Mixing, chaotic advection, and turbulence

Annual Review of Fluid Mechanics

Volumn 22, Issue 1, 1990, Pages 207-253

  Ottino, J M ^a  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC DYNAMICS; MIXING; POROUS MEDIA; REYNOLDS NUMBER; TURBULENCE;

EID: 0025169297     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.fluid.22.1.207     Document Type: Article

References (122)

1. Abraham, R., Marsden, J. E. 1985. Foundations of Mechanics. Reading, Mass: Benjamin/Cummings. 5th printing, with corrections
2. Abraham, R. H., Shaw, C. D. 1985. Dynamics - the Geometry of Behavior: Part 1, Periodic Behavior; Part 2, Chaotic Behavior; Part 3, Global Behavior. Santa Cruz, Calif: Aerial. 3rd printing
3. Acrivos, A. 1983. The breakup of small drops and bubbles in shear flows. Ann. NY Acad. Sci. 404: 1-11
4. Allègre, C. J., Turcotte, D. L. 1986. Implications of a two-component marble-cake mantle. Nature 323: 123-27
5. Aref, H. 1983. Integrable, chaotic, and turbulent vortex motion in two-dimensional flows. Annu. Rev. Fluid Mech. 15: 345-89
6. Aref, H. 1984. Stirring by chaotic advection. J. Fluid Mech. 143: 1-21
7. Aref, H., Balachandar, S. 1986. Chaotic advection in a Stokes flow. Phys. Fluids 29: 3515-21
8. Aref, H., Jones, S. W. 1989. Enhanced separation of diffusing particles by chaotic advection. Phys. Fluids A 1: 470-74
9. Arnold, V. I. 1965. Surla topologie des écoulements stationnaires des fluids parfaits. C. R. Acad. Sci. Paris Ser. A 261: 17-20
10. Aubry, N., Holmes, P., Lumley, J. L., Stone, E. 1988. The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192: 115-73
11. Ballal, B. Y., Rivlin, R. S. 1976. Flow of a Newtonian fluid between eccentric rotating cylinders: inertial effects. Arch. Ration. Mech. Anal. 62: 237-94
12. Batchelor, G. K. 1952. The effect of homogeneous turbulence on material lines and surfaces. Proc. R. Soc. London Ser. A 213: 349-66
13. Beloshapkin, V. V., Chernikov, A. A., Natenzon, M. Ya., Petrovichev, B. A., Sagdeev, R. Z., Zaslavsky, G. M. 1989. Chaotic streamlines in pre-turbulent states. Nature 337: 133-37
14. Bentley, B. J., Leal, L. G. 1986. An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows. J. Fluid Mech. 167: 241-83
15. Birkhoff, G. D. 1920. Surface transformations and their dynamical applications. Acta Math. 43: 1-119
16. Bowen, R. M. 1976. Theory of mixtures. In Continuum Physics, ed. A. C. Eringen, 3: 1-127. London: Academic
17. Broomhead, D. S., Ryrie, S. C. 1988. Particle paths in wavy vortices. Nonlinearity 1: 409-34
18. Chaiken, J., Chevray, R., Tabor, M., Tan, Q. M. 1986. Experimental study of Lagrangian turbulence in Stokes flow. Proc. R. Soc. London Ser. A 408: 165-74
19. Chaiken, J., Chu, C. K., Tabor, M., Tan, Q. M. 1987. Lagrangian turbulence and spatial complexity in a Stokes flow. Phys. Fluids 30: 687-94
20. Chapman, G. T., Tobak, M. 1985. Observations, theoretical ideas, and modelling of turbulent flows - past, present, and future. In Theoretical Approaches to Turbulence, ed. D. L. Dwoyer, M. Y. Hussaini, R. G. Voigt, pp. 19-49. New York: Springer-Verlag
21. Chella, R., Ottino, J. M. 1984. Conversion and selectivity modifications due to mixing in unpremixed reactors. Chem. Eng. Sci. 39: 551-67
22. Chella, R., Ottino, J. M. 1985a. Stretching in some classes of fluid motions and asymptotic mixing efficiencies as a measure of flow classification. Arch. Ration. Mech. Anal. 90: 15-42
23. Chella, R., Ottino, J. M. 1985b. Fluid mechanics of mixing in a single screw extruder. Ind. Eng. Chem. Fundam. 24: 170-80
24. Chien, W.-L., Rising, H., Ottino, J. M. 1986. Laminar mixing and chaotic mixing in several cavity flows. J. Fluid Mech. 170: 355-77
25. Dallmann, U. 1983. Topological structures of three-dimensional flow separation. DFVLR Rep. No. IB 221-82-A07, Göttingen, West Germ.
