The curvature of material lines in a three-dimensional chaotic flow

Physics of Fluids

Volumn 10, Issue 8, 1998, Pages 1942-1952

  Hobbs, D M ^a   Muzzio, F J ^a  

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

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; COMPUTATIONAL FLUID DYNAMICS; DROP BREAKUP; EQUATIONS OF MOTION; FLOW PATTERNS; MIXING; PROBABILITY DENSITY FUNCTION; RUNGE KUTTA METHODS; STATISTICAL METHODS; THREE DIMENSIONAL; TURBULENT FLOW;

CHAOTIC FLOW; DUCT FLOW; FLOW GEOMETRY; THREE DIMENSIONAL FLOW;

LAMINAR FLOW;

EID: 0032133537     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869710     Document Type: Article

References (29)

1. V. Rom-Kedar, A. Leonard, and S. Wiggins, "An analytical study of transport, mixing and chaos in an unsteady vortical flow," J. Fluid Mech. 214, 347 (1990).
2. R. T. Pierrehumbert, "Large-scale horizontal mixing in planetary atmospheres," Phys. Fluids A 3, 1250 (1991).
3. F. J. Muzzio, P. D. Swanson, and J. M. Ottino, "The statistics of stretching and stirring in chaotic flows," Phys. Fluids A 3, 822 (1991).
4. F. Varosi, T. M. Antonsen, and E. Ott, "The spectrum of fractal dimensions of passively convected scalar gradients in chaotic fluid flows," Phys. Fluids A3, 1017 (1991).
5. D. Beigie, A. Leonard, and S. Wiggins, "A global study of enhanced stretching and diffusion in chaotic tangles," Phys. Fluids A 3, 1039 (1991).
6. S. Wiggins, Chaotic Transport in Dynamical Systems (Springer-Verlag, New York, 1992).
7. M. Liu, R. L. Peskin, F. J. Muzzio, and C. W. Leong, "Structure of the stretching field in chaotic cavity flows," AIChE. J. 40, 1273 (1994).
8. S. B. Pope, "The evolution of surfaces in turbulence," Int. J. Eng. Sci. 26, 445 (1988).
9. S. B. Pope, P. K. Yeung, and S. S. Girimaji, "The curvature of material surfaces in isotropic turbulence," Phys. Fluids A 1, 2010 (1989).
10. S. S. Girimaji, "Asymptotic behavior of curvature of surface elements in isotropic turbulence," Phys. Fluids A 3, 1772 (1991).
11. I. T. Drummond and W. Munch, "Distortion of line and surface elements in model turbulent flows," J. Fluid Mech. 225, 529 (1991); T. Ishihara and Y. Kaneda, "Stretching and distortion of material line elements in two-dimensional turbulence," J. Phys. Soc. Jpn. 61, 3547 (1992).
12. I. T. Drummond and W. Munch, "Distortion of line and surface elements in model turbulent flows," J. Fluid Mech. 225, 529 (1991); T. Ishihara and Y. Kaneda, "Stretching and distortion of material line elements in two-dimensional turbulence," J. Phys. Soc. Jpn. 61, 3547 (1992).
13. B. J. Gluckman, H. Willaime, and J. P. Gollub, "Geometry of isothermal and isoconcentration surfaces in thermal turbulence," Phys. Fluids A 5, 647 (1993).
14. I. T. Drummond, "Stretching and bending of line elements in random flows," J. Fluid Mech. 252, 479 (1994).
15. J. G. Franjione, "Development and application of techniques for the analysis of chaotic mixing in two- and three-dimensional flows," Ph.D. thesis, University of Massachusetts, 1991.
16. M. Tjahjadi and J. M. Ottino, "Stretching and breakup of droplets in chaotic flows," J. Fluid Mech. 232, 191 (1991).
17. M. Liu and F. J. Muzzio, "The curvature of material lines in chaotic cavity flows," Phys. Fluids 8, 75 (1996).
18. D. M. Hobbs, M. M. Alvarez, and F. J. Muzzio, "Mixing in globally chaotic flows: A self-similar process," Fractals 3, 395 (1997).
19. D. M. Hobbs, P. D. Swanson, and F. J. Muzzio, "Numerical characterization of low Reynolds number flow in the Kenics static mixer," Chem. Eng. Sci. (to appear).
20. D. M, Hobbs and F. J. Muzzio, "The Kenics static mixer. A three-dimensional chaotic flow," Chem. Eng. J. 67, 153 (1997).
21. D. M. Hobbs and F. J. Muzzio, "Optimization of a static mixer using dynamical systems techniques," Chem. Eng. Sci. (to appear).
22. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes (The Art of Scientific Computing) (Cambridge University Press, Cambridge, 1986).
23. D. M. Hobbs and F. J. Muzzio, "Reynolds number effects on laminar mixing in the kenics static mixer," Chem. Eng. Sci. (to appear).
24. D. M. Hobbs and F. J. Muzzio, "The effect of injection location, flow ratio, and geometry on kenics mixer performance," AIChe. J. (to appear).
25. M. Liu, F. J. Muzzio, and R. L. Peskin, "Quantification of mixing in aperiodic chaotic flows," Chaos Solitons Fractals 4, 869 (1994).
26. F. J. Muzzio, P. D. Swanson, and J. M. Ottino, "Mixing distributions produced by multiplicative stretching in chaotic flows," Int. J. Bifurc. Chaos 2, 37 (1992).
27. Giona, M, A. Adrover, F. J. Muzzio, S. Cerbelli, and M. Alvarez, "The geometry of nixing in time periodic chaotic flows," submitted to J. Fluid Mech.
28. M. Liu, F. J. Muzzio, and R. L. Peskin, "Effects of manifolds and corner singularities on stretching in chaotic cavity flows," Chaos Solitons Fractals 4, 2145 (1994).
29. F. J. Muzzio, C. Meneveau, P. D. Swanson, and J. M. Ottino, "Scaling and multifractal properties of mixing in chaotic flows," Phys. Fluids A 4, 1439 (1992).