Mobility and settling rate of agglomerates of polydisperse nanoparticles.

Agglomerate settling impacts nanotoxicology and nanomedicine as well as the stability of engineered nanofluids. Here, the mobility of nanostructured fractal-like SiO agglomerates in water is investigated and their settling rate in infinitely dilute suspensions is calculated by a Brownian dynamics algorithm tracking the agglomerate translational and rotational motion. The corresponding friction matrices are obtained using the HYDRO++ algorithm [J. G. de la Torre, G. del Rio Echenique, and A. Ortega, J. Phys. Chem. B 111, 955 (2007)] from the Kirkwood-Riseman theory accounting for hydrodynamic interactions of primary particles (PPs) through the Rotne-Prager-Yamakawa tensor, properly modified for polydisperse PPs. Agglomerates are generated by an event-driven method and have constant mass fractal dimension but varying PP size distribution, mass, and relative shape anisotropy. The calculated diffusion coefficient from HYDRO++ is used to obtain the agglomerate mobility diameter d and is compared with that from scaling laws for fractal-like agglomerates. The ratio d/d of the mobility diameter to the gyration diameter of the agglomerate decreases with increasing relative shape anisotropy. For constant d and mean d, the agglomerate settling rate, u, increases with increasing PP geometric standard deviation σ (polydispersity). A linear relationship between u and agglomerate mass to d ratio, m/d, is revealed and attributed to the fast Brownian rotation of such small and light nanoparticle agglomerates. An analytical expression for the u of agglomerates consisting of polydisperse PPs is then derived, u=1-ρρg3πμmd (ρ is the density of the fluid, ρ is the density of PPs, μ is the viscosity of the fluid, and g is the acceleration of gravity), valid for agglomerates for which the characteristic rotational time is considerably shorter than their settling time. Our calculations demonstrate that the commonly made assumption of monodisperse PPs underestimates u by a fraction depending on σ and agglomerate mass mobility exponent. Simulations are in excellent agreement with deposition rate measurements of fumed SiO agglomerates in water.