Time-dependent modeling of Cd competitive adsorption in sediment–microplastic heterogeneous systems

• Developed HCAM for time-dependent Cd competitive adsorption in heterogeneous system adsorption. • HCAM fits heterogeneous adsorption using only individual adsorption data ( R ² > 0.94). • Sediment dominates Cd adsorption while microplastics inhibit it by competing for high-affinity sites. • Microplastic-induced competition mainly occurs in initial 0-30 min, at Cd > 4 mg/L and 2%–5% PP proportions. Emerging contaminants such as microplastics introduce heterogeneity that alters metal adsorption on particulate matters in depositional environments. However, adsorption models–crucial for elucidating the dynamic competitive mechanisms in heterogeneous systems–remain inadequately developed. Here, we propose a time-dependent model to indicate the competitive adsorption within sediment–microplastic heterogeneous systems, validated through Cd adsorption experiments conducted under varying metal concentrations and particle proportions. Results demonstrate that: (1) The model accurately characterizes competitive adsorption mechanisms in heterogeneous systems ( R ²=0.94, RMSE=0.0144 mg/g) based on individual sediment and microplastic particles adsorption; (2) Sediment dominates adsorption, exhibiting a higher weight contribution ( f ) and equilibrium constant ( K eq ) (68.16% greater than microplastics), while microplastics inhibit system capacity by occupying high-affinity sites; (3) Asymmetric competition is most evident during the initial adsorption (0-30 min), particularly at elevated Cd concentrations (Cd > 4mg/L) and PP-to-sediment proportion of 2%-5%. This model provides a mechanistic framework for heterogeneous particulate interactions and enables its integration into hydrodynamic-pollutant transport model and ecological risk assessments, thereby advancing the understanding of heavy metal fate and transformation in aquatic sediments.