A state-of-the-art review of explicit multicomponent isotherm models for the modeling of equilibrium data: From fundamentals to applications

This review provided a comprehensive analysis of explicit multicomponent isotherm models for the modeling of equilibrium data in adsorption processes, covering their fundamental principles and practical applications. The complexity of multicomponent adsorption was highlighted, and the potential effects of water molecules, pH, and initial concentration on the adsorption process were emphasized. The review systematically categorized explicit multicomponent isotherm models into predictive and correlative approaches, discussing their underlying assumptions, thermodynamic consistency, and practical applications. The predictive models relied only on singlecomponent isotherm parameters but usually failed to account for the complex adsorption processes. In contrast, the correlative models could offer higher fitting quality due to the incorporation of interaction factors or competition coefficients. The review addressed common mistakes encountered in data processing, model selection, and parameter estimation, emphasizing the importance of accurate determination of isotherm data. Some typical cases were presented to demonstrate the practical application of these models in predicting competitive adsorption in water and wastewater treatment. Moreover, the review emphasized the necessity of using advanced statistical methods like Akaike information criterion (AIC) and Bayesian information criterion (BIC) for model comparison and indicated future research directions. This work aimed to enhance readers' understanding of explicit multicomponent isotherm models and improve the design and optimization of adsorption-based separation processes.