42
3 Computational Analysis of Flow and Mixing in Micromixers
points are calculated by interpolating values at adjacent computational nodes. For
better accuracy, the number of sampling points must be relatively high with respect
to the number of nodes. It is to be noted that 0 < σ < 0.5.
The mixing index is defined as:
M = 1 −
σ
σ max
(3.6)
The variance is taken to be the maximum for completely unmixed fluids (σ max
= 0.5) and the minimum for completely mixed fluids. The mixing index varies
from 0 (0% mixing) to 1 (100% mixing). A higher mixing index indicates a more
homogeneous concentration and better mixing performance.
References
1. Chung YC, Hsu YL, Jen CP, Lu MC, Lin YC (2004) Design of passive mixers utilizing microfluidic self-circulation in the mixing chamber. Lab Chip 4:70–77. https://doi.org/10.1039/B31
0848C
2. Afzal A, Kim KY (2015) Convergent-divergent micromixer coupled with pulsatile flow. Sens
Actuators B Chem 211:198–205. https://doi.org/10.1016/j.snb.2015.01.062
3. Glasgow I, Aubry N (2003) Enhancement of microfluidic mixing using time pulsing. Lab Chip
3:114–120. https://doi.org/10.1039/B302569A
4. Kockmann N, Kiefer T, Engler M, Woias P (2006) Convective mixing and chemical reactions
in microchannels with high flow rates. Sens Act B 117:495–508. https://doi.org/10.1016/j.snb.
2006.01.004
5. 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
6. 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
7. Hong CC, Choi JW, Ahn CH (2004) A novel in-plane passive microfluidic mixer with modified
Tesla structures. Lab Chip 4:109–113. https://doi.org/10.1039/B305892A
8. Tsai RT, Wu CY (2011) An efficient micromixer based on multidirectional vortices due to
baffles and channel curvature. Biomicrofluidics 5:1–13. https://doi.org/10.1063/1.3552992
9. Chung CK, Shih TR (2008) Effect of geometry on fluid mixing of the rhombic micromixers.
Microfluid Nanofluid 4:419–425. https://doi.org/10.1007/s10404-007-0197-9
10. Afzal A, Kim KY (2015) Multi-objective optimization of a passive micromixer based on
periodic variation of Velocity profile. Chem Eng Commun 202:322–333. https://doi.org/10.
1080/00986445.2013.841150
11. Yakhshi-Tafti E, Kumar R, Cho HJ (2008) Effect of laminar velocity profile variation on mixing
in microfluidic devices: the sigma micromixer. Appl Phys Lett 93:1–3. https://doi.org/10.1063/
1.2996564
12. CFX-12.1 Solver Theory (2006) ANSYS Inc., Canonsburg, Pennsylvania
13. Cortes-Quiroz CA, Zangeneh M, Goto A (2009) On multi-objective optimization of geometry
of staggered hertringbone micromixer. Microfluid Nanofluid 7:29–43. https://doi.org/10.1007/
s10404-008-0355-8
3 Computational Analysis of Flow and Mixing in Micromixers
points are calculated by interpolating values at adjacent computational nodes. For
better accuracy, the number of sampling points must be relatively high with respect
to the number of nodes. It is to be noted that 0 < σ < 0.5.
The mixing index is defined as:
M = 1 −
σ
σ max
(3.6)
The variance is taken to be the maximum for completely unmixed fluids (σ max
= 0.5) and the minimum for completely mixed fluids. The mixing index varies
from 0 (0% mixing) to 1 (100% mixing). A higher mixing index indicates a more
homogeneous concentration and better mixing performance.
References
1. Chung YC, Hsu YL, Jen CP, Lu MC, Lin YC (2004) Design of passive mixers utilizing microfluidic self-circulation in the mixing chamber. Lab Chip 4:70–77. https://doi.org/10.1039/B31
0848C
2. Afzal A, Kim KY (2015) Convergent-divergent micromixer coupled with pulsatile flow. Sens
Actuators B Chem 211:198–205. https://doi.org/10.1016/j.snb.2015.01.062
3. Glasgow I, Aubry N (2003) Enhancement of microfluidic mixing using time pulsing. Lab Chip
3:114–120. https://doi.org/10.1039/B302569A
4. Kockmann N, Kiefer T, Engler M, Woias P (2006) Convective mixing and chemical reactions
in microchannels with high flow rates. Sens Act B 117:495–508. https://doi.org/10.1016/j.snb.
2006.01.004
5. 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
6. 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
7. Hong CC, Choi JW, Ahn CH (2004) A novel in-plane passive microfluidic mixer with modified
Tesla structures. Lab Chip 4:109–113. https://doi.org/10.1039/B305892A
8. Tsai RT, Wu CY (2011) An efficient micromixer based on multidirectional vortices due to
baffles and channel curvature. Biomicrofluidics 5:1–13. https://doi.org/10.1063/1.3552992
9. Chung CK, Shih TR (2008) Effect of geometry on fluid mixing of the rhombic micromixers.
Microfluid Nanofluid 4:419–425. https://doi.org/10.1007/s10404-007-0197-9
10. Afzal A, Kim KY (2015) Multi-objective optimization of a passive micromixer based on
periodic variation of Velocity profile. Chem Eng Commun 202:322–333. https://doi.org/10.
1080/00986445.2013.841150
11. Yakhshi-Tafti E, Kumar R, Cho HJ (2008) Effect of laminar velocity profile variation on mixing
in microfluidic devices: the sigma micromixer. Appl Phys Lett 93:1–3. https://doi.org/10.1063/
1.2996564
12. CFX-12.1 Solver Theory (2006) ANSYS Inc., Canonsburg, Pennsylvania
13. Cortes-Quiroz CA, Zangeneh M, Goto A (2009) On multi-objective optimization of geometry
of staggered hertringbone micromixer. Microfluid Nanofluid 7:29–43. https://doi.org/10.1007/
s10404-008-0355-8