C.S. Andreasen, A.R. Gersborg, O. Sigmund, Topology optimization of microfluidic mixers. Int. J. Numer. Methods Fluids 61, 498–513 (2009)
MathSciNet
Article
Google Scholar
M.A. Ansari, K.Y. Kim, Shape optimization of a micromixer with staggered herringbone groove. Chem. Eng. Sci. 62, 6687–6695 (2007)
Article
Google Scholar
M.A. Ansari, K.Y. Kim, Evaluation of surrogate models for optimization of herringbone groove micromixer. J. Mech. Sci. Technol. 22, 387–396 (2008)
Article
Google Scholar
T. Borrvall, J. Petersson, Topology optimization of fluid in Stokes flow. Int. J. Numer. Methods Fluids 41, 77–107 (2003)
MathSciNet
MATH
Article
Google Scholar
R.H. Byrd, P. Lu, J. Nocedal, A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Statist. Comput. 16, 1190–1208 (1995)
MathSciNet
MATH
Article
Google Scholar
R. Choudhary, T. Bhakat, R.K. Singh, A. Ghubade, S. Mandal, A. Ghosh, A. Rammohan, A. Sharma, S. Bhattacharya, Bilayer staggered herringbone micro-mixers with symmetric and asymmetric geometries. Microfluid Nanofluid 10, 271–286 (2011)
Article
Google Scholar
C.K. Chung, T.R. Shih, Effect of geometry on fluid mixing of the rhombic micromixers. Microfluid Nanofluid 4, 419–425 (2008)
Article
Google Scholar
C.K. Chung, T.R. Shih, T.C. Chen, B.H. Wu, Mixing behavior of the rhombic micromixers over a wide Reynolds number range using Taguchi method and 3D numerical simulations. Biomed. Microdevices 10, 739–748 (2008)
Article
Google Scholar
C.A. Cortes-Quiroza, M. Zangeneh, A. Goto, On multi-objective optimization of geometry of staggered herringbone micromixer. Microfluid Nanofluid 7, 29–43 (2009)
Article
Google Scholar
C.A. Cortes-Quiroza, A. Azarbadegana, M. Zangeneha, A. Goto, Analysis and multi-criteria design optimization of geometric characteristics of grooved micromixer. Chem. Eng. J. 160, 852–864 (2010)
Article
Google Scholar
P. Danckwerts, The difinition and measurement of some characteristics of mixtures. Appl. Sci. Res. A3, 279–296 (1952)
Google Scholar
Y. Deng, Z. Liu, P. Zhang, Y. Wu, J.G. Korvink, in Optimization of No-Moving Part Fluidic Resistance Microvalves with Low Reynolds Number. Proceedings IEEE International Conference on Micro Electro MechanicalSystems (MEMS) (2010), pp. 67–70
Y. Deng, Y. Wu, M. Xuan, J.G. Korvink, Z. Liu, in Dynamic Optimization of Valveless Micropump. Proceedings IEEE International Conference on Solid-State Sensors, Actuators, and Microsystems (Transducers) (2011), pp. 442–445
J. Donea, A. Hureta, Finite Element Methods for Flow Problems (Wiley, West Sussex, 2003)
Book
Google Scholar
Y. Du, Z. Zhang, C.H. Yim, M. Lin, X. Cao, A simplified design of the staggered herringbone micromixer for practical applications. Biomicrofluidics 4, 024105 (2010)
Article
Google Scholar
A. Gersborg-Hansen, O. Sigmund, R.B. Haber, Topology optimization of channel flow problems. Struct. Multidisc. Optim. 29, 1–12 (2005)
MathSciNet
Article
Google Scholar
I. Glasgow, N. Aubry, Enhancement of microfluidic mixing using time pulsing. Lab Chip. 3, 114–120 (2003)
Article
Google Scholar
M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich, Optimization with PDE constraints (Springer, 2009)
S. Hossain, A. Husain, K.Y. Kim, Shape optimization of a micromixer with staggered-herringbone grooves patterned on opposite walls. Chem. Eng. J. 162, 730–737 (2010)
Article
Google Scholar
