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Parameters and simplified model approaches for describing the fate of engineered nanoparticles (ENPs) are crucial to advance the risk assessment of these materials. Sedimentation behavior of ENPs in natural waters has been shown to follow apparent first order behavior, a ‘black box’ phenomenon that is insufficiently understood and therefore of limited applicability. Here we use a detailed Smoluchowski-Stokes model that accounts for homo- and heteroaggregation and sedimentation of ENPs and natural colloids (NCs), to simulate and interpret experimental ENP aggregation–sedimentation data. The model adequately simulated the observed time and initial concentration dependence of CeO2 settling data, and also predicted the conditions for aggregation rate-limitations of overall removal. Heteroaggregation with natural colloids was identified as the dominating removal process. Finally, the empirical apparent first order model data were calibrated against the mechanistic Smoluchowski-Stokes model simulation data, showing excellent fits for a range of NC initial concentrations. Using first order removal rates thus can be considered a valid and informed approximation when modeling ENP fate in the aquatic environment.

Exposure modeling of engineered nanomaterials requires input parameters such as sedimentation rates and heteroaggregation rates. Here, we estimate these rates using quiescent settling experiments under environmentally relevant conditions. We investigated 4 different nanomaterials (C60, CeO2, SiO2-Ag and PVP-Ag) in 6 different water types ranging from a small stream to seawater. In the presence of natural colloids, sedimentation rates ranged from 0.0001 m d(-1) for SiO2-Ag to 0.14 m d(-1) for C60. The apparent rates of heteroaggregation between nanomaterials and natural colloids were estimated using a novel method that separates heteroaggregation from homoaggregation using a simplified Smoluchowski-based aggregation-settling equation applied to data from unfiltered and filtered waters. The heteroaggregation rates ranged between 0.007 and 0.6 L mg(-1) day(-1), with the highest values observed in seawater. We argue that such system specific parameters are key to the development of dedicated water quality models for ENMs.