Quantitative Evaluation of Passive Scalar Flow Mixing – A Review of Recent Developments
Corresponding Author
Ben Xu
The University of Texas Rio Grande Valley, Department of Mechanical Engineering, 78539 Edinburg, USA
Correspondence: Ben Xu ([email protected]), Department of Mechanical Engineering, The University of Texas Rio Grande Valley, Edinburg, TX, 78539, USA.Search for more papers by this authorYuchun Li
University of California, Department of Computer Engineering, 95064 Santa Cruz, USA
Search for more papers by this authorXiankun Xu
The University of Arizona, Department of Aerospace and Mechanical Engineering, 85721 Tucson, USA
Search for more papers by this authorXinhai Xu
Harbin Institute of Technology (Shenzhen), School of Mechanical Engineering and Automation, 518055 Shenzhen, Guangdong, China
Search for more papers by this authorCorresponding Author
Ben Xu
The University of Texas Rio Grande Valley, Department of Mechanical Engineering, 78539 Edinburg, USA
Correspondence: Ben Xu ([email protected]), Department of Mechanical Engineering, The University of Texas Rio Grande Valley, Edinburg, TX, 78539, USA.Search for more papers by this authorYuchun Li
University of California, Department of Computer Engineering, 95064 Santa Cruz, USA
Search for more papers by this authorXiankun Xu
The University of Arizona, Department of Aerospace and Mechanical Engineering, 85721 Tucson, USA
Search for more papers by this authorXinhai Xu
Harbin Institute of Technology (Shenzhen), School of Mechanical Engineering and Automation, 518055 Shenzhen, Guangdong, China
Search for more papers by this authorAbstract
Flow mixing has always been of particular interest for chemical engineering, combustion, and energy industries as well as other related engineering applications. Mixing always plays a crucial role because of its ability to uniformly distribute the passive scalar in the flow field without dynamic influences to the flow field itself. This paper reviews studies which quantitatively evaluated passive scalar mixing in various engineering applications. On the one hand, passive scalar mixing in turbulence has been reviewed from the aspect of energy spectrum cascades and small temporal-spatial scale analysis, mixing time, unmixedness, mixing time-scale ratio, and relative mixing intensity ratio using DNS. Secondly, several different concepts (percentage mixing, mixing intensity and degree of mixing) to quantify the flow mixing in microfluidic systems were introduced and compared thoroughly, and it is believed that these methods can be extended to other macro fluid engineering systems. Furthermore, a CFD-based approach using the statistics of temporal and spatial distribution of fluid particles was reviewed, but cannot be extended to engineering applications with special requirements of mixing time.
References
- 1 J. M. Ottino, Chem. Eng. Sci. 2000, 55, 2749–2765. DOI: 10.1016/S0009-2509(00)00019-1
- 2 R. Everson, D. Manin, L. Sirovich, M. Winter, AIAA J. 1998, 36, 121–127. DOI: 10.2514/2.7492
- 3 P. E. Dimotakis, Annu. Rev. Fluid Mech. 2005, 37, 329–56. DOI: 10.1146/annurev.fluid.36.050802.122015
- 4 P. A. Davidson, Turbulence: An Introduction for Scientists and Engineers, Oxford University Press, New York 2004.
- 5 K. R. Sreenivasan, Proc. R. Soc. London 1991, 434, 165–182. DOI: 10.1098/rspa.1991.0087
- 6 K. R. Sreenivasan, R. A. Antonia, Ann. Rev. Fluid Mech. 1997, 29, 435–72. DOI: 10.1146/annurev.fluid.29.1.435
- 7 B. I. Shraiman, E. D. Siggia, Nature 2000, 405, 639–46. DOI: 10.1038/35015000
- 8 D. G. Perez, Ph.D. Thesis, Universidad Nacional de La Plata, Buenos Aires 2002.
- 9 L. M. Pickett, J. B. Ghandhi, Phys. Fluids. 2002, 14, 985–98. DOI: 10.1063/1.1445421
- 10 E. Kuznetsov, A. C. Newell, V. E. Zakharov, Phys. Rev. Lett. 1991, 67, 3243–46. DOI: 10.1103/PhysRevLett.67.3243
- 11 A. Celani, A. Lanotte, A. Mazzino, M. Vergassola, Phys. Rev. Lett. 2000, 84, 2385–88. DOI: 10.1103/PhysRevLett.84.2385
- 12
U. Frisch, Turbulence: The Legacy of AN Kolmogorov, Cambridge University Press, Cambridge
1995.