P.B. Howell, Jr., D.R. Mott, F.S. Ligler, J.P. Golden, C.R. Kaplan, E.S. Oran, A combinatorial approach to microfluidic mixing. J. Micromechanics Microengineering 18, 115019, 7 pp (2008)
Google Scholar
M.Z. Huang, R.J. Yang, C.H. Tai, C.H. Tsai, L.M. Fu, Application of electrokinetic instability flow for enhanced micromixing in cross-shaped microchannel. Biomed. Microdevices 8, 309–315 (2006)
Article
Google Scholar
A. Jameson, in Optimum Aerodynamic Design Using Control Theory. CFD Review (Wiley, 1995)
G.S. Jeong, S. Chung, C.B. Kim, S.H. Lee, Applications of micromixing technology. Analyst 135, 460–473 (2010)
Article
Google Scholar
T.G. Kang, M.K. Singh, T.H. Kwon, P.D. Anderson, Chaotic mixing using periodic and aperiodic sequences of mixing protocols in a micromixer. Microfluid Nanofluid 4, 589–599 (2008)
Article
Google Scholar
T.G. Kang, M.K. Singh, P.D. Anderson, H.E.H. Meijer, A chaotic serpentine mixer efficient in the creeping flow regime: from design concept to optimization. Microfluid Nanofluid 7, 783–794 (2009)
Article
Google Scholar
G. Karniadakis, A. Beskok, N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation (Springer, 2005)
S.P. Kee, A. Gavriilidis, Design and characterisation of the staggered herringbone mixer. Chem. Eng. J. 142, 109–121 (2008)
Article
Google Scholar
D.H. Kelley, N.T. Ouellette, Separating stretching from folding in fluid mixing. Nat. Phys. 7, 477–480 (2011)
Article
Google Scholar
H.Y. Lee, J. Voldman, Optimizing micromixer design for enhancing dielectrophoretic microconcentrator performance. Anal. Chem. 79, 1833–1839 (2007)
Article
Google Scholar
C.Y. Lee, C.L. Chang, Y.N. Wang, L.M. Fu, Microfluidic mixing: a review. Int. J. Mol. Sci. 12, 3263–3287 (2011)
Article
Google Scholar
D. Li, Encyclopedia of Microfluidics and Nanofluidics (Springer, 2007)
C.H. Lin, L.M. Fu, Y.S. Chien, Microfluidic T-form mixer utilizing switching electroosmotic flow. Anal. Chem. 76, 5265–5276 (2004)
Article
Google Scholar
C.H. Lin, C.H. Tsai, C.W. Pan, L.M. Fu, Rapid circular microfluidic mixer utilizing unbalanced driving force. Biomed. Microdevices 9, 43–50 (2007)
Article
Google Scholar
R.H. Liu, M.A. Stremler, K.V. Sharp, M.G. Olsen, J.G. Santiago, R.J. Adrian, H. Aref, D.J. Beebe, Passive mixing in a three-dimensional serpentine microchannel. J. Microelectromechanical Syst. 9, 190–197 (2000)
Article
Google Scholar
Y.Z. Liu, B.J. Kim, H.J. Sung, Two-fluid mixing in a microchannel. Int. J. Heat Fluid Flow 25, 986–995 (2004)
Article
Google Scholar
Z. Liu, Y. Deng, S. Lin, M. Xuan, Optimization of micro Venturi diode in steady flow at low Reynolds number. Eng. Optim. (2012). doi:10.1080/0305215X.2011.652100
Google Scholar
N.S. Lynn, D.S. Dandy, Geometrical optimization of helical flow in grooved micromixers. Lab Chip 7, 580–587 (2007)
Article
Google Scholar
K. Malecha, L.J. Golonka, J. Baldyga, M. Jasińska, P. Sobieszuk, Serpentine microfluidic mixer made in LTCC. Sens. Actuators B 143, 400–413 (2009)
Article
Google Scholar
D.R. Mott, P.B. Howell, Jr., J.P. Golden, C.R. Kaplan, F.S. Ligler, E.S. Oran, Toolbox for the design of optimized microfluidic components. Lab Chip 6, 540–549 (2006)
Article
Google Scholar
D.R. Mott, P.B. Howell, Jr., K.S. Obenschain, E.S. Oran, The numerical toolbox: an approach for modeling and optimizing microfluidic components. Mech. Res. Commun. 36, 104–109 (2009)
