Reactive dynamics of inertial particles in nonhyperbolic chaotic flows

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 5 2, 2003, Pages 563071-563075

  Motter, Adilson E ^a   Lai, Ying Cheng ^b   Grebogi, Celso ^c  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^b ARIZONA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSOLS; BOUNDARY CONDITIONS; BUBBLES (IN FLUIDS); CATALYST ACTIVITY; COMPUTATIONAL METHODS; FRACTALS; HAMILTONIANS; LAGRANGE MULTIPLIERS; PROBABILITY; REACTION KINETICS; SET THEORY;

AUTOCATALYTIC REACTIONS; FRACTAL DIMENSIONS; INERTIAL PARTICLES;

FLOW OF FLUIDS;

EID: 0942278428     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. S. Edouard, B. Legras, F. Lefevre, and R. Eymard, Nature (London) 384, 444 (1996).
2. E.R. Abraham, Nature (London) 391, 577 (1998).
3. Z. Toroczkai, G. Károlyi, Á. Péntek, T. Tél, and C. Grebogi, Phys. Rev. Lett. 80, 500 (1998).
4. See, for example, Active chaotic flow, focus issue of Chaos 12, (2002), and references therein.
5. Inertial effects on reactive particles have been previously considered for turbulent flows [R. Reigada, F. Sagués, and J.M. Sancho, Phys. Rev. E 64, 026307 (2001)] and for cellular flows [T. Nishikawa, Z. Toroczkai, C. Grebogi, and T. Tél, ibid. 65, 026216 (2002); Z.H. Liu, Y.-C. Lai, and J.M. Lopez, Chaos 12, 417 (2002)].
6. Inertial effects on reactive particles have been previously considered for turbulent flows [R. Reigada, F. Sagués, and J.M. Sancho, Phys. Rev. E 64, 026307 (2001)] and for cellular flows [T. Nishikawa, Z. Toroczkai, C. Grebogi, and T. Tél, ibid. 65, 026216 (2002); Z.H. Liu, Y.-C. Lai, and J.M. Lopez, Chaos 12, 417 (2002)].
7. Inertial effects on reactive particles have been previously considered for turbulent flows [R. Reigada, F. Sagués, and J.M. Sancho, Phys. Rev. E 64, 026307 (2001)] and for cellular flows [T. Nishikawa, Z. Toroczkai, C. Grebogi, and T. Tél, ibid. 65, 026216 (2002); Z.H. Liu, Y.-C. Lai, and J.M. Lopez, Chaos 12, 417 (2002)].
8. M.R. Maxey and J.J. Riley, Phys. Fluids 26, 883 (1983).
9. Equation (4) is an approximation of the Maxey-Riley equation obtained by neglecting the Faxén corrections, the Basset-Boussinesq history force, and the term [(v-u)·∇]u [A. Babiano, J.H.E. Cartwright, O. Piro, and A. Provenzale, Phys. Rev. Lett. 84, 5764 (2000)].
10. I.J. Benczik, Z. Toroczkai, and T. Tél, Phys. Rev. Lett. 89, 164501 (2002).
11. M.R. Maxey, Phys. Fluids 30, 1915 (1987); E. Balkovsky, G. Falkovich, and A. Fouxon, Phys. Rev. Lett. 86, 2790 (2001).
12. M.R. Maxey, Phys. Fluids 30, 1915 (1987); E. Balkovsky, G. Falkovich, and A. Fouxon, Phys. Rev. Lett. 86, 2790 (2001).
13. A.E. Motter and Y.-C. Lai, Phys. Rev. E 65, 015205 (2002).
14. Y.-T. Lau, J.M. Finn, and E. Ott, Phys. Rev. Lett. 66, 978 (1991).
15. A similar scaling law can be derived in the continuous-time limit τ → 0.
16. T. Tél, T. Nishikawa, A. E. Motter, C. Grebogi, and Z. Toroczkai (unpublished).
17. For α=1, this equation reduces to the first-order approximation of the bailout embedding map introduced by [J.H.E. Cartwright, M.O. Magnasco, and O. Piro, Phys. Rev. E 65, 045203 (2002)] to study the advection dynamics of neutrally buoyant particles.
18. B still reaches a steady state. Since we focus on the area covered by B particles, our results do not depend on the coalescence.
19. f, the reaction undergoes an emptying transition and the Cantori structures near the KAM tori cannot be neglected. In this regime, almost all the particles along the unstable manifold escape between successive reactions, and the hypothesis that reagent B is distributed along approximately uniform stripes breaks down outside the Cantori. However, since Cantori are obstacles to the transport of particles, for small enough σ, a high concentration of particles can still be found inside the hierarchy of Cantori structures. For details we refer to A. P. S. de Moura and C. Grebogi (unpublished).
20. C. Grebogi, S.W. McDonald, E. Ott, and J.A. Yorke, Phys. Lett. 99A, 415 (1983).
21. I.Z. Kiss, J.H. Merkin, S.K. Scott, P.L. Simon, S. Kalliadasis, and Z. Neufeld, Physica D 176, 67 (2003).