10.1017/CBO9781139170666 Google Scholar
- 13
G. I. Taylor, Proc. R. Soc. London A
1935, 151, 421–464. DOI: 10.1098/rspa.1935.0158
10.1098/rspa.1935.0158 Google Scholar
- 14 A. N. Kolmogorov, Physics-Uspekhi 1968, 10 (6), 734–746. DOI: 10.1070/PU1968v010n06ABEH003710
- 15 G. K. Batchelor, J. Fluid Mech. 1959, 5, 113–1959. DOI: 10.1017/S002211205900009X
- 16 M. Holzer, E. D. Siggia, Phys. Fluids 1998, 6 (5), 1820–1837. DOI: 10.1063/1.868243
- 17 A. Pumir, Phys. Fluids 1994, 6 (6), 2118–2132. DOI: 10.1063/1.868216
- 18 B. S. Williams, D. Marteau, J. P. Gollub, Phys. Fluids 1997, 9 (7), 2061–2080. DOI: 10.1063/1.869326
- 19 P. E. Dimotakis, P. L. Miller, Phys. Fluids 1990, 2 (11), 1919–1920. DOI: 10.1063/1.857666
- 20 W. Bos, Ph.D. Thesis, Laboratoire de Mécanique des Fluides et d'Acoustique, Lyon 2005.
- 21 S. A. Orszag, V. Yakhot, Phys. Rev. Lett. 1986, 56 (16), 1691. DOI: 10.1103/PhysRevLett.56.1691
- 22 V. Yakhot, S. A. Orszag, Phys. Rev. Lett. 1986, 57 (14), 1722. DOI: 10.1103/PhysRevLett.57.1722
- 23
V. Yakhot, S. A. Orszag, SIAM J. Sci. Comput.
1986, 1 (1), 3–51. DOI: 10.1007/BF01061452
10.1007/BF01061452 Google Scholar
- 24 S. Hickel, N. A. Adams, N. N. Mansour, Phys. Fluids 2007, 19 (9), 095102. DOI: 10.1063/1.2770522
- 25 B. Wegner, Y. Huai, A. Sadiki, Int. J. Heat Fluid Flow 2004, 25 (5), 767–775. DOI: 10.1016/j.ijheatfluidflow.2004.05.015
- 26 C. H. Liu, M. C. Barth, J. Appl. Meteorol. 2002, 41 (6), 660–673. DOI: 10.1175/1520-0450(2002)041<0660:LESOFA>2.0.CO;2
- 27 P. Gravesen, J. Branebjerg, O. S. Jensen, J. Micromech. Microeng. 1993, 3, 168–182. DOI: 10.1088/0960-1317/3/4/002
- 28 V. Hessel, H. Löwe, F. Schönfeld, Chem. Eng. Sci. 2005, 60, 2479–2501. DOI: 10.1016/j.ces.2004.11.033
- 29 C. Y. Lee, C. L. Chang, Y. N. Wang, L. M. Fu, Int. J. Mol. Sci. 2011, 12, 3263–3287. DOI: 10.3390/ijms12053263
- 30 T. J. Johnson, D. Ross, L. E. Locascio, Anal. Chem. 2002, 74, 45–51. DOI: 10.1021/ac010895d
- 31 A. P. Sudarsan, V. M. Ugaz, Lab Chip 2006, 6, 74–82. DOI: 10.1039/B511524H
- 32 I. Glasgow, N. Aubry, Lab Chip 2003, 3, 114–120. DOI: 10.1039/B302569A
- 33 M. Camesasca, I. Manas-Zloczower, M. Kaufman, J. Micromech. Microeng. 2005, 15, 2038–2044. DOI: 10.1088/0960-1317/15/11/007
- 34 M. Camesasca, M. Kaufman, I. Manas-Zloczower, Macromol. Theory Simul. 2006, 15, 595–607. DOI: 10.1002/mats.200600037
- 35 P. A. Allen, M. Kaufman, A. F. Smith, R. E. Propper, Psychol. Aging 1998, 13, 501–518. DOI: 10.1037/0882-7974.13.3.501
- 36 D. R. Brooks, E. O. Wiley, D. R. Brooks, Evolution as Entropy, University of Chicago Press, Chicago 1988.
