Fate Models of Nanoparticles in the Environment: A Critical Review and Prospects

The increasing use of nanoparticles (NPs) has raised concerns about their environmental risk. The dynamics of NPs' fate and the interplay between NPs and organisms make it challenging to perform accurate and process-based hazard and risk characterization. It's crucial to use NPs' concentrations after they are transported and transformed for 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 NPs' fate has become a promising alternative, but previous reviews lack systematically evaluated these models' strengths and weaknesses. This review is the first to analyze and evaluate NPs' fate models from a mathematical perspective. It discusses the calculation methods and parameters for quantifying transport processes and transformation reactions of NPs in environmental compartments (including water, soil, sediment, and atmosphere) used by different models, sorts out and compares these processes in each compartment. Besides, this study provides recommendations for the further development of NPs' fate models 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 NPs' fate considering explicitly knowledge of uncertainties. Furthermore, we provide suggestions for constructing fate models for novel NPs and applying machine learning in fate models, to improve NPs' fate models and environmental risk assessment.