Transient current, sensitivity and resistance of biosensors acting in a trigger mode: Theoretical study

Modelling of Irreversible Homogeneous Reaction on Finite Diffusion Layers

The mathematical model proposed by Chapman and Antano (Electrochimica Acta, 56 (2010), 128–132) for the catalytic electrochemical–chemical (EC’) processes in an irreversible second-order homogeneous reaction in a microelectrode is discussed. The mass-transfer boundary layer neighbouring an electrode can contribute to the electrode’s measured AC impedance. This model can be used to analyse membrane-transport studies and other instances of ionic transport in semiconductors and other materials. Two efficient and easily accessible analytical techniques, AGM and DTM, were used to solve the steady-state non-linear diffusion equation’s infinite layers. Herein, we present the generalized approximate analytical solution for the solute, product, and reactant concentrations and current for the small experimental values of kinetic and diffusion parameters. Using the Matlab/Scilab program, we also derive the numerical solution to this problem. The comparison of the analytical and numerical/computational results reveals a satisfactory level of agreement.

Modelling of Biotrickling Filters for Treatment of NOx Analytical Expressions for the NOx Concentration in Both Gas and Biofilm Phases

A mathematical model of an ideal biotrickling filter (BF) system that inoculates a recently identified strain of Chelatococcus daeguensis TAD1 and brings about efficient nitrogen oxide treatment is discussed. The proposed model is based on nonlinear mass transport equations at the gas–biofilm interface. Using Akbari–Ganji’s technique, approximate analytical expressions for the nitric oxide concentration in the gaseous and biofilm phases were developed for all feasible system parameters. In addition, to investigate the dynamic behaviour of the system, a numerical analysis of the problem is provided using MATLAB tools. To demonstrate this new approach, graphical data are provided and quantitatively discussed. This theoretical result has good agreement with the numerical simulation (MATLAB) results for the experimental values of parameters.

Theoretical and Numerical Analysis of Nonlinear Processes in Amperometric Enzyme Electrodes with Cyclic Substrate Conversion

A theoretical model of amperometric enzyme electrodes has been developed in which chemical amplification occurs in a single enzyme membrane via cyclic substrate conversion. The system is based on non-stationary diffusion equations with a nonlinear factor related to the Michaelis–Menten kinetics of the enzymatic reaction. By solving the nonlinear equations using the AGM technique, simple analytical expressions of concentration substrate, product, and amperometric current response are derived. Further, biosensor sensitivity, resistance, and gain are obtained from the current. MATLAB programming was used to carry out the digital simulation. The analytical results are validated with the numerical results. The effect of substrate concentration, maximum enzymatic rate, and membrane thickness on biosensor response was evaluated.