26. Danckwerts, P. V. 1952. The definition and measurement of some characteristics of mixtures. Appl. Sci. Res. Sect. A 3: 279-96
27. Danielson, T. 1989. Chaos and turbulence in two model flows: the Kelvin cat eyes flow and flows near walls. PhD thesis. Dept. Chem. Eng., Univ. Mass., Amherst. In progress
28. Devaney, R. L. 1986. An Introduction to Chaotic Dynamical Systems. Menlo Park, Calif: Benjamin/Cummings
29. Doherty, M. F., Ottino, J. M. 1988. Chaos in deterministic systems: strange attractors, turbulence, and applications in chemical engineering. Chem. Eng. Sci. 43: 139-83
30. Dombre, T., Frisch, U., Greene, J. M., Hénon, M., Mehr, A., Soward, A. M. 1986. Chaotic streamlines in the ABC flows. J. Fluid Mech. 167: 353-91
31. Eckmann, J.-P. 1981. Roads to turbulence in dissipative dynamical systems. Rev. Mod. Phys. 53: 643-54
32. Feigenbaum, M. J. 1978. Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 19: 25-52
33. Feigenbaum, M. J. 1979a. The universal metric properties of nonlinear transformations. J. Stat. Phys. 21: 669-706
34. Feigenbaum, M. J. 1979b. The onset spectrum of turbulence. Phys. Lett. A 74: 375-78
35. Feigenbaum, M. J. 1980. Universal behavior in nonlinear systems. Los Alamos Sci. 1: 4-27
36. Feingold, M., Kadanoff, L. P., Piro, O. 1988. Passive scalars, three-dimensional volume preserving maps, and chaos. J. Stat. Phys. 50: 529-65
37. Fenstermacher, P. R., Swinney, H. L., Gollub, J. P. 1979. Dynamical instabilities and the transition to chaotic Taylor vortex flow. J. Fluid Mech. 94: 103-28
38. Fern, A. 1973. Mixing-controlled supersonic combustion. Annu. Rev. Fluid Mech. 5: 301-38
39. Finn, J. M., Ott, E. 1988. Chaotic flows and fast magnetic dynamos. Phys. Fluids 31: 2992-3011
40. Franjione, J. G. 1989. Mixing in chaotic duct flows. PhD thesis. Dept. Chem. Eng., Univ. Mass., Amherst. In progress
41. Franjione, J. G., Leong, C-W., Ottino, J. M. 1989. Symmetries within chaos: a route to effective mixing. Phys. Fluids A. In press
42. Franjione, J. G., Ottino, J. M. 1987. Feasibility of numerical tracking of material lines and surfaces in chaotic flows. Phys. Fluids 30: 3641-43
43. Galloway, D., Frisch, U. 1986. Dynamo action in a family of flows with chaotic streamlines. Geophys. Astrophys. Fluid Dyn. 36: 53-83
44. Gargett, A. E. 1989. Ocean turbulence. Annu. Rev. Fluid Mech. 21: 419-51
45. Gibson, C. H. 1968. Fine structure of scalar fields mixed by turbulence: I. Zero-gradient points and minimal gradient surfaces. Phys. Fluids 11: 2305-15
46. Guckenheimer, J. 1986. Strange attractors in fluids: another view. Annu. Rev. Fluid Mech. 18: 15-31
47. Guckenheimer, J., Holmes, P. 1983. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. New York: Springer-Verlag. Reprinted, 1986
48. Hama, F. R. 1962. Streaklines in a perturbed shear flow. Phys. Fluids 5: 644-50
49. Helleman, R. H. G. 1980. Self-generated chaotic behavior in nonlinear mechanics. In Fundamental Problems in Statistical Mechanics V, ed. E. G. D. Cohen, pp. 165-275. Amsterdam: North-Holland
50. Heller, J. P. 1960. An unmixing demonstration. Am. J. Phys. 28: 348-56
51. Hénon, M. 1966. Sur la topologie des lignes de courant dans un cas particulier. C. R. Acad. Sci. Paris Ser. A 262: 312-14
52. Heslot, F., Castaing, B., Libchaber, A. 1987. Transitions to turbulence in helium gas. Phys. Rev. A 36: 5870-73
53. Hiby, J. W. 1962. Longitudinal and transverse mixing during single-phase flow through granular beds. Proc. Symp. Interact. Between Fluids and Part., pp. 312-25. London: Inst. Chem. Eng.
