Eigenvalue-eigenfunction analysis of infinitely fast reactions and micromixing regimes in regular and chaotic bounded flows

Chemical Engineering Science

Volumn 59, Issue 11, 2004, Pages 2125-2144

  Cerbelli, Stefano ^a   Vitacolonna, Valerio ^a   Adrover, Alessandra ^a   Giona, Massimiliano ^a  

^a Dipartimento di Ingegneria Chimica   (Italy)

Author keywords

Fluid dynamics; Micromixing; Reacting flows

Indexed keywords

COMPACTION; DIFFUSION; SPECTRUM ANALYSIS; STIRLING CYCLE;

EIGENVALUE; FAST KINETICS; INCOMPRESSIBLE;

REACTION KINETICS;

CHAOS; EIGENVALUE; FLUID DYNAMICS; MIXING;

EID: 2542452798     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2004.02.005     Document Type: Article

References (44)

1. Adrover A. Cerbelli S. Giona M. A spectral approach to reaction-diffusion kinetics in chaotic flows Comput. Chem. Eng. 26 2002 125-139
2. Baldyga J. Bourne J.R. The effect of micromixing on parallel reactions Chem. Eng. Sci. 45 1990 907-916
3. Baldyga J. Bourne J.R. Turbulent Mixing and Chemical Reaction 1999 Wiley Chichester
4. Bourne J.R. Mixing on the molecular scale (micromixing) Chem. Eng. Sci. 38 1983 5-8
5. Bourne J.R. Kozicki F. Mixing effects during the bromination of 1,3,5-trimetoxybenzene Chem. Eng. Sci. 32 1977 1538-1539
6. Castiglione P. Mazzino A. Muratore-Gianneschi P. Vulpiani A. On strong anomalous diffusion Physica D 134 1999 75-93
7. Cerbelli S. Adrover A. Giona M. Enhanced diffusion regimes in bounded chaotic flows Phys. Lett. A 312 2003 355-362
8. Chella R. Ottino J.M. Conversion and selectivity modifications due to mixing in unpremixed reactors Chem. Eng. Sci. 39 1984 551-567
9. Danckwertz P.V. Measurement of molecular homogeneity in a mixture Chem. Eng. Sci. 7 1957 116-117
10. Faierman M. On the spectral theory of an elliptic boundary value problem involving an indefinite weight Gohberg I. Langer H. Operator Theory and Boundary Eigenvalue Problems 1995 Birkhäuser Basel
11. Fannjiang A. Papanicolaou G. Convection-enhanced diffusion for periodic flows SIAM J. Appl. Math. 54 1994 333-408
12. Fannjiang A. Papanicolaou G. Convection-enhanced diffusion for random flows J. Stat. Phys. 88 1997 1033-1076
13. Fox R.O. On the relationship between Lagrangian micromixing models and computational fluid dynamics Chem. Eng. Proc. 37 1998 521-535
14. Franjione J.G. Ottino J.M. Symmetry concepts for geometric analysis of mixing flows Philos. Trans. R. Soc. London A 338 1992 301-323
15. Garcia-Rosas J. Petrozzi S. Influence of mixing in the azo coupling of 1-naphtol and diatosized aniline Chimia 44 1990 366-368
16. Giona M. Adrover A. Nonuniform stationary measure of the invariant unstable foliation in Hamiltonian and fluid mixing systems Phys. Rev. Lett. 81 1998 3864-3867
17. Giona M. Cerbelli S. Adrover A. Quantitative analysis of mixing structures in chaotic flows generated by infinitely fast reaction in the presence of diffusion J. Phys. Chem. 106 2002 5722-5736
18. Giona M. Cerbelli S. Adrover A. Geometry of reaction interfaces in chaotic flows Phys. Rev. Lett. 88 2002 024501
19. Giona, M., Cerbelli, S., Adrover, A., 2004. Homogenization exponents in regular and chaotic bounded flows, in preparation.