MathSciNet
Article
Google Scholar
P.E. Neerincx, R.P.J. Denteneer, S. Peelen, H.E.H. Meijer, Compact mixing using multiple splitting, stretching, and recombining flows. Macromol. Mater. Eng. 296, 349–361 (2011)
Article
Google Scholar
W.Y. Ng, S. Goh, Y.C. Lam, C. Yang, I. Rodriguez, DC-biased AC-electroosmotic and AC-electrothermal flow mixing in microchannels. Lab Chip 9, 802–809 (2009)
Article
Google Scholar
N.T. Nguyen, Micromixer: Fundamentals, Design and Fabrication (William Andrew, 2008)
N.T. Nguyen, Z. Wu, Micromixers—a review. J. Micromechanics Microengineering 15, 1–16 (2005)
Article
Google Scholar
J. Nocedal, S.J. Wright, Numerical Optimization (Springer, 1998)
F. Okkels, H. Bruus, in Design of Micro-Fluidic Bio-Reactors Using Topology Optimization. ECCOMAS CFD (2006)
L.H. Olesen, F. Okkels, H. Bruus, A high-level programming-language implementation of topology optimization applied to steady-state Navier–Stokes flow. Int. J. Numer. Methods Eng. 65, 975–1001 (2006)
MathSciNet
MATH
Article
Google Scholar
J.M. Park, T.H. Kwon, Numerical characterization of three-dimensional serpentine micromixers. AIChE J. 54, 1999–2008 (2008)
Article
Google Scholar
J.M. Park, D.S. Kim, T.G. Kang, T.H. Kwon, Improved serpentine laminating micromixer with enhanced local advection. Microfluid Nanofluid 4, 513–523 (2008)
Article
Google Scholar
E. Schall, Y.L. Guer, S. Gibout, in An Anisotropic Unstructured Meshes Mapping Method (AUM3) to Optimize Mixing in Laminar Periodic Flows. Proceedings of PSFVIP-4, Chamonix, France, 3–5 June 2003
O. Sigmund, Morphology-based black and white filters for topology optimization. Struct. Multidisc. Optim. 33, 401–424 (2007)
Article
Google Scholar
M.K. Singh, T.G. Kang, H.E.H. Meijer, P.D. Anderson, The mapping method as a toolbox to analyze, design, and optimize micromixers. Microfluid Nanofluid 5, 313–325 (2008)
Article
Google Scholar
M.K. Singh, T.G. Kang, P.D. Anderson, H.E.H. Meijer, A.N. Hrymak, Analysis and optimization of low-pressure drop static mixers. AIChE J. 55, 2208–2216 (2009)
Article
Google Scholar
H. Song, X.Z. Yin, D.J. Bennett, Optimization analysis of the staggered herringbone micromixer based on the slip-driven method. Chem. Eng. Res. Des. 86, 883–891 (2008)
Article
Google Scholar
H. Song, Z. Cai, H. Noh, D. Bennett, Lab Chip 10, 734–740 (2010)
Article
Google Scholar
A.D. Stroock, S.K.W. Dertinger, A. Ajdari, I. Mezić, H.A. Stone, G.M. Whitesides, Chaotic mixer for microchannels. Science 295, 647 (2002)
Article
Google Scholar
A.P. Sudarsan, V.M. Ugaz, Multivortex micromixing. PNAS 103, 7228–7233 (2006)
Article
Google Scholar
M.S. Williams, K.J. Longmuirb, P. Yager, A practical guide to the staggered herringbone mixer. Lab Chip 8, 1121–1129 (2008)
Article
Google Scholar
C.H. Wu, R.J. Yang, Improving the mixing performance of side channel type micromixers using an optimal voltage control model. Biomed. Microdevices 8, 119–131 (2006)
Article
Google Scholar
Z. Xu, C. Li, D. Vadilloc, X. Ruanb, X. Fu, Numerical simulation on fluid mixing by effects of geometry in staggered oriented ridges micromixers. Sens. Actuators B, Chem. 153, 284–292 (2011)
Article
Google Scholar
C. Zhu, R.H. Byrd, J. Nocedal, L-BFGS-B: algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization. ACM Trans. Math. Softw. 23, 550–560 (1997)
MathSciNet
MATH
Article
Google Scholar