Attraction of minute particles to invariant regions of volume preserving flows by transients

Physical Review Letters

Volumn 86, Issue 7, 2001, Pages 1207-1210

  Shinbrot, T ^a   Alvarez, M M ^a   Zalc, J M ^a   Muzzio, F J ^a  

^a The State University of New Jersey   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; COMPUTER SIMULATION; DENSITY (SPECIFIC GRAVITY); DYES; FERROMAGNETIC MATERIALS; FLUID MECHANICS; GLYCEROL; MIXING; PARTICLE SIZE ANALYSIS; TANKS (CONTAINERS); TRACE ANALYSIS; VOLUME MEASUREMENT;

STIRRED TANK; TRANSIENT EFFECTS; VOLUME PRESERVING FLOWS;

LAMINAR FLOW;

EID: 0035252585     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.86.1207     Document Type: Article

References (23)

1. For example, A. Duvaille, Nature (London) 402, 756 (1999).
2. For example, M. C. Facchini, M. Mircea, S. Fuzzi, and R. J. Charlson, Nature (London) 401, 257 (1999).
3. For example, D. S. Jenkinson, K. Goulding, and D. S. Powlson, Nature (London) 400, 629 (1999).
4. W. A. M. N. Smith, S. A. Thorpe, and A. Graham, Nature (London) 400, 251 (1999).
5. P. L. Richardson, Am. Sci. 81, 261 (1993).
6. P. R. ten Wolde and D. Frenkel, Science 277, 1975 (1997).
7. L. da Vinci, Codex on the flight of birds (c. 1505), from anatomical manuscripts and drawings in the Royal Library, Windsor Castle, reproduced in C. Pedretti, Leonardo, The Machines (Giunti, Florence, Italy, 1999), p. 48.
8. D. Leighton and A. Acrivos, J. Fluid Mech. 177, 109 (1987).
9. H. S. Husain, F. Hussain, and M. Goldshtik, Phys. Rev. E 52, 4909 (1995).
10. M. R. Maxey, Philos. Trans. R. Soc. London A 333, 289 (1990).
11. R. Gore and C. T. Crowe, Int. J. Multiph. Flow 15, 279 (1989).
12. P. D. Swanson, F. J. Muzzio, A. Annapragada, and A. Adjei, Int. J. Pharm. 142, 33 (1996); M. Liu, R. L. Peskin, and F. J. Muzzio, Phys. Rev. E 50, 4245 (1994).
13. P. D. Swanson, F. J. Muzzio, A. Annapragada, and A. Adjei, Int. J. Pharm. 142, 33 (1996); M. Liu, R. L. Peskin, and F. J. Muzzio, Phys. Rev. E 50, 4245 (1994).
14. J. C. Sommerer and E. Ott, Science 259, 335 (1993).
15. At low concentration, the red dye appears yellow in these photographs.
16. J. B. Weiss, Phys. Fluids A 3, 1379 (1991).
17. Reduction in buoyancy is a well known result of stretching of a tracer solution: see, e.g., L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Addison-Wesley, Reading, MA, 1959), p. 66.
18. For example, K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems (Springer, New York, 1997), p. 69.
19. 0 = 0.64, and Γ = 0.99; essentially similar results have been obtained for other parameter values.
20. n/(1 - Γ) from a torus boundary remain trapped.
21. 0 = 0.0064, Γ = 0.99, and τ = 400 iterates. As before, 200 iterates of 500 initial points are plotted.
22. J. M. Zalc, M. M. Alvarez, B. E. Arik, and F. J. Muzzio, "Extensive Validation of Computed Laminar Flow Fields in a Stirred Tank Equipped with Three Rushton Turbines" (to be published).
23. 4 tracers to compute the correlation functions shown [cf. R. C. Hilborne, Chaos and Nonlinear Dynamics (Oxford University Press, Oxford, U.K., 1994), p. 441].