Topological chaos in inviscid and viscous mixers

Journal of Fluid Mechanics

Volumn 493, Issue , 2003, Pages 345-361

  Finn, M D ^a   Cox, S M ^a   Byrne, H M ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; COMPUTER SIMULATION; MATHEMATICAL MODELS; TOPOLOGY;

TOPOLOGICAL CHAOS; VISCOUS MIXERS;

VISCOUS FLOW;

CHAOS; LAMINAR FLOW; MIXING; STIRRING;

EID: 0242594648     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003005858     Document Type: Article

References (41)

1. ACHESON, D. J. 1996 Elementary Fluid Dynamics. Clarendon.
2. AREF, H. & BALACHANDAR, S. 1986 Chaotic advection in a Stokes flow. Phys. Fluids 29, 3515-3521.
3. AREF, H. & JONES, S. W. 1989 Enhanced separation of diffusing particles by chaotic advection. Phys. Fluids A 3, 34-38.
4. AVUDAINAYAGAM, A. & JOTHIRAM, B. 1988 A circle theorem for plane Stokes flows. Q. J. Mech. Appl. Maths 41, 383-393.
5. BOUROT, J.-M. 1969 Sur l'application d'une méthode de moindre carrés à la résolution approchée du problème aux limites, pour certaines catégories d'écoulements. J. Méc. 8, 301-322.
6. BOYLAND, P. 2002 Fluid mechanics and mathematical structures. In An Introduction to the Geometry and Topology of Fluid Flows (ed. R. L. Ricca), pp. 105-134. Kluwer.
7. BOYLAND, P, STREMLER, M. & AREF, H. 2003 Topological fluid mechanics of point vortex motions. Physica D 175, 69-95.
8. BOYLAND, P. L., AREF, H. & STREMLER, M. A. 2000 Topological fluid mechanics of stirring. J. Fluid Mech. 403, 277-304.
9. BUTLER, J. P. & TSUDA, A. 1997 Effect of convective stretching and folding on aerosol mixing deep in the lung, assessed by approximate entropy. J. Appl. Phys. 83, 800-809.
10. CLIFFORD, M. J., COX, S. M. & ROBERTS, E. P. L. 1998 Lamellar modelling of reaction diffusion and mixing in a two-dimensional flow. Chem. Engng J. 71, 49-56.
11. CLIFFORD, M. J., COX, S. M. & ROBERTS, E. P. L. 2000 The influence of a lamellar structure upon the yield of a chemical reaction. Inst. Chem. Engrs 78, 371-377.
12. DRISCOLL, T. A. & TREFETHEN, L. N. 2002 Schwarz-Christoffel Mapping. Cambridge University Press.
13. FINN, M. D. & COX, S. M. 2001 Stokes flow in a mixer with changing geometry. J. Engng Maths 41, 75-99.
14. FRAZER, R. A. 1925 On the motion of circular cylinders in a viscous fluid. Phil. Trans. R. Soc. Lond. A 225, 93-130.
15. GIONA, M. & ADROVER, A. 2001 Global geometry and coarse-grained formulation of the evolution of pointwise intermaterial interface measure in chaotic flows. Chem. Engng Sci. 56, 3387-3399.
16. JANA, S. C., METCALFE, G. & OTTINO, J. M. 1994 Experimental and computational studies of mixing in complex Stokes flows: the vortex mixing flow and multicellular cavity flows. J. Fluid Mech. 269, 199-246.
17. JONES, S. W., THOMAS, O. M. & AREF, H. 1989 Chaotic advection by laminar flow in a twisted pipe. J. Fluid Mech. 209, 335-357.
18. KRASNOPOLSKAYA, T. S.. MELESHKO, V. V., PETERS, G. W. M. & MEIJER, H. E. H. 1999 Mixing in Stokes flow in an annular wedge cavity. J. Mech. B/Fluids 18, 793-822.
