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Advective coalescence in chaotic flows.

T Nishikawa¹, Z Toroczkai, C Grebogi

¹Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA.

Physical Review Letters

|July 20, 2001

Summary

Inertial particles in chaotic flows exhibit universal reaction kinetics. Their reaction rate decays as t(-1), forming filamentary structures due to nonlinear dynamics.

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Area of Science:

Fluid dynamics
Chemical kinetics
Nonlinear dynamics

Background:

Investigating reaction kinetics of inertial particles in complex fluid flows.
Understanding particle dynamics governed by nonlinear Maxey-Riley equations.
Observing chaotic spatial dynamics and filament formation in reactant distribution.

Purpose of the Study:

To analyze the reaction kinetics of inertial particles in time-periodic hydrodynamical flows.
To characterize the universal behavior of reaction kinetics in chaotic advection.
To determine the relationship between particle dynamics, reactant distribution, and reaction rate.

Main Methods:

Modeling particle dynamics using the nonlinear Maxey-Riley equations.
Employing a stochastic description based on the natural measure of the chaotic flow attractor.
Analyzing reaction kinetics in the limit of slow reaction rates.

Main Results:

Particle dynamics exhibit chaotic behavior, leading to filamentary reactant structures.
A universal reaction kinetics behavior is observed, characterized by a t(-1) decay in reagent amounts.
Reactants distribute on a subset of dimension D2, corresponding to the chaotic flow's correlation dimension.

Conclusions:

The study reveals universal reaction kinetics for inertial particles in chaotic flows.
The t(-1) decay in reaction rate is a key finding, linked to the chaotic dynamics.
The fractal dimension of the attractor governs the distribution and reaction of particles.

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