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.

中文翻译：

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非 Michaelis-Menten 反应动力学的任意形状电催化薄膜中的非线性输运和动力学

讨论了非 Michael-Menten 动力学的数学模型，该模型描述了与固定催化剂产生复合物的底物。本文解析求解任意形状电催化薄膜中的非线性反应扩散方程。我们提供了一个数学过程，可以对非线性边值问题进行全面的解析解。给出了一般几何形状（平面、圆柱形和球形）的底物浓度分布近似表达式的封闭且简单的形式以及相应的稳态电流响应。然后将三种分析方法获得的结果与数值解进行比较。比较已以图形方式表示，Tabler 形式显示了特色技术的有效性和优势。还讨论了参数对浓度的影响。