- 37
N. Georgescu-Roegen, The Entropy Law and the Economic Process, Vol. 13, Harvard University Press, Cambridge
1971.
10.4159/harvard.9780674281653 Google Scholar
- 38
L. Arnold, V. Wihstutz, Lyapunov Exponents: A Survey, Springer, Heidelberg
1986.
10.1007/BFb0076829 Google Scholar
- 39 L. M. Pecora, T. L. Carroll, Phys. Rev. Lett. 1990, 64, 821–24. DOI: 10.1103/PhysRevLett.64.821
- 40 V. I. Oseledec, Trans. Moscow Math. Soc. 1968, 19, 197–231.
- 41 S. Wiggin, Chaotic Transport in Dynamical Systems, Springer-Verlag, New York 1992.
- 42 D. D'Alessandro, M. Dahleh, I. Mezic, IEEE Trans. Autom. Control. 1999, 44, 1852–64. DOI: 10.1109/9.793724
- 43 J. P. Eckmann, D. Ruelle, Rev. Mod. Phys. 1985, 57 (3), 617. DOI: 10.1103/RevModPhys.57.617
- 44 P. Ashwin, M. Nicol, N. Kirkby, Physica A. 2002, 310, 347–63. DOI: 10.1016/S0378-4371(02)00774-4
- 45 D. Rothstein, E. Henry, J. P. Gollub, Nature 1999, 401, 770–772. DOI: 10.1038/44529
- 46 J. L. Thiffeault, S. Childress, Chaos 2003, 13, 502–507. DOI: 10.1063/1.1568833
- 47 M. Volpert, C. D. Meinhart, I. Mezic, M. Dahleh, 1st Int. Conf. on Heat Transfer, Fluid Mechanics and Thermodynamics, Kruger Park, April 2002.
- 48 G. Mathew, I. Mezic, L. Petzold, Physica D. 2005, 211, 23–46. DOI: 10.1016/j.physd.2005.07.017
- 49 B. Xu, P. W. Li, P. Waller, Renewable Energy 2014, 62, 249–257. DOI: 10.1016/j.renene.2013.06.049
- 50 B. Xu, P. W. Li, P. Waller, M. Huesemann, Algal Res. 2015, 9, 27–39. DOI: 10.1016/j.algal.2015.02.027
- 51
Y. K. Lee, S. J. Pirt, Microbiology
1981, 124 (1), 43–52. DOI: 10.1099/00221287-124-1-43
10.1099/00221287‐124‐1‐43 Google Scholar
- 52 J. C. Merchuk, A. Contreras, F. Garcia, E. Molina, Chem. Eng. Sci. 1998, 53 (4), 709–719. DOI: 10.1016/S0009-2509(97)00340-0
- 53 J. C. Ogbonna, H. Yada, H. Tanaka, J. Ferment. Bioeng. 1995, 79 (2), 152–157. DOI: 10.1016/0922-338X(95)94083-4
- 54S. Attalah, P. Waller, G. Khawam, R. Ryan, 2012 ASABE Conf., Dallas, TX, July 2012. DOI: 10.13031/2013.42179
- 55 P. V. Danckwerts, Chem. Eng. Sci. 1958, 8, 93–102. DOI: 10.1016/0009-2509(58)80040-8
- 56 T. N. Zwietering, Chem. Eng. Sci. 1959, 11, 1–15. DOI: 10.1016/0009-2509(59)80068-3
- 57 D. B. Spalding, Chem. Eng. Sci. 1958, 9, 74–77. DOI: 10.1016/0009-2509(58)87010-4
- 58 M. Sandberg, Build. Environ. 1981, 16, 123–135. DOI: 10.1016/0360-1323(81)90028-7
- 59 J. N. Baléo, P. Le Cloirec, AIChE J. 2000, 46, 675–683. DOI: 10.1002/aic.690460403
- 60 M. Liu, J. N. Tilton, AIChE J. 2010, 56, 2561–2572. DOI: 10.1002/aic.12151
- 61 M. Liu, Chem. Eng. Sci. 2011, 66, 3045–3048. DOI: 10.1016/j.ces.2011.03.049
- 62 D. F. Gerson, M. M. Kole, Biochem. Eng. J. 2001, 7, 153–156. DOI: 10.1016/S1369-703X(00)00115-7
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