54. Hill, J. C. 1976. Homogeneous turbulent mixing with chemical reaction. Annu. Rev. Fluid Mech. 8: 135-61
55. Hirsch, M. W., Smale, S. 1974. Differential Equations, Dynamical Systems, and Linear Algebra. New York: Academic
56. Hoffman, N. R. A., McKenzie, D. P. 1985. The destruction of geochemical heterogeneities by differential fluid motion during mantle convection. Geophys. J. R. Astron. Soc. 82: 163-206
57. Holloway, G. 1986. Eddies, waves, circulation, and mixing: statistical geofluid mechanics. Annu. Rev. Fluid Mech. 18: 91-147
58. Holmes, P. 1984. Some remarks on chaotic particle paths in time-periodic, three dimensional swirling flows. Contemp. Math. 28: 393-404
59. Jeffery, G. B. 1922. The rotation of two cylinders in a viscous fluid. Proc. R. Soc. London Ser. A 101: 169-74
60. Jones, S. W., Aref, H. 1988. Chaotic advection in pulsed source-sink systems. Phys. Fluids 31: 469-85
61. Jones, S. W., Thomas, O. M., Aref, H. 1989. Chaotic advection by laminar flow in a twisted pipe. Submitted for publication
62. Khakhar, D. V. 1986. Fluid mechanics of laminar mixing: dispersion and chaotic flows. PhD thesis. Dept. Chem. Eng., Univ. Mass., Amherst
63. Khakhar, D. V., Franjione, J. G., Ottino, J. M. 1987. A case study of chaotic mixing in deterministic flows: the partitioned pipe mixer. Chem. Eng. Sci. 42: 2909-26
64. Khakhar, D. V., Ottino, J. M. 1986. Fluid mixing (stretching) by time periodic sequences of weak flows. Phys. Fluids 29: 3503-5
65. Khakhar, D. V., Rising, H., Ottino, J. M. 1986. An analysis of chaotic mixing in two chaotic flows. J. Fluid Mech. 172: 419-51