19. KUSCH, H. A. & OTTINO, J. M. 1992 Experiments on mixing in continuous chaotic flows. J. Fluid Mech. 236, 319-348.
20. LAMB, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
21. MACAGNO, E. O. & CHRISTENSEN, J. 1980 Fluid mechanics of the duodenum. Annu. Rev. Fluid Mech. 12, 139-158.
22. MACKAY, R. S. 2001 Complicated dynamics from simple topological hypotheses. Phil. Trans. R. Soc. Lond. A 359, 1479-1496.
23. MELESHKO, V. V., GALAKTIONOV, O. S., PETERS, G. W. M. & MEIJER, H. E. H. 1999 Three-dimensional mixing in Stokes flow: the partitioned pipe mixer problem revisited. Eur. J. Mech. B/Fluids 18, 783-792.
24. METCALFE, G. & OTTINO, J. M. 1994 Autocatalytic processes in mixing flows. Phys. Rev. Lett. 72, 2875-2878.
25. MILNE-THOMSON, L. M. 1968 Theoretical Hydrodynamics. Macmillan.
26. MUZZIO, F. J., ALVAREZ, M. M., CERBELLI, S., GIONA, M. & ADROVER, A. 1999 The intermaterial area density generated by time- and spatially periodic 2D chaotic flows. Chem. Engng Sci. 55, 1497-1508.
27. MUZZIO, F. J. & OTTINO, J. M. 1989 Dynamics of a lamellar system with diffusion and reaction: scaling analysis and global kinetics. Phys. Rev. A 40, 7182-7192.
28. MUZZIO, F. J. & OTTINO, J. M. 1990 Diffusion and reaction in a lamellar system: self-similarity with finite rates of reaction. Phys. Rev. A 42, 5873-5884.
29. MUZZIO, F. J. & SWANSON, P. D. 1991 The statistics of stretching and stirring in chaotic flows. Phys. Fluids A 3, 822-834.
30. POLLICOTT, M. & YURI, M. 1998 Dynamical Systems and Ergodic Theory. Cambridge University Press.
31. PRAKASH, S. & KOKINI, J. L. 2000 Estimation and prediction of shear rate distribution as a model mixer. J. Food Engng 44, 135-148.
32. PRICE, T. J., MULLIN, T. & KOBINE, J. J. 2003 Numerical and experimental characterization of a family of two-roll-mill flows. Proc. R. Soc. Lond. A 459, 117-135.
33. RICCA, R. L. & BERGER, M. A. 1996 Topological ideas and fluid mechanics. Physics Today December, 28-34.
34. RUDMAN, M., METCALFE, G., BRYDON, A. & GRAHAM, L. 2001 Numerical mixing experiments in the rotated arc mixer (RAM). In Proceedings of the 6th World Congress of Chemical Engineering.
35. SAATDJIAN, E. & MIDOUX, N. 1996 Chaotic mixing and heat transfer between confocal ellipses: experimental and numerical results. Phys. Fluids 8, 677-691.
36. SAATDJIAN, E., MIDOUX, N. & ANDRÉ, J. C. 1994 On the solution of Stokes' equations between confocal ellipses. Phys. Fluids 6, 3833-3846.
37. SAWYERS, D. R., SEN, M. & CHANG, H. 1996 Effect of chaotic interfacial stretching on bimolecular chemical reaction in helical-coil reactors. Chem. Engng J. 64, 129-139.
38. SEN, S. K. 1989 Circle theorems for steady Stokes flow. Z. Angew. Math. Phys. 40, 139-145.
39. TUFILLARO, N. B., ABBOT, T. & REILLY, J. 1992 An Experimental Approach to Nonlinear Dynamics and Chaos. Addison Wesley.
40. VIKHANSKY, A. 2003 Simulation of topological chaos in laminar flows. Chaos (submitted).
41. ZUMBRUNNEN, D. A. & INAMDAR, S. 2001 Novel sub-micron highly multi-layered polymer films formed by continuous flow chaotic mixing. Chem. Engng Sci. 56, 3893-3897.