Nonlinear transport and kinetics in electrocatalytic thin film of arbitrary shape for non-Michaelis-Menten reaction kinetics

•Non-Michaelis- Menten kinetics in thin electrocatalytic film is discussed.•The analytical solution of the nonlinear problem is solved for general geometry.•The amperometric current response for polymer-modified electrodes is derived.•Analytical results are compared with simulation results. The mathematical model for non-Michael-Menten kinetics, which describes a substrate that produces a complex with the immobilised catalyst, is discussed. This paper analytically solves the nonlinear reaction–diffusion equation in an electrocatalytic thin film of arbitrary shape. We provide a mathematical process that enables a comprehensive analytical solution to the nonlinear boundary value problem. Closed and simple forms of the approximate expression for substrate concentration profiles for general geometry (planar, cylindrical, and spherical) and corresponding steady-state amperometric current response are presented. The results obtained by three analytical methods are then compared with numerical solutions. The comparison has been represented graphically, and the Tabler form shows the effectiveness and advantages of the featured techniques. The effect of the parameters on concentration is also discussed.