Mixing measures for a two-dimensional chaotic Stokes flow

Journal of Engineering Mathematics

Volumn 48, Issue 2, 2004, Pages 129-155

  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; CHEMICAL ANALYSIS; CORRELATION METHODS; MIXING; SIEVES;

CHAOTIC STOKES FLOW; EFFECTIVE PROTOCOLS;

FLOW PATTERNS;

FLUID FLOW; LAMINAR FLOW; MATHEMATICAL METHOD; MIXING; STIRRED TANK; STOKES FLOW;

EID: 1342328975     PISSN: 00220833     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:ENGI.0000011930.55539.69     Document Type: Article

References (49)

1. J.M. Ottino, Mixing and chemical reactions: a tutorial. Chem. Eng. Sci. 49 (1994) 4005-4027.
2. J.M. Zalc and F.J. Muzzio, Parallel-competitive reactions in a two-dimensional chaotic flow. Chem. Eng. Sci. 54 (1999) 1053-1069.
3. M.D. Finn and S.M. Cox, Stokes flow in a mixer with changing geometry. J. Engng. Math. 41 (2001) 75-99.
4. M.D. Finn, S.M. Cox and H.M. Byrne, Topological chaos in inviscid and viscous mixers. To appear J. Fluid Mech. (2003).
5. H. Aref, Stirring by chaotic advection. J. Fluid Mech. 143 (1984) 1-21.
6. H. Aref, The development of chaotic advection. Phys. Fluids 14 (2002) 1315-1325.
7. D. D'Alessandro, M. Dahleh and I. Mezić, Control of mixing in fluid flow: a maximum entropy approach. IEEE Trans. Automatic Control 44 (1999) 1852-1863.
8. H. Aref and S. Balachandar, Chaotic advection in a Stokes flow. Phys. Fluids 29 (1986) 3515-3521.
9. D.M. Hobbs and F.J. Muzzio, Reynolds number effects on laminar mixing in the kenics static mixer, Chem. Engng. J. 70 (1998) 93-104.
10. T. Hwu, D. Young and Y. Chen, Chaotic advections for Stokes flows in circular cavity. J. Engng. Mech. August (1997) 774-782.
11. S.W. Jones, O.M. Thomas and H. Aref, Chaotic advection by laminar flow in a twisted pipe. J. Fluid Mech. 209 (1989) 335-357.
12. J.G. Franjione, C. Leong and J.M. Ottino, Symmetries within chaos: a route to effective mixing. Phys. Fluids 1 (1989) 1772-1783.
13. J.G. Franjione and J.M. Ottino, Symmetry concepts for geometric analysis of mixing flows. Phil. Trans. R. Soc. London A 338 (1992) 301-323.
14. O.S. Galaktionov, P.D. Anderson and G.W.M. Peters, Symmetry of periodic structures in a 3d mixing cavity flow. Phys. Fluids 12 (2000) 469-471.
15. T.S. Krasnopolskaya, V.V. Meleshko, G.W.M. Peters and H.E.H. Meijer, Mixing in Stokes flow in an annular wedge cavity. J. Mech. B/Fluids 18 (1999) 793-822.
16. F.H. Ling, Chaotic mixing in a spatially periodic continuous mixer. Phys. Fluids A 5 (1993) 2147-2160.
17. V.V. Meleshko and G.W.M. Peters, Periodic points for two-dimensional Stokes flow in a rectangular cavity. Phys. Lett. A. 216 (1996) 87-96.
18. T. Hwu, Stretches of fluid materials for Stokes flow in circular cavity. J. Engng. Mech. 126 (2000) 554-557.
19. F.J. Muzzio and P.D. Swanson, The statistics of stretching and stirring in chaotic flows. Phys. Fluids A 3 (1991) 822-834.
20. F.H. Ling, The effect of mixing protocol on mixing in discontinuous cavity flows. Phys. Lett. A 177 (1993) 331-337.
21. D. Rothstein, E. Henry and J.P. Gollub, Persistent patterns in transient chaotic fluid mixing. Nature 401 (1999) 770-772.
22. D.M. Hobbs and F.J. Muzzio, The kenics static mixer: a three dimensional chaotic flow. Chem. Engng. J. 67 (1997) 153-166.
23. H. Aref and S.W. Jones, Enhanced separation of diffusing particles by chaotic advection. Phys. Fluids A 1 (1989) 470-474.
24. F.J. Muzzio, P.D. Swanson and J.M. Ottino, The statistics of stretching and stirring in chaotic flows. Phys. Fluids A 3 (1991) 822-834.
25. M. Giona and A. Adrover, Global geometry and coarse-grained formulation of the evolution of pointwise intermaterial interface measure in choatic flows. Chem. Engng. Sci. 56 (2001) 3387-3399.