20. Golub G.H. Van Loan C.F. Matrix Computations 1983 Johns Hopkins University Press Baltimore, MD
21. Harvey III A.D. Rogers S.E. Steady and unsteady computation of impeller-stirred reactor A.I.Ch.E. J. 42 1996 2701-2712
22. Hess P. On the asymptotic distribution of eigenvalues of some non selfadjoint problems Bull. London Math. Soc. 18 1986 181-184
23. Karpeshina Y.E. Perturbation Theory for the Schrödinger Operator with a Periodic Potential 1997 Springer Berlin
24. Liu M. Muzzio F.J. Peskin R.L. Quantification of mixing in aperiodic flows Chaos Solitons Fractals 4 1994 869-893
25. Majda A.J. Kramer P.R. Simplified model for turbulent diffusion: Theory, numerical modelling and physical phenomena Phys. Rep. 314 1999 237-574
26. Muzzio F.J. Liu M. Chemical reactions in chaotic flows Chem. Eng. J. 64 1996 117-127
27. Muzzio F.J. Ottino J.M. Evolution of a lamellar system with diffusion and reaction: A scaling approach Phys. Rev. Lett. 63 1989 47-50
28. Nienow A.W. Drain S.M. Boyes A.P. Mann R. El-Hamouz A.M. Carpenter K.J. A new pair of reactions to characterize imperfect macro-mixing and partial segregation in a stirred semi-batch reactor Chem. Eng. Sci. 47 1992 2825-2830
29. Ottino J.M. The Kinematics of Mixing. Stretching, Chaos, and Transport 1989 Cambridge University Press Cambridge
30. Ranz W.E. Application of a stretch model to mixing, diffusion and reaction in laminar and turbulent flows A.I.Ch.E. J. 25 1979 41-47
31. Reed M. Simon B. Methods of Modern Mathematical Physics: I-Functional Analysis 1980 Academic Press New York
32. Reigada R. Sagues F. Sokolov I.M. Sancho J.M. Blumen A. Kinetics of the A+B→ O under steady and turbulent flow J. Chem. Phys. 105 1996 10925-10933
33. Reigada R. Sagues F. Sokolov I.M. Sancho J.M. Blumen A. Fluctuation dominated kinetics under stirring Phys. Rev. Lett. 78 1997 741-744
34. Robinson J.C. Infinite-dimensional Dynamical Systems 2001 Cambridge University Press Cambridge
35. Rosenbluth M.N. Berk H.L. Doxas I. Horton W. Effective diffusion in laminar convective flows Phys. Fluids 30 1987 2636-2647
36. Sell G.R. You Y. Dynamics of Evolutionary Equations 2000 Springer New York
37. Sokolov I.M. Blumen A. Mixing in reaction diffusion problems Int. J. Mod. Phys. 20 1991 3127
38. Sukhatme J. Pierrehumbert R.T. 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 2002 056302
39. Temam R. Infinite-dimensional Mechanical Systems in Mechanics and Physics 1997 Springer New York
40. Toussaint V. Carriere P. Raynal F. A numerical Eulerian approach to mixing by chaotic advection Phys. Fluids 7 1995 2587-2600
41. Toussaint V. Carriere P. Scott J. Gence J.-N. Spectral decay of a passive scalar in chaotic mixing Phys. Fluids 12 2000 2834-2844
42. Villermaux J. Mixing effects on complex chemical reactions in a stirred reactor Rev. Chem. Eng. 7 1991 51-108
43. Zalc J.M. Muzzio F.J. Parallel-competitive reactions in a two-dimensional chaotic flow Chem. Eng. Sci. 54 1999 1053-1069
44. Zalc J.M. Alvarez M.M. Muzzio F.J. Arick B.E. Extensive validation of computed laminar flow in a stirred tank with three Rushton turbines A.I.Ch.E. J. 47 2001 2144-2154