Fractional differentiation method: Application to the trapping reactions in the comb-like structures with relaxation

Area of Science:

• Physical Chemistry
• Chemical Kinetics
• Complex Systems

Background:

• Subdiffusion and reactions in confined geometries are crucial in diverse scientific fields.
• Previous work has explored diffusion transport with and without inertial effects.
• Comb-like structures present unique challenges for modeling diffusion and reaction dynamics.

Purpose of the Study:

• To investigate trapping diffusion-controlled reactions within the backbone of a 2D comb structure.
• To incorporate inertial effects into the reaction-diffusion model.
• To analytically derive the reaction rate coefficient.

Main Methods:

• Utilized Compte-Metzler analysis to select a fractional diffusive Cattaneo system.
• Derived a diffusion equation with a 1/2-order fractional time derivative.
• Employed fractional differentiation methods for analytical evaluation.

Main Results:

• An analytical expression for the trapping reaction rate coefficient was derived.
• The derived expressions are valid for both short and long time regimes.
• Numerical calculations demonstrated excellent agreement with the analytical results.

Conclusions:

• The fractional diffusive Cattaneo system effectively models inertial effects in subdiffusion-controlled reactions.
• Accurate analytical predictions of reaction rate coefficients are achievable.
• This approach provides a robust framework for studying complex reaction-diffusion systems.