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This article presents a theoretical analysis of homogeneous redox catalysis in electrochemical reactions. A nonlinear differential system is used as a model in which a nonlinear term is linked to homogeneous reactions. The concentration of the mediator and substrate at a planar electrode is computed using an analytical method under pure kinetic conditions and constant substrate concentration. This simplifies the analysis, which can be achieved with slow-scan rates and concentrations in real-world scenarios. The resulting current–potential responses have an S shape and are independent of the scan rate. The impact of two essential parameters on the current is investigated. The derived analytical expressions show high accuracy when compared to numerical results, which show satisfactory agreement. The limiting cases for the concentration characteristics and current–potential response are also investigated. [ABSTRACT FROM AUTHOR]

In this contribution, a Langmuir–Hinshelwood–Hougen–Watson (LHHW) type kinetic model is discussed for simple one-dimensional geometry of porous catalysts such as a sphere, infinite cylinder, and flat pellets. The system is described in finite-range Fickian diffusion and nonlinear reaction kinetics to produce a nonlinear reaction–diffusion equation. This paper aims to employ efficient and reliable approximate analytical methods to derive semi-analytical expressions for species concentrations and the effectiveness factor for the underlying kinetic model. The accuracy of the derived approximate analytical expressions of the concentrations is validated by directed comparison with derived numerical simulations. The analytical expressions will simplify investigating the effect of various parameters on the concentration and effectiveness factor. [ABSTRACT FROM AUTHOR]

A mathematical model of immobilized enzyme system in a porous planar, cylindrical, and spherical particle is discussed. The model is based on a nonlinear factor associated with reversible Michaelis–Menten kinetics of the enzyme process. The reliable semi-analytical is a special case of Akbari-Ganji method is used to solve the nonlinear reaction–diffusion equation in the immobilized enzymes system. Hence, closed-form approximate analytic expressions for the concentration and effectiveness factors profile are derived. The effect of various parameters on the governing equation is analytically studied. The accuracy of the derived analytical results is validated by direct comparison with MATLAB-generated numerical simulations, where significant agreement between the numerical and analytical expressions is noted. The proposed method is extendable to various nonlinear reaction–diffusion models that emerge in immobilized enzyme systems. [ABSTRACT FROM AUTHOR]

A mathematical model of an amperometric biosensor response for uncompetitive inhibition detection is discussed. The model is based on a system of reaction–diffusion equations containing a nonlinear term related to Michaelis–Menten kinetics of the enzymatic reaction. Two highly accurate and easily accessible analytical methods are used to solve the nonlinear differential equations that describe the diffusion coupled with a reaction term. Semi-analytical expressions for the concentrations of substrate, inhibitor, and product in addition to the corresponding current response are derived. The effects of various parameters such as layer thickness, bulk substrate concentration, Michaelis–Menten constant, maximum reaction velocity on current, and the sensitivity and resistance of a biosensor are investigated. A direct comparison with a numerical solution of the governing system is presented to confirm the accuracy of the derived approximate analytical solutions. [ABSTRACT FROM AUTHOR]

Analysis of the hysteresis of the enzyme-substrate due to enzyme flow calorimetry is presented based on the mathematical modeling of an immobilized enzyme using kinetic and diffusion parameters. The model is represented by ordinary differential equations containing a nonlinear term representing the substrate inhibition kinetics of the enzymatic reaction. In this paper, analytical expressions of substrate concentration for planar, cylindrical, and spherical particles at steady state condition are derived using a new analytical method. To confirm the validity and accuracy of the proposed method, the results will be compared with those obtained by the well-established homotopy perturbation method and the numerical results obtained by the highly-reputed fourth order Runge-Kutta method. Also, the results of the proposed method will be used to conduct a sensitivity analysis to understand the effect of parameters on concentration profiles. [ABSTRACT FROM AUTHOR]