Analytical Solutions and Dynamic Analysis of Nonlinear Langmuir Adsorption–Desorption Kinetics in Liquid Media

ABSTRACT In this study, a Langmuir‐based kinetic model is formulated to describe solute adsorption from a well‐mixed liquid phase onto a solid adsorbent surface. The closed‐form analytical solutions are obtained for the coupled nonlinear ordinary differential equations describing the bulk solute concentration and surface coverage. A simple Rajendran–Joy approximation is also derived and validated against the exact solution, showing excellent agreement over a broad range of kinetic parameters. Parametric, sensitivity, time‐series, and phase‐plane analyses are performed to elucidate transient dynamics and equilibrium behavior. The proposed analytical framework provides an efficient tool for kinetic interpretation, parameter estimation, and optimization of adsorption‐phenomena.