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29. Yang JT, Huang KJ, Lin YC (2005) Geometric effects on fluid mixing in passive grooved
micromixers. Lab Chip 5:1140–1147. https://doi.org/10.1039/B500972C
30. Hassell DG, Zimmerman WB (2006) Investigation of the convective motion through a staggered
herringbone micromixer at low Reynolds number flow. Chem Eng Sci 61:2977–2985. https://
doi.org/10.1016/j.ces.2005.10.068
31. Wang L, Yang JT (2006) An overlapping crisscross micromixer using chaotic mixing principles.
J Micromech Microeng 16:2684. https://doi.org/10.1088/0960-1317/16/12/022
32. Wang L, Yang JT, Lyu PC (2007) An overlapping crisscross micromixer. Chem Eng Sci 62:711–
720. https://doi.org/10.1016/j.ces.2006.09.048
33. Dean WR (1927) Note on the motion of fluid in a curved pipe. Philos Mag 4:208–223. https://
doi.org/10.1080/14786440708564324
34. Dean WR (1928) The stream-line motion of fluid in a curved pipe. Philos Mag 5:673–695.
https://doi.org/10.1080/14786440408564513
35. Vanka SP, Luo G, Winkler CM (2004) Numerical study of scalar mixing in curved channels at
low Reynolds number. AIChE J 50:2359–2368. https://doi.org/10.1002/aic.10196
36. Howell PB Jr, Mott DR, Golden JP, Ligler FS (2004) Design and Evaluation of a Dean VortexBased Micromixer. Lab Chip 4:663–669. https://doi.org/10.1039/B407170K
37. Jiang F, Drese KS, Hardt S, Küpper M, Schönfeld F (2004) Helical flows and chaotic mixing
in curved micro channels. AIChE J. 50:2297–2305. https://doi.org/10.1002/aic.10188
38. Liu RH, Stremler MA, Sharp KV, Olsen MG, Santiago JG, Adrian RJ, Aref H, Beebe DJ
(2000) Passive mixing in a three-Dimensional serpentine microchannel. J Microelectromech
Syst 9:190–197. https://doi.org/10.1109/84.846699
39. Lin KW, Yang JT (2007) Chaotic mixing of fluids in a planar serpentine channel. Int J Heat
Mass Transf 50:1269–1277. https://doi.org/10.1016/j.ijheatmasstransfer.2006.09.016
40. Mengeaud V, Josserand J, Girault HH (2002) Mixing processes in a zigzag microchannel: finite
element simulations and optical study. Anal Chem 74:4279–4286. https://doi.org/10.1021/ac0
25642e
41. Afzal A, Kim KY (2013) Mixing Performance of a passive micromixer with sinusoidal channel
walls. J Chem Eng Jpn 46:230–238. https://doi.org/10.1252/jcej.12we144
42. Bertsch A, Heimgartner S, Cousseau P, Renaud P (2001) Static mixers based on large-scale
industrial mixer geometry. Lab Chip 1:56–60. https://doi.org/10.1039/B103848F
43. Bhagat AA, Peterson ET, Papautsky I (2010) A passive planar micromixer with obstructions
for mixing at low Reynolds number. J Micromech Microeng 20:1–10. https://doi.org/10.1088/
0960-1317/17/5/023
44. Alam A, Afzal A, Kim KY (2014) Mixing Performance of a planar micromixer with circular
obstructions in curved microchannel. Chem Eng Res Des 92:423–434. https://doi.org/10.1016/
j.cherd.2013.09.008
45. Lee SW, Kim DS, Lee SS, Kwon TH (2006) A split and recombination micromixer fabricated
in a PDMS three-dimensional structure. J Micromach Microeng 16:1067–1072. https://doi.
org/10.1088/0960-1317/16/5/027
46. Lee SW, Lee SS (2008) Rotation effect in split and recombination micromixing. Sens Actuat
B 129:364–371. https://doi.org/10.1016/j.snb.2007.08.038
47. Ansari MA, Kim KY, Anwar K, Kim SM (2010) A novel passive micromixer based on unbalanced splits and collisions of fluid streams. J Micromech Microeng 20:1–10. https://doi.org/
10.1088/0960-1317/20/5/055007
48. Ansari MA, Kim KY (2010) Mixing performance of unbalanced split and recombine
micromixers with circular and rhombic sub-channels. Chem Eng J 162:760–767. https://doi.
