Continuous fixed-bed adsorption of cationic dyes by starch nanocrystals with breakthrough modeling of competitive interactions in multicomponent systems

The removal of synthetic dyes from industrial wastewater remains a major environmental challenge due to their persistence and toxicity. This study investigated starch nanocrystals (SNCs), a carbohydrate-based biological macromaterial, as a sustainable biosorbent for the continuous removal of malachite green (MG), methylene blue (MB), and crystal violet (CV) from single-, binary-, and ternary-component systems using fixed-bed column adsorption. Breakthrough behavior was evaluated using six models, including Thomas, Yoon–Nelson, Adams–Bohart, mass-transfer, dose–response, and bed-depth service time (BDST) models. Model performance was assessed using the coefficient of determination (R 2 ) and normalized root mean square error (NRMSE). SNCs exhibited high adsorption affinity toward all three dyes under single-component conditions, with removal efficiencies of 70.87–71.88% and saturation capacities ranging from 5.16 to 5.44 mg/g. Competitive adsorption in binary and ternary systems reduced removal efficiency (59.24–73.01%), adsorption capacity (3.67–4.95 mg/g), and column service time (1772.73–1942.86 min) relative to single-component systems. However, the extent of performance reduction varied among different dye combinations, with systems containing MB and CV exhibiting less severe reductions than other mixed-dye systems, indicating composition-dependent competitive interactions rather than net synergistic effects. Among the evaluated models, the dose–response and BDST models provided the most accurate predictions across all adsorption systems (R 2 > 0.99, NRMSE = 3.00–6.02%). The Thomas model also showed good fit quality (R 2 = 98.78–99.46%) but exhibited variable NRMSE values (5.25–9.21%), with the highest errors observed in binary systems, indicating that its accuracy is system-dependent and its parameters have limited interpretability under competitive conditions. The Yoon–Nelson model showed moderate predictive capability (R 2 = 97.92–99.15%, NRMSE = 6.10–12.51%), while the Adams–Bohart and mass-transfer models exhibited the highest NRMSE values (8.65–32.89% and 21.03–25.71%, respectively), indicating limited applicability under multicomponent conditions. A statistical regression framework incorporating dummy variables and interaction effects was developed to quantify the combined influence of adsorption time (quantitative variable) and system composition (qualitative variable: single-, binary-, and ternary-component systems) on breakthrough behavior. The model structure includes linear and quadratic time terms, categorical dummy variables representing different dye systems, and interaction terms (time × system composition) to account for composition-dependent adsorption kinetics. This framework successfully described competitive adsorption behavior and explained more than 98% of the variability in the experimental data (R 2 = 98.02%, adjusted R 2 = 97.72%, NRMSE = 0.053%), with the interaction terms revealing that the effect of adsorption time on breakthrough behavior was significantly modulated by system composition, particularly in mixed-dye systems containing MB and CV. The results demonstrate the potential of SNCs as environmentally friendly adsorbents for dye-contaminated wastewater and provide useful insights for the design and optimization of fixed-bed adsorption systems operating under realistic multicomponent conditions.