The significance of early and late stages of coupled aggregation and sedimentation in the fate of nanoparticles: measurement and modelling

Despite aggregation’s crucial role in controlling the environmental fate of nanoparticles (NP), the extent to which current models can describe the progressive stages of NP aggregation/sedimentation is still unclear. In this paper, 24 model combinations of two population-balance models (PBMs) and various collision frequency and settling velocity models are used to analyse spatiotemporal variations in the size and concentration of hydroxyapatite (HAp) NP. The impact of initial conditions and variability in attachment efficiency, α, with aggregate size are investigated. Although permeability models perform well in calculating collision frequencies, they are not appropriate for describing settling velocity because of their negative correlation or insensitivity in respect to fractal dimension. Considering both early and late stages of aggregation, both experimental and model data indicate overall mass removal peaks at an intermediate ionic strength (5 mM CaCl2) even though the mean aggregate size continued to increase through higher ionic strengths (to 10 mM CaCl2). This trend was consistent when different approaches to the initial particle size distribution (PSD) were used and when a variable or constant α was used. These results point to the importance of accurately considering different stages of aggregation in modeling NP fate within various environmental conditions.