66. Knobloch, E., Weiss, J. B. 1987. Chaotic advection by modulated travelling waves. Phys. Rev. A 36: 1522-24
67. Kühn, T. S. 1970. The Structure of Scientific Revolutions. Chicago: Univ. Press. 2nd ed.
68. Kusch, H. A. 1989. Chaotic mixing of viscous liquids in the eccentric helical annular mixer. PhD thesis. Dept. Chem. Eng., Univ. Mass., Amherst. In progress
69. Lanford, O. E. III. 1982. The strange attractor theory of turbulence. Annu. Rev. Fluid Mech. 14: 347-64
70. Leonard, A. 1985. Computing three-dimensional incompressible flows with vortex elements. Annu. Rev. Fluid Mech. 17: 523-59
71. Leonard, A., Rom-Kedar, V., Wiggins, S. 1987. Fluid mixing and dynamical systems. Nucl. Phys. B (Proc. Suppl.) 2: 179-90
72. Leong, C.-W. 1989, A detailed experimental analysis of chaotic mixing produced by two-dimensional time-periodic cavity flows. PhD thesis. Dept. Chem. Eng., Univ. Mass., Amherst. In progress
73. Leong, C.-W., Ottino, J. M. 1989. Experiments on mixing due to chaotic advection in a cavity. J. Fluid Mech. In press
74. Libchaber, A., Maurer, J. 1980. Une experience de Rayleigh-Bénard de geometrie reduite: multiplication, accrochage et multiplication de frequencies. J. Phys. Colloq. C3 41: 51-56
75. Lorenz, E. N. 1963. Deterministic nonperiodic flow. J. Atmos. Sci. 20: 130-41
76. Mandelbrot, B. B. 1982. The Fractal Geometry of Nature. San Francisco: Freeman
77. McKenzie, D. P., Roberts, J. M., Weiss, N. O. 1974. Convection in the earth's mantle: towards a numerical simulation. J. Fluid Mech. 62: 465-538
78. Middleman, S. 1977. Fundamentals of Polymer Processing. New York: McGraw-Hill
79. Moffatt, H. K., Proctor, M. R. E. 1985. Topological constraints associated with fast dynamo action. J. Fluid Mech. 154: 493-507
80. Moser, J. 1973. Stable and Random Motion in Dynamical Systems. Princeton, NJ: Princeton Univ. Press
81. Muzzio, F. J., Ottino, J. M. 1988. Coagulation in chaotic flows. Phys. Rev. A 38: 2516-24
82. Muzzio, F. J., Ottino, J. M. 1989. Evolution of a lamellar system with diffusion and reaction: a scaling approach. Phys. Rev. Lett. 63: 47-50
83. Ott, E., Antonsen, T. M. 1988. Chaotic fluid convection and the fractal nature of passive scalar gradients. Phys. Rev. Lett. 61: 2839-42
84. Ottino, J. M. 1982. Description of mixing with diffusion and reaction in terms of the concept of material interfaces. J. Fluid Mech. 114: 83-103
85. Ottino, J. M. 1983. Mechanical mixing parameter for continuous mixing systems. AIChE J. 29: 159-61
86. Ottino, J. M. 1989a. The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge: Univ. Press
87. Ottino, J. M. 1989b. The mixing of fluids. Sci. Am. 260: 56-67
88. Ottino, J. M., Chella, R. 1983. Mixing of polymeric liquids: a brief review and recent theoretical developments. Polym. Eng. Sci. 23: 357-79
89. Ottino, J. M., Leong, C.-W., Rising, H., Swanson, P. D. 1988. Morphological structures produced by mixing in chaotic flows. Nature 333: 419-25
90. Ottino, J. M., Macosko, C. W. 1980. An efficiency parameter for batch mixing of viscous liquids. Chem. Eng. Sci. 35: 1454-57
91. Ottino, J. M., Macosko, C. W., Ranz, W. E. 1981. Framework for the description of mechanical mixing of fluids. AIChE J. 27: 565-77
92. Ottino, J. M., Ranz, W. E., Macosko, C. W. 1979. A lamellar model for analysis of liquid-liquid mixing. Chem. Eng. Sci. 34: 877-90
93. Pasmanter, R. 1988. Anomalous diffusion and anomalous stretching in vortical flows. Fluid Mech. Res. 3: 320-26
94. Percival, I., Richards, D. 1982. Introduction to Dynamics. Cambridge: Univ. Press
95. Perry, A. E., Chong, M. S. 1986. A seriesexpansion study of the Navier-Stokes equations with applications to threedimensional separation patterns. J. Fluid Mech. 173: 207-23
96. Perry, A. E., Chong, M. S. 1987. A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19: 125-55
97. Rallison, J. M. 1984. The deformation of small viscous drops and bubbles in shear flows. Annu. Rev. Fluid Mech. 16: 45-66
98. Ranz, W. E. 1979. Application of a stretch model to mixing, diffusion, and reaction in laminar and turbulent flows. AIChE J. 25: 41-47
99. Rising, H. 1989. Applications of chaos and dynamical systems approaches to mixing in fluids. PhD thesis. Dept. Math. Stat., Univ. Mass., Amherst
100. Roberts, F. A. 1985. Effects of a periodic disturbance on structure and mixing in turbulent shear layers and wakes. PhD thesis. Grad. Aeronaut. Lab., Calif. Inst. Technol.
