Characterization of stationary mixing patterns in a three-dimensional open Stokes flow: Spectral properties, localization and mixing regimes

Journal of Fluid Mechanics

Volumn 639, Issue , 2009, Pages 291-341

  Giona, M ^a   Cerbelli, S ^a   Garofalo, F ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CYLINDERS (SHAPES); MIXING; SPECTRUM ANALYSIS;

CREEPING FLOW REGIME; DOMINANT EIGENVALUES; INDEPENDENT VARIABLES; LOCALIZATION PROPERTIES; OPERATING CONDITION; OPERATING PARAMETERS; SIMPLIFYING ASSUMPTIONS; SPECTRAL PROPERTIES;

EIGENVALUES AND EIGENFUNCTIONS;

COUETTE FLOW; DIMENSIONLESS NUMBER; EIGENVALUE; FLOW MODELING; FLUID DYNAMICS; GEOMETRY; HOMOGENEITY; NAVIER-STOKES EQUATIONS; NUMERICAL MODEL; OPEN CHANNEL FLOW; RADIAL DIFFUSION; SPECTRAL ANALYSIS; THREE-DIMENSIONAL FLOW; TURBULENT DIFFUSION; TURBULENT MIXING;

EID: 76349093389     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009991066     Document Type: Article

References (60)

