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Persistent effects of inertia on diffusion-influenced reactions: Theoretical methods and applications
Sangyoub Lee1, Sergey D Traytak2, Kazuhiko Seki3
1Department of Chemistry, Seoul National University, Seoul 08826, South Korea.
The Journal of Chemical Physics
|October 10, 2023
Summary
This study modifies the Cattaneo-Vernotte model to include reaction effects, clarifying how reaction current density is expressed. It reveals how momentum relaxation and inertial effects impact reaction rates, particularly when reactant velocity dependence is considered.
Area of Science:
- Chemical kinetics
- Transport phenomena
- Statistical mechanics
Background:
- The Cattaneo-Vernotte model is crucial for understanding momentum relaxation in transport equations.
- The influence of reactions on this model, especially reaction current density, remains incompletely understood.
Purpose of the Study:
- To derive a modified Cattaneo-Vernotte model incorporating reaction effects.
- To elucidate the expression of reaction current density within this framework.
- To analyze the impact of inertial and momentum relaxation effects on reaction rates.
Main Methods:
- Application of the projection operator method to the Fokker-Planck-Kramers equation with a reaction sink.
- Derivation using a Grad procedure.
- Analysis of the modified Smoluchowski equation with memory kernels.
Main Results:
- A modified Cattaneo-Vernotte model accounting for reactions was successfully derived.
- Inertial effects were shown to modulate reaction rate coefficients based on velocity dependence.
- Momentum relaxation effects were incorporated via a modified Smoluchowski equation with a memory kernel.
Conclusions:
- The derived model clarifies reaction current density expression in the Cattaneo-Vernotte framework.
- The study highlights the complex interplay between momentum relaxation, inertial effects, and reaction kinetics.
- Velocity-dependent reaction rate constants necessitate memory kernels due to competing fluxes.
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