Fate models of nanoparticles in the environment: a critical review and prospects†

The increasing use of nanoparticles (NPs) has raised concerns about their risks to the environment. However, the dynamics of the fate of NPs and their interplay with organisms make it challenging to perform an accurate and process-based hazard and risk characterization. Thus, it is crucial to estimate the concentrations of NPs after they are transported and transformed for their risk assessment (i.e., evaluating the fate of NPs). This will provide more accurate results than using the mass of released NPs. However, experimental limitations make it challenging to directly quantify and track NPs. Hence, using mathematical models to simulate the fate of NPs has become a promising alternative, but previous reviews failed to systematically evaluate the strengths and weaknesses of these models. Accordingly, this review is the first to analyze and evaluate the fate models of NPs from a mathematical perspective. Specifically, we discuss the calculation methods and parameters for quantifying the transport processes and transformation reactions of NPs in environmental compartments (including water, soil, sediment, and atmosphere) used by different models and categorize and compare these processes in each compartment. Besides, this study provides recommendations for the further development of fate models of NPs and proposes an optimal modeling procedure for simulating the fate of NPs. The procedure provides the optimal simulation equations and parameters for each transport and transformation process in each compartment, intending to quantify these processes and the fate of NPs, explicitly considering the knowledge of uncertainties. Furthermore, we provide suggestions for constructing fate models for novel NPs and applying machine learning in these models to improve the fate models of NPs and environmental risk assessment.