26. F.J. Muzzio, M.M. Alvarez, S. Cerbelli, M. Giona and A. Adrover, The intermaterial area density generated by time-and spatially periodic 2D chaotic flows. Chem. Engng. Sci. 55 (1999) 1497-1508.
27. J.M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport. Cambridge: Cambridge University Press (1989) 364 pp.
28. F. Raynal and J. Gence, Energy saving in chaotic laminar mixing. Int. J. Heat Mass Transfer 40 (1997) 3267-3273.
29. V.V. Meleshko and H. Aref, A blinking rotlet model for chaotic advection. Phys. Fluids 8 (1996) 3215-3217 (Errata in Phys. Fluids 10 (1998) 1543).
30. M.J. Clifford, S.M. Cox and E.P.L. Roberts, Lamellar modelling of reaction diffusion and mixing in a two-dimensional flow. Chem. Engng. J. 71 (1998) 49-56.
31. M.J. Clifford, S.M. Cox and E.P.L. Roberts, The influence of a lamellar structure upon the yield of a chemical reaction. Inst. Chem. Engng. 78 (2000) 371-377.
32. G. Metcalfe and J.M. Ottino, Autocatalytic processes in mixing flows. Phys. Rev. Lett. 72 (1994) 2875-2878.
33. F.J. Muzzio and J.M. Ottino, Dynamics of a lamellar system with diffusion and reaction: Scaling analysis and global kinetics. Phys. Rev. A 40 (1989) 7182-7192.
34. F.J. Muzzio and J.M. Ottino, Diffusion and reaction in a lamellar system: Self-similarity with finite rates of reaction. Phys. Rev. A 42 (1990) 5873-5884.
35. D.R. Sawyers, M. Sen and H. Chang, Effect of chaotic interfacial stretching on bimolecular chemical reaction in helical-coil reactors. Chem. Engng. J. 64 (1996) 129-139.
36. S.C. Jana, G. Metcalfe and J.M. Ottino, Experimental and computational studies of mixing in complex Stokes flows: the vortex mixing flow and multicellular cavity flows. J. Fluid Mech. 269 (1994) 199-246.
37. S.C. Jana, M. Tjahjadi and J.M. Ottino, Chaotic mixing of viscous fluids by periodic changes in geometry: baffled cavity flow. Am. Inst. Chem. Engrs. J. 40 (1994) 1769-1781.
38. G.H. Wannier, A contribution to the hydrodynamics of lubrication. Q. Appl. Math. 8 (1950) 1-32.
39. E.P.L. Roberts and M.R. Mackley, The simulation of stretch rates for the quantitative prediction and mapping of mixing within a channel flow. Chem. Engng. Sci. 50 (1995) 3727-3746.
40. A. Adrover, M. Giona, F.J. Muzzio, S. Cerbelli and M.M. Alvarez, Analytic expression for the short-time rate of growth of the intermaterial contact perimeter in two-dimensional chaotic flows and hamiltonian systems. Phys. Rev. E 58 (1998) 447-458.
41. M.M. Alvarez, F.J. Muzzio, S. Cerbelli, A. Adrover and M. Giona, Self-similar spatiotemporal structure of intermaterial boundaries in chaotic flows. Phys. Rev. Lett. 81 (1998) 3395-3398.
42. F.J. Muzzio and M. Liu, Chemical reactions to chaotic flows. Chem. Engng. J. 64 (1996) 117-127.
43. M.J. Clifford, S.M. Cox and E.P.L. Roberts, Measuring striation widths. Phys. Lett. A 260 (1999) 209-217.
44. O. Levenspiel, Chemical Reaction Engineering. 3rd ed. New York:Wiley (1999) 668 pp.
45. T. Atobe, M. Funakoshi and S. Inoue, Orbital instability and chaos in the Stokes flow between two eccentric cylinders. Fluid Dyn. Res. 16 (1995) 115-129.
46. J. Chaiken, R. Chevray, M. Tabor and Q.M. Tan, Experimental study of Lagrangian turbulence in a Stokes flow. Proc. R. Soc. London A 408 (1986) 165-174.
47. H.R. Neave and P.L.B. Worthington, Distribution Free Tests. London: Unwin Hyman (1988) 430 pp.
48. R.L. Davidchack and Y. Lai, Efficient algorithm for detecting unstable periodic orbits in chaotic systems. Phys. Rev. E 60 (1999) 6172-6175.
49. M. D. Finn, S. M. Cox and H. M. Byrne, Chaotic advection in a braided pipe mixer. Phys. Fluids 15 (2003) 77-80.