Chaotic mixing of immiscible impurities in a two-dimensional flow

Physics of Fluids

Volumn 10, Issue 2, 1998, Pages 342-350

  Solomon, T H ^a   Tomas, S ^a   Warner, J L ^a  

^a BUCKNELL UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; DIFFUSION; DROP FORMATION; DYES; IMPURITIES; MAGNETOHYDRODYNAMICS; OILS AND FATS; OSCILLATIONS; SOLUBILITY; SURFACE TENSION; VORTEX FLOW;

CHAOTIC MIXING; RAYLEIGH-BENARD CONVECTION; TWO DIMENSIONAL; URANINE DYE;

MIXING;

CHAOS; FLUID FLOW; IMMISCIBLE FLUID; MIXING;

EID: 0032004612     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869526     Document Type: Article

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15. See, e.g., W. Young, A. Pumir, and Y. Pomeau, "Anomalous diffusion of tracers in convection rolls," Phys. Fluids A 1, 462 (1989); O. Cardoso and P Taheling, "Anomalous diffusion in a linear system of vortices," Eur. J. Mech. B, Fluids 8, 459 (1989); B. D. Hughes, M. F. Shlesinger, and E. W. Montroll, "Random walks with sell-similar clusters," Proc. Natl. Acad. Sci. USA 78, 3287 (1981); M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, "Strange kinetics," Nature (London) 363, 31 (1993).
16. See, e.g., W. Young, A. Pumir, and Y. Pomeau, "Anomalous diffusion of tracers in convection rolls," Phys. Fluids A 1, 462 (1989); O. Cardoso and P Taheling, "Anomalous diffusion in a linear system of vortices," Eur. J. Mech. B, Fluids 8, 459 (1989); B. D. Hughes, M. F. Shlesinger, and E. W. Montroll, "Random walks with sell-similar clusters," Proc. Natl. Acad. Sci. USA 78, 3287 (1981); M. F. Shlesinger, G. M. Zaslavsky, and J. Klafter, "Strange kinetics," Nature (London) 363, 31 (1993).
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30. ion, points in the some direction for all ions, resulting in bulk fluid motion.
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33. P. DeRoussel and J. Ottino (private communication).
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36. The area under the profiles is reduced early in the run in Fig. 4, due to saturation of the dye. (The initial concentration in the center vortex is intentionally made to be very high, so that there will be enough dye to make good measurements after the distribution has spread.)
37. There is a very small long-range transport of some tiny droplets that are produced by tip streaming of the oil, but this accounts for less than 1% of the total oil in the system.
38. Note: we are neglecting inertial effects and Stokes drag in this simplified analysis. A complete analysis will have to account for these effecls to verify whether or not small oil droplets truly behave as passive tracers.
39. Most of this is done automatically, using erosion and dilation techniques to separate the different clusters while maintaining their area. However, it is still necessary to review the images manually and separate some clusters interactively.