Analytical solution of the Langmuir-based linear driving force model and its application to the adsorption kinetics of boscalid onto granular activated carbon

The application of intraparticle diffusion models is generally difficult because of complex mathematical structure. The linear driving force (LDF) approach reduces the mathematical effort and provides a reasonable approximation of the intraparticle diffusion theory. In this work, an exact analytical solution of a LDF equation based on the Langmuir equilibrium model (LLDF) was derived. The LLDF model depends on three unknown parameters, namely the adsorbed amount at equilibrium, the maximum adsorbent capacity and the mass transfer coefficient. The LLDF model was used for analyzing the adsorption kinetics of boscalid onto granular activated carbon. The experimental results at equilibrium showed that the maximum adsorption capacity of activated carbon for boscalid and the Langmuir equilibrium constant of the process were 167 mg g−1 and 0.53 L mg−1, respectively. The LLDF equation was successfully applied to the kinetic data, allowing the evaluation of the mass transfer coefficient of boscalid (8.4 × 10−3 h−1). The LLDF model has general validity for describing intraparticle diffusion-adsorption onto porous media and its reliability can be assessed by a simple graphical method.