101. Rom-Kedar, V., Leonard, A., Wiggins, S. 1989. An analytical study of transport, mixing and chaos in an unsteady vortical flow. Calif. Inst. of Technol. Preprint
102. Ruelle, D., Takens, F. 1971. On the nature of turbulence. Commun. Math. Phys. 20: 167-92
103. Sherman, F. S., Imberger, J., Corcos, G. M. 1978. Turbulence and mixing in stably stratified waters. Annu. Rev. Fluid Mech. 10: 267-88
104. Smale, S. 1967. Differentiable dynamical systems. Bull. Am. Math. Soc. 73: 747-817
105. Sobey, I. J. 1985. Dispersion caused by separation during oscillatory flow through a furrowed channel. Chem. Eng. Sci. 40: 2129-34
106. Solomon, T. H., Gollub, J. P. 1988. Chaotic particle transport in time-dependent Rayleigh-Bénard convection. Phys. Rev. A 38: 6280-86
107. Sreenivasan, K., R. 1985. Transition and turbulence in fluid flows and low-dimensional chaos. In Frontiers of Fluid Mechanics, ed. S. H. Davis, J. L. Lumley, pp. 41-67. New York: Springer-Verlag
108. Stone, H., Bentley, B. J., Leal, L. G. 1986. An experimental study of transient effects in the breakup of liquid drops. J. Fluid Mech. 173: 131-58
109. Swanson, P. D., Ottino, J. M. 1989. A comparative computational and experimental study of chaotic mixing of viscous fluids. J. Fluid Mech. In press
110. Swinney, H. L. 1985. Observations of complex dynamics and chaos. In Fundamental Problems in Statistical Mechanics VI, ed. E. G. D. Cohen, pp. 253-89. Amsterdam: Elsevier
111. Swinney, H. L., Gollub, J. P. 1985. Hydrodynamic Instabilities and the Transition to Turbulence. Top. Appl. Phys., Vol. 45. Berlin: Springer-Verlag. 2nd ed.
112. Tadmor, Z., Gogos, C. G. 1979. Principles of Polymer Processing. New York: Wiley-Interscience
113. Taylor, G. I. 1972. Low-Reynolds-number creeping flows. Film produced by the National Committee for Fluid Mechanics Films. The script of the film appears in Illustrated Experiments in Fluid Mechanics. Cambridge, Mass: MIT Press
114. Tennekes, H., Lumley, J. L. 1980. A First Course in Turbulence. Cambridge, Mass: MIT Press. 6th printing
115. Tjahjadi, M. 1989. Chaotic mixing of immiscible liquids. PhD thesis. Dept. Chem. Eng., Univ. Mass., Amherst. In progress
116. Truesdell, C. A. 1954. The Kinematics of Vorticity. Bloomington: Ind. Univ. Press
117. Truesdell, C. A., Toupin, R. 1960. The classical field theories. In Handbuch der Physik III/I, ed. S. Flügge, pp. 226-793. Berlin: Springer-Verlag
118. von Neumann, J. 1963. Recent theories of turbulence. In Collected Works, ed. A. H. Taub, 6: 437-72. New York: PergamonMacmillan
119. Wannier, G. H. 1950. A contribution to the hydrodynamics of lubrication. Q. Appl. Math. 8: 1-32
120. Weiss, J. B. 1988. Stochastic and deterministic oscillations. PhD thesis. Univ. Calif., Berkeley
121. Weiss, J. B., Knobloch, E. 1989. Mass transport and mixing by modulated travelling waves. Univ. Calif, Berkeley. Preprint
122. Wiggins, S. 1988. Global Bifurcation and Chaos: Analytical Tools. New York: Springer-Verlag