A general kinetic model for adsorption: Theoretical analysis and modeling

Adsorption technology has been widely applied for water and wastewater treatment due its low cost and easy operation. Understanding the adsorption kinetic could help to design the adsorption system. The pseudo-first-order (PFO) and pseudo-second-order (PSO) kinetic models were usually used, however their specific theoretical meanings and the application conditions were still unclear. In addition, for a practical adsorption system, the kinetic process is complex, which may include both the PFO and PSO kinetic process. Therefore, it is necessary to develop a general kinetic model to describe the whole adsorption process more accurately. In this paper, based on the Langmuir kinetics, and the theoretical analysis of the PFO and PSO models, a general form of adsorption kinetic model was developed. The experimental data from our previous studies and literature were used to fit the mixed-order (MO) model. The results showed that it is capable of describing both the PFO and PSO kinetic process and suitable for whole adsorption process, suggesting that it can describe the kinetics of whole adsorption process better. The MO kinetic model can be solved by using 4–5 order Runge-Kutta method, and the solving program as well as the method illustration was provided in Appendixes, which can be used by the readers who are interested in this model.