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Persistent localized states for a chaotically mixed bistable reaction.

Stephen M Cox1

  • 1School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom. stephen.cox@nottingham.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2007
PubMed
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A bistable chemical reaction in chaotic flow can spread globally or vanish. We discovered a new intermediate case where a persistent, localized "hot spot" forms under specific mixing conditions.

Area of Science:

  • Fluid Dynamics
  • Chemical Kinetics
  • Nonlinear Dynamics

Background:

  • Bistable chemical reactions in chaotic laminar flow exhibit dichotomous behavior based on fluid mixing rates.
  • Slow mixing promotes global spread of localized disturbances, while rapid mixing leads to extinction.

Purpose of the Study:

  • To investigate the evolution of bistable chemical reactions in a two-dimensional chaotic laminar flow.
  • To identify and characterize previously unremarked intermediate behaviors in such systems.

Main Methods:

  • Simulating a bistable chemical reaction within a closed two-dimensional chaotic laminar flow.
  • Analyzing the influence of fluid mixing rates and the Damköhler number on reaction dynamics.
  • Employing a reduced, lamellar model to study localized disturbance behavior.

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Main Results:

  • A novel intermediate regime was identified, characterized by a persistent, highly localized disturbance or "hot spot."
  • This localized state emerges when the Damköhler number is sufficient to sustain the hot spot but insufficient for global spread.
  • The localized disturbance is found to be associated with the neighborhood of an unstable periodic orbit of the flow.

Conclusions:

  • The study reveals a new mode of bistable chemical reaction evolution in chaotic flows, distinct from global spread or extinction.
  • The existence of persistent localized states is contingent on a balance between reaction kinetics (Damköhler number) and fluid mixing.
  • Understanding these localized states, linked to unstable periodic orbits, offers new insights into pattern formation in reactive fluid systems.