Hu IC, Lyu PC. A chaotic micromixer modulated by constructive vortex agitation. Journal of Micromechanics and Microengineering 2007; 17:2084-2092. DOI: 10.1088/0960-1317/17/10/021.
38. Li C, Chen T. Simulation and optimization of chaotic micromixer using lattice Boltzmann method. Sensors and Actuators B 2005; 106(2):871-877. DOI: 10.1016/j.snb.2004.09.006.