Mathematical modeling of submerged membrane adsorption hybrid system and parameter estimation for adsorption of cesium from radioactive wastewater implementing eco-friendly adsorbent

Abstract This study presents a comprehensive mathematical modeling and experimental investigation of a submerged membrane adsorption hybrid system (SMAHS) for the removal of cesium (Cs(I)) from radioactive wastewater. An eco-friendly adsorbent was synthesized and characterized for its adsorption performance. The homogeneous surface diffusion model (HSDM) model integrates surface diffusion as the dominant mass transfer mechanism and estimates key parameters, including the external mass transfer coefficient (K), surface diffusion coefficient (Ds), and membrane correlation coefficient (MCC). The pore and surface diffusion model (PSDM) is a comprehensive diffusion-based model that accounts for all diffusion processes in the solid phase. Experiments identified optimal operational conditions: pH 6.5, adsorbent dose 1.5 g/L, and contact time of 90 min, achieving over 95 % cesium removal. Ion selectivity tests demonstrated preferential adsorption of cesium in the presence of competing metal ions such as Na + , K + , and Ca 2+ . Regeneration studies showed that the adsorbent maintained over 85 % removal efficiency after five adsorption-desorption cycles, indicating cost-effectiveness. Model validation against experimental data exhibited strong agreement ( R 2 = 0.98), confirming the model’s suitability for design and scale-up of hybrid treatment systems. This work provides new insights into adsorption kinetics, hybrid system optimization, and eco-friendly adsorbent applications for radionuclide wastewater remediation.