Analisis Numerik Proses Difusi-Reaksi pada Biofuel Cell Berbasis Enzim Termediasi

Abstract

Model matematis untuk proses difusi-reaksi pada elektroda biofuel cell berbasis enzim dirancang dari persamaan difusi dengan suku nonlinear Michaelis-Menten yang menggambarkan kinetika reaksi enzimatik pada lapisan polimer redoks. Model ini diselesaikan secara numerik menggunakan metode beda hingga eksplisit dalam aplikasi pemrograman Octave. Solusi numerik menunjukkan kesesuaian yang sangat baik dengan solusi analitik, baik dalam respon rapat arus dan rapat daya pada kondisi transien, maupun profil konsentrasi substrat dan mediator di sepanjang film polimer redoks. Pengaruh parameter yang dapat dikendalikan seperti koefisien difusi mediator, potensial Nernst, ketebalan lapisan film polimer redoks, dan konsentrasi substrat terhadap rapat arus juga disajikan secara grafis dan dibahas secara rinci. Hasil numerik menunjukkan bahwa perubahan parameter tersebut memberikan dampak signifikan pada respon arus biofuel cell berbasis enzim.

A mathematical model for the reaction-diffusion process occurring at the electrode of an enzymatic biofuel cell was formulated using the reaction-diffusion equation. This equation includes a nonlinear Michaelis-Menten term that characterizes the dynamics of enzymatic reactions within the redox polymer film. The model was numerically solved using the explicit finite difference method, which was developed within the Octave programming software. The numerical solutions show excellent agreement with the analytical results, both in terms of current and power density respons under transient conditions, as well as the concentration profiles of the substrate and mediator across the redox polymer film. The influence of controllable parameters such as diffusion coefficient of the mediator, Nernst potential, redox polymer film thickness, and bulk concentration of the substrate on the current density are also presented graphically and discussed in detail. Numerical results show that changes in these parameters have a significant impact on the current response of the enzyme-based biofuel cell.