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.

The nonlinear reactions-diffusion process describes a chemical reaction that involves three species, two reactions, and diffusion. The system of equations coupled with the nonlinear reaction terms with mixed Dirichlet and Neumann boundary conditions is solved analytically. The hyperbolic function method is used an approximate analytical expression of species concentrations. These analytical results are compared with numerical and previous available analytical results and are in good agreement.

The mathematical models of biofiltration of mixtures of hydrophilic (methanol) and hydrophobic ( pinene) volatile organic compounds (VOCs) are explored in this paper. This model is based on diffusion equations that contain a nonlinear term linked to the enzymatic reaction's Michaelis-Menten kinetics. An approximate analytical expression of methanol and pinene concentration profiles in the air and biofilm phase were derived using Taylor's series and Akbari-Ganji's methods. In addition, the numerical simulation of the problem using the Matlab programme to investigate the system's dynamics is reported in this work. Graphic results are presented to illustrate the solution, and numerical data is analyzed. The analytical and numerical data are in good agreement.