Effective dimensions and chemical reactions in fluid flows

  • Károlyi G
  • Tél T
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Abstract

We show that chemical activity in hydrodynamical flows can be understood as the outcome of three basic effects: the stirring protocol of the flow, the local properties of the reaction, and the global folding dynamics which also depends on the geometry of the container. The essence of each of these components can be described by simple functional relations. In an ordinary differential equation approach, they determine a new chemical rate equation for the concentration, which turns out to be coupled to the dynamics of an effective fractal dimension. The theory predicts an exponential convergence to the asymptotic chemical state. This holds even in flows characterized by a linear stirring protocol where transient fractal patterns are shown to exist despite the lack of any chaotic set of the advection dynamics. In the exponential case the theory applies to flows of chaotic time dependence (chaotic flows) as well.

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