Exploring Nonlinear Reaction-Diffusion in Enzyme Immobilized Systems: Integer and Fractional Order Modeling.

Area of Science:

• Chemical Engineering
• Biocatalysis
• Reaction Kinetics

Background:

• Porous catalysts and immobilized enzymes are crucial in various chemical and biological processes.
• Modeling reaction kinetics in these systems is complex due to diffusion and reaction interactions.
• Existing models often lack the ability to capture complex dynamics within porous matrices.

Purpose of the Study:

• To develop a Langmuir-Hinshelwood-Hougen-Watson (LHHW) kinetic model for porous catalysts with simple 1D geometry.
• To apply the LHHW model to systems involving immobilized enzymes, considering reaction-diffusion.
• To introduce fractional derivatives for a more accurate representation of enzyme reaction kinetics.

Main Methods:

• Developed a nonlinear reaction-diffusion equation incorporating finite-range Fickian diffusion and nonlinear reaction kinetics.
• Introduced fractional derivatives to model substrate concentration and reaction rates within porous supports.
• Employed the Lucas Wavelet Method (LWM) for analytical solutions and compared with the fourth-order Runge-Kutta method.

Main Results:

• The LHHW model effectively described kinetics in heterogeneous porous catalysts and immobilized enzymes.
• Fractional derivatives accurately captured complex substrate interaction and reaction dynamics.
• LWM provided accurate analytical solutions for substrate concentration and effectiveness factors, validated by numerical methods.

Conclusions:

• The developed fractional kinetic model optimizes diffusion and reaction kinetics in biocatalysis.
• This research advances the understanding and design of efficient enzyme reactors.
• The findings pave the way for improved biocatalytic processes and enzyme reusability.