### Abstract

Chemical and biological processes often take place in fluid flows. Many of them, like environmental or microfluidical ones, generate filamentary patterns which have a fractal structure, due to the presence of chaos in the underlying advection dynamics. In such cases, hydrodynamical stirring strongly couples to the reactivity of the advected species: the outcome of the reaction is then typically different from that of the same reaction taking place in a well-mixed environment. Here we review recent progress in this field, which became possible due to the application of methods taken from dynamical system theory. We place special emphasis on the derivation of effective rate equations which contain singular terms expressing the fact that the reaction takes place on a moving fractal catalyst, on the unstable foliation of the reaction free advection dynamics. (c) 2005 Elsevier B.V All rights reserved.

Original language | English |
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Pages (from-to) | 91-196 |

Number of pages | 105 |

Journal | Physics Reports |

Volume | 413 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - Jul 2005 |

### Keywords

- reaction
- chaotic advection
- diffusion
- filamentary fractal
- advection-reaction-diffusion
- population dynamics
- inertial effect
- non-hyperbolic effect
- OPEN HYDRODYNAMICAL FLOWS
- CHLORITE IODIDE REACTION
- OPEN CHAOTIC FLOWS
- PLANKTON DYNAMICS
- 2-DIMENSIONAL TURBULENCE
- AUTOCATALYTIC REACTIONS
- MULTIFRACTAL STRUCTURE
- ZHABOTINSKY REACTION
- PHYTOPLANKTON BLOOM
- STRANGE ATTRACTORS

### Cite this

*Physics Reports*,

*413*(2-3), 91-196. https://doi.org/10.1016/J.PHYSREP.2005.01.005