Investigating adsorption behavior of methylene blue on nonmagnetic slag: An integrated evaluation of isotherm-kinetic frameworks

This study systematically describes the multiscale adsorption behavior of methylene blue on nonmagnetic slag by uniquely combining several underexplored classical and advanced isotherm and kinetic models. Experimental results were established based on optimal conditions such as 5 $\text{mg}/L$ initial concentration, 4 g adsorbent dosage, pH 8, 35 °C, 35 min contact time, and 200 RPM stirring rate. Classical isotherms describe surface heterogeneity but cannot account for complex site interactions and pore-scale irregularities. At the same time, advanced models such as fractal-like, hybrid, and cooperative forms show extensive energy dispersions, progressive site deactivation, and fractal-governed diffusion pathways. Kinetic study confirms that pseudo-order fits underpredict delayed equilibrium due to pore diffusion and steric hindrance. At the same time, advanced kinetics show biphasic sorption, subdiffusive transport, and new ferrokinetic effects from residual iron microdomains. These synergistic statistical tests with reduced chi-square and actual regression coefficient confirm reasonable fitting and acceptable error estimates. The ATR–FTIR and SEM–EDS analysis confirmed the adsorption of methylene blue onto the nonmagnetic slag surface, thereby supporting the claims of isotherm-kinetic frameworks. In addition, good performance of the slag was found for three regeneration cycles, demonstrating functional reusability. This multi-model association overcomes the gap between empirical fitting and actual physicochemical behavior, validating nonmagnetic slag as a cost-effective, structurally complex sorbent for dye removal. The results provide a predictive basis for designing sustainable adsorption systems and propose future validation under real effluent conditions and dynamic operation to further develop waste-derived adsorbents in circular economy systems.