1. Ananthakrishnan, V., Gill, W. N. & Barduhn, A. J. 1965 Laminar dispersion in capillaries. Part I. Mathematical analysis. AIChE J. 11, 1063-1072.
2. Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1-21.
3. Aris, R. 1956 On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. A 235, 67-77.
4. Bajer, K., Bassom, A. P. & Gilbert, A. D. 2001 Accelerated diffusion in the centre of a vortex. J. Fluid Mech. 437, 395-411.
5. Baldyga, J. & Bourne, J. R. 1999 Turbulent Mixing and Chemical Reactions. Wiley & Sons.
6. Beebe, D. J., Mensing, G. A. & Walker, G. M. 2002 Physics and applications of microfluidics in biology. Annu. Rev. Biomed. Engng 4, 261-286.
7. Beigie, D., Leonard, A. & Wiggins, S. Invariant manifold templates for chaotic advection. Chaos Solitons Fractals 4, 749-868.
8. Bensoussan, A., Lions, J.-L. & Papanicolau, G. 1978 Asymptotic Analysis for Periodic Structures. North-Holland.
9. Bohm, D. 1952 A suggested interpretation of the quantum theory in terms of "hidden" variables. I. Phys. Rev. 85, 166-179.
10. Boyland, P. L., Aref, H. & Stremler, M. A. 2000 Topological fluid mechanics of stirring. J. Fluid Mech. 403, 277-304.
11. Castelain, C., Mokrani, A., Legentilhomme, P. & Peerhossaini, H. 1997 Residence time distribution in twisted pipe flows: helical coiled system and chaotic system. Exp. Fluids 22, 359-368.
12. Cerbelli, S., Vitacolonna, V., Adrover, A. & Giona, M. 2004 Eigenvalue-eigenfunction analysis of infinitely fast reactions and micromixing regimes in regular and chaotic bounded flows. Chem. Engng Sci. 59, 2125-2144.
13. Childress, S. & Gilbert, A. D. 1995 Stretch, Twist and Fold: The Fast Dynamo. Springer.
14. Danckwerts, P. V. 1953 Continuous flow systems. Chem. Engng Sci. 2, 1-13.
15. Danckwerts, P. V. 1958 The effect of incomplete mixing on homogeneous reactions. Chem. Engng Sci. 8, 93-102.
16. Fannjiang, A. & Papanicolaou, G. 1994 Convection enhanced diffusion for periodic flows. SIAM J. Appl. Math. 54, 333-408.
17. Giona, M., Adrover, A. & Cerbelli, S. 2005 On the use of the pulsed-convection approach for modelling advection-diffusion in chaotic flows-a prototypical example and direct numerical simulations. Physica A 348, 37-73.
18. Giona, M., Adrover, A. & Cerbelli, S. 2009 Spectral analysis of the weighted Laplacian in slip and no-slip flows, Phys. Rev. E (submitted).
19. Giona, M. Cerbelli, S. & Creta, F. 2008 Spectral properties and universal behaviour of advecting-diffusing scalar fields in finite-length channels. J. Fluid Mech. 612, 387-406.
20. Giona, M., Cerbelli, S. & Vitacolonna, V. 2004a Spectral properties and transport mechanisms of partially chaotic bounded flows in the presence of diffusion. Phys. Rev. Lett. 92, 114101.
21. Giona, M., Cerbelli, S. & Vitacolonna, V. 2004b Universality and imaginary potentials in advection-diffusion equations in closed flows. J. Fluid Mech. 513, 221-237.
22. Giona, M., Vitacolonna, V., Cerbelli, S. & Adrover, A. 2004c Advection-diffusion in non-chaotic closed flows: non-Hermitian operators, universality and localization. Phys. Rev. E 70, 046224 I-XII.
23. Gleeson, J. P. 2005 Transient micromixing: examples of laminar and chaotic stirring. Phys. Fluids 17, 100614.
24. Gleeson, J. P., Roche, O. M., West, J. & Gelb, A. 2004 Modelling annular micromixers. SIAM J. Appl. Math. 64, 1294-1310.
25. Hardt, S., Drese, K. S., Hessel, V. & Schönfeld, F. 2005 Passive micromixers for applications in the microreactor and μTA S fi e l d s. Microfluid Nanofluid 1, 108-118.
26. Ho, C.-M. & Tai, Y.-C. 1998 Micro-electro-mechanical systems (MEMS) and fluid flows. Annu. Rev. Fluid Mech. 30, 579-612.
27. Hobbs, D. M. & Muzzio, F. J. 1998 Optimization of static mixer using dynamical system techniques. Chem. Engng Sci. 53, 3199-3213.
28. Jen, C.-P., Wu, C.-Y., Lin, Y.-C. & Wu, C.-Y. 2003 Design and simulation of the micromixer with chaotic advection in twisted microchannels. Lab on a Chip 3, 77-81.
29. Karniandakis, G., Beskok, A. & Aluru, N. 2005 Microflows and Nanoflows. Springer.
30. Kim, H. J. K. & Beskok, A. 2007 Quantification of chaotic strength and mixing in a micro fluidic system. J. Micromech. Microengng 17, 2197-2210.
