Analysis of Langmuir-Hinshelwood Kinetics Model for Photocatalytic Degradation of Aqueous Direct Blue 71 Through Analytical Expression

Abstract

An analysis of the Langmuir-Hinshelwood expression is presented for the photocatalytic degradation of Aqueous Direct Blue 71. This analysis contains a nonlinear term that explains the kinetics of the heterogeneous catalytic processes. In this paper, we obtain approximate analytical solutions for the nonlinear equation by employing the Perturbation-Iteration Algorithms (PIA). The main objective is to propose an analytical method of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Furthermore, in this work decolorization efficiency (DE%) and the numerical solution to the problem is also reported using MATLAB program. The analytical results are compared with the numerical and limiting case result. The obtained results are valid for the whole solution domain. A good agreement between the theoretical predictions and numerical results is observed. Langmuir-Hinshelwood model is analyzed with the help of analytical result for the different values of $H_{2}O_{2}$ and $SiO_{2}$-NP to describe photocatalytic degradation of the dye.