org/10.1016/j.cej.2010.05.068
49. Afzal A, Kim KY (2012) Passive split and recombination micromixer with convergentdivergent walls. Chem Eng J 203:182–192. https://doi.org/10.1016/j.cej.2012.06.111
50. Sudarsan AP, Ugaz VM (2006a) Fluid mixing in planar spiral microchannels. Lab Chip 6:74–82
33
28. Stroock AD, Dertinger SK, Ajdari A, Mezi´ c I, Stone HA, Whitesides GM (2002) Chaotic mixer
for microchannels. Science 295:647–651. https://doi.org/10.1126/science.1066238
29. Yang JT, Huang KJ, Lin YC (2005) Geometric effects on fluid mixing in passive grooved
micromixers. Lab Chip 5:1140–1147. https://doi.org/10.1039/B500972C
30. Hassell DG, Zimmerman WB (2006) Investigation of the convective motion through a staggered
herringbone micromixer at low Reynolds number flow. Chem Eng Sci 61:2977–2985. https://
doi.org/10.1016/j.ces.2005.10.068
31. Wang L, Yang JT (2006) An overlapping crisscross micromixer using chaotic mixing principles.
J Micromech Microeng 16:2684. https://doi.org/10.1088/0960-1317/16/12/022
32. Wang L, Yang JT, Lyu PC (2007) An overlapping crisscross micromixer. Chem Eng Sci 62:711–
720. https://doi.org/10.1016/j.ces.2006.09.048
33. Dean WR (1927) Note on the motion of fluid in a curved pipe. Philos Mag 4:208–223. https://
doi.org/10.1080/14786440708564324
34. Dean WR (1928) The stream-line motion of fluid in a curved pipe. Philos Mag 5:673–695.
https://doi.org/10.1080/14786440408564513
35. Vanka SP, Luo G, Winkler CM (2004) Numerical study of scalar mixing in curved channels at
low Reynolds number. AIChE J 50:2359–2368. https://doi.org/10.1002/aic.10196
36. Howell PB Jr, Mott DR, Golden JP, Ligler FS (2004) Design and Evaluation of a Dean VortexBased Micromixer. Lab Chip 4:663–669. https://doi.org/10.1039/B407170K
37. Jiang F, Drese KS, Hardt S, Küpper M, Schönfeld F (2004) Helical flows and chaotic mixing
in curved micro channels. AIChE J. 50:2297–2305. https://doi.org/10.1002/aic.10188
38. Liu RH, Stremler MA, Sharp KV, Olsen MG, Santiago JG, Adrian RJ, Aref H, Beebe DJ
(2000) Passive mixing in a three-Dimensional serpentine microchannel. J Microelectromech
Syst 9:190–197. https://doi.org/10.1109/84.846699
39. Lin KW, Yang JT (2007) Chaotic mixing of fluids in a planar serpentine channel. Int J Heat
Mass Transf 50:1269–1277. https://doi.org/10.1016/j.ijheatmasstransfer.2006.09.016
40. Mengeaud V, Josserand J, Girault HH (2002) Mixing processes in a zigzag microchannel: finite
element simulations and optical study. Anal Chem 74:4279–4286. https://doi.org/10.1021/ac0
25642e
41. Afzal A, Kim KY (2013) Mixing Performance of a passive micromixer with sinusoidal channel
walls. J Chem Eng Jpn 46:230–238. https://doi.org/10.1252/jcej.12we144
42. Bertsch A, Heimgartner S, Cousseau P, Renaud P (2001) Static mixers based on large-scale
industrial mixer geometry. Lab Chip 1:56–60. https://doi.org/10.1039/B103848F
43. Bhagat AA, Peterson ET, Papautsky I (2010) A passive planar micromixer with obstructions
for mixing at low Reynolds number. J Micromech Microeng 20:1–10. https://doi.org/10.1088/
0960-1317/17/5/023
44. Alam A, Afzal A, Kim KY (2014) Mixing Performance of a planar micromixer with circular
obstructions in curved microchannel. Chem Eng Res Des 92:423–434. https://doi.org/10.1016/
j.cherd.2013.09.008
45. Lee SW, Kim DS, Lee SS, Kwon TH (2006) A split and recombination micromixer fabricated
in a PDMS three-dimensional structure. J Micromach Microeng 16:1067–1072. https://doi.
org/10.1088/0960-1317/16/5/027
46. Lee SW, Lee SS (2008) Rotation effect in split and recombination micromixing. Sens Actuat
B 129:364–371. https://doi.org/10.1016/j.snb.2007.08.038
47. Ansari MA, Kim KY, Anwar K, Kim SM (2010) A novel passive micromixer based on unbalanced splits and collisions of fluid streams. J Micromech Microeng 20:1–10. https://doi.org/
10.1088/0960-1317/20/5/055007
48. Ansari MA, Kim KY (2010) Mixing performance of unbalanced split and recombine
micromixers with circular and rhombic sub-channels. Chem Eng J 162:760–767. https://doi.
org/10.1016/j.cej.2010.05.068
49. Afzal A, Kim KY (2012) Passive split and recombination micromixer with convergentdivergent walls. Chem Eng J 203:182–192. https://doi.org/10.1016/j.cej.2012.06.111
50. Sudarsan AP, Ugaz VM (2006a) Fluid mixing in planar spiral microchannels. Lab Chip 6:74–82