Significance of Early and Late Stages of Coupled Aggregation and Sedimentation in the Fate of Nanoparticles: Measurement and Modeling

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 and various collision frequency and settling velocity models
are used to analyze 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 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.