31. Kim, D. S., Lee, S. H., Kwon, T. H. & Ahn, C. H. 2005 A serpentine laminating micromixer combining splitting/recombination and advection. Lab on a Chip 5, 739-747.
32. Liu, W. & Haller, G. 2004 Inertial manifolds and completeness of eigenmodes for unsteady magnetic dynamos. Physica D 194, 297-319.
33. Liu, W. & Haller, G. 2004 Strange eigenmodes and decay of variance in the mixing of diffusive tracers. Physica D 188, 1-39.
34. Majda, A. J. & Kramer, P. R. 1999 Simplified models for turbulent diffusion: theory, numerical modelling and physical phenomena. Phys. Rep. 314, 237-574.
35. Metcalfe, G., Rudman, M., Brydon, A., Graham, L. J. W. & Hamilton, R. 2006 Composing chaos: an experimental and numerical study of an open duct mixing flow. AIChE J. 52, 9-28.
36. Nguyen, N.-T. & Wereley, S. T. 2006 Fundamentals and Applications of Microfluidics. Artech House.
37. Nguyen, N.-T. & Wu, Z. 2005 Micromixers-a review. J. Micromech. Microengng 15, R1-R16.
38. Pelesko, J. A. & Bernstein, D. H. 2003 Modelling MEMS and NEMS. CRC.
39. Perugini, D., Poli, G. & Mazzuoli, R. 2003 Chaotic advection, fractals and diffusion during mixing of magmas: evidence from lava flows. J. Volcanol. Geotherm. Res. 124, 255-279.
40. Pikovsky, A., & Popovich, O. 2003, Persistent patterns in deterministic mixing flows. Europhys. Lett. 61, 625-631.
41. Raynal, F., Beuf, A., Plaza, F., Scott, J., Carriere, P., Cabrera, M., Cloarec, J.-P. & Souteyrand, E. 2007 Towards better DNA chip hybridization using chaotic advection. Phys. Fluids 19, 017112.
42. Rhines, P. B. & Young, W. R. 1983 How rapidly is a passive scalar mixed within closed streamlines? J. Fluid Mech. 133, 133-145.
43. Salmon, J.-B. & Ajdari, A. 2007 Transverse transport of solutes between co-flowing pressure-driven streams for microfluidic studies of diffusion/reaction processes. J. Appl. Phys. 101, 074902 1-7.
44. Scheuring, I., Karolyi, G., Pentek, A., Tel, T. & Toroczkai, Z. 2000 A model for resolving the plankton paradox: coexistence in open flows. Freshwater Biol. 45, 123-132.
45. Scheuring, I., Karolyi, G., Toroczkai, Z., Tel, T. & Pentek, A. 2003 Competing populations in flows with chaotic mixing. Theor. Popul. Biol. 63, 77-90.
46. Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.
47. Shepherd, T. G., Koshyk, J. G. & Ngan, K. 2000 On the nature of large-scale mixing in the stratosphere and mesosphere. J. Geophys. Res. 105, 12433-12446.
48. Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanonliter scale. Rev. Mod. Phys. 77, 977-1026.
49. Straube, A. V. & Pikovsky, A. 2007 Mixing-induced global modes in open active flows. Phys. Rev. Lett. 99, 184503.
50. Sukhatme, J. & Pierrehumbert, R. T. 2002 Decay of passive scalars under the action of single scale smooth velocity fields in bounded domains: from non self-similar probability distribution functions to self-similar eigenmodes. Phys. Rev. E 66, 056302.
51. Szalai, E. & Muzzio, F. J. 2003 Fundamental approach to the design and optimization of static mixers. AIChE J. 49, 2687-2699.
52. Taylor, G. 1953 Dispersion of soluble matter in a solvent flowing slowly through a tube. Proc. R. Soc. A 219, 186-203.
53. Tel, T., de Moura, A., Grebogi, C., Karolyi, G. 2005 Chemical and biological activity in open flows: a dynamical system approach. Phys. Rep. 413, 91-196.
54. Thyagaraja, A., Loureiro, N. & Knight, P. J. 2002 Spectral and evolutionary analysis of the advection-diffusion equations and the shear flow paradigm. J. Plasma Phys. 68, 363-388.
55. Toussaint, V., Carriere, P. & Raynal, F. 1995 A numerical Eulerian approach to mixing by chaotic advection. Phys. Fluids 7, 2587-2600.
56. Toussaint, V., Carriere, P., Scott, J. & Gence, J.-N. 2000 Spectral decay of a passive scalar in chaotic mixing. Phys. Fluids 12, 2834-2844.
57. Trachsel, F., Günther, A., Khan, S. & Jensen, K. F. 2005 Measurement of residence time distribution in microfluidic systems. Chem. Engng Sci. 60, 5729-5737.
58. Voth, G. A., Haller, G. & Gollub, J. P. 2002 Experimental measurements of stretching fields in fluid mixing. Phys. Rev. Lett. 88, 254-501.
59. Wu, Z. & Nguyen, N.-T. 2005 Convective-diffusive transport in parallel lamination micromixers. Microfluid Nanofluid 1, 208-217.
60. Zwietering, T. N. 1959 The degree of mixing in continuous flow systems. Chem. Engng Sci. 11, 1-15.