Modeling the fate of engineered titanium dioxide nanoparticles from an industrial effluent to a river

Understanding the environmental fate of engineered titanium dioxide nanoparticles (TiO₂ NPs) is essential due to their increasing industrial use and potential ecological risks. This study presents SAPaTin (Smoluchowski Aggregation of nano-Particle of Titanium), a mechanistic modeling framework based on Smoluchowski aggregation kinetics, to simulate the transport and transformation of TiO₂ NPs discharged from an industrial effluent into a river system. The model integrates experimental data and field observations to account for the spatial variability in water chemistry, particle size distribution, and aggregation behavior. Results show that while the fractal dimension of aggregates (D_f=1.5 or 2.3) does not affect the initial size distribution at the pipe inlet due to the dominance of Brownian motion, it significantly influences the concentration of particles within size classes. In the river, heteroaggregation between TiO₂ NPs and suspended particulate matter (SPM) is found to be primarily driven by differential settling rather than Brownian or shear-induced collisions. The residence time of aggregates in the river exponentially increases the fraction of sedimented heteroaggregates, a process controlled largely by SPM density. This study highlights the critical role of heteroaggregation and aggregate structure in predicting nanoparticle behavior in fluvial environments and offers a validated modeling tool for environmental risk assessment of nano-enabled industrial discharges.