### Abstract

Agglomerate settling impacts nanotoxicology and nanomedicine as well as the stability of engineered nanofluids. Here, the mobility of nanostructured fractal-like SiO_{2} 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_{m} and is compared with that from scaling laws for fractal-like agglomerates. The ratio d_{m}/d_{g} of the mobility diameter to the gyration diameter of the agglomerate decreases with increasing relative shape anisotropy. For constant d_{m} and mean d_{p}, the agglomerate settling rate, u_{s}, increases with increasing PP geometric standard deviation σ_{p,g} (polydispersity). A linear relationship between u_{s} and agglomerate mass to d_{m} ratio, m/d_{m}, is revealed and attributed to the fast Brownian rotation of such small and light nanoparticle agglomerates. An