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

Abstract

This paper presented a kinetic model of the Langmuir-Hinshelwood-Hougen-Watson (LHHW) type for porous catalysts with simple one-dimensional geometry, including spheres, infinite cylinders, and flat pellets. The model was applied to systems involving immobilized enzymes, where enzymes are attached to porous support materials to enhance stability and reusability. The LHHW model provided a tool for understanding and modeling reaction kinetics in heterogeneous porous catalysts and immobilized enzymes. A nonlinear reaction-diffusion equation was generated using finite-range Fickian diffusion and nonlinear reaction kinetics, crucial for accurately modeling the behavior of immobilized enzymes. This research addressed a gap in the existing literature by introducing fractional derivatives to investigate enzyme reaction kinetics, capturing the complex dynamics of substrate interaction and reaction rates within the porous matrix. An approximation method based on Lucas wavelets was employed to find solutions for substrate concentration and effectiveness factors across various parameter values. The analytical solutions derived from the Lucas wavelet method (LWM) were evaluated against the fourth-order Runge-Kutta method, showing great agreement between the LWM solutions and numerical counterparts. These results optimized diffusion and reaction kinetics, paving the way for advancements in biocatalysis and efficient enzyme reactor design.