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Mixing and reaction fronts in laminar flows
M Leconte1, J Martin, N Rakotomalala
1Laboratoire Fluides Automatique et Systèmes Thermiques, Universités P. et M. Curie and Paris Sud, C.N.R.S. (UMR7608), Bâtiment 502, Campus Universitaire, 91405 Orsay, France.
The Journal of Chemical Physics
|July 23, 2004
Summary
Autocatalytic reaction fronts are modeled using Taylor dispersion for slow kinetics and eikonal equations for fast kinetics. Numerical simulations confirm these theories, applicable to microfluidics and larger scales respectively.
Area of Science:
- Chemical kinetics
- Fluid dynamics
- Mathematical modeling
Background:
- Autocatalytic reaction fronts propagate as solitary waves without flow.
- Fluid flow introduces advection and diffusion, enhancing mixing and leading to Taylor hydrodynamic dispersion.
Purpose of the Study:
- To develop asymptotic theories for autocatalytic reaction fronts under imposed flow.
- To analyze the interplay of flow, diffusion, and reaction kinetics.
Main Methods:
- Asymptotic theories for small and large Thiele modulus (slow and fast kinetics).
- Incorporation of flow, diffusion, and reaction into theoretical models.
- Numerical simulations using a lattice gas model.
Main Results:
- For slow kinetics (small Thiele modulus), Taylor dispersion accurately describes front propagation.
- For fast kinetics (large Thiele modulus), the eikonal equation governs the leading-order behavior.
- Numerical simulations show good agreement with both theoretical models.
Conclusions:
- The study provides theoretical frameworks for understanding reaction front dynamics in flowing systems.
- The Taylor dispersion model is relevant for microfluidics.
- The eikonal model is applicable to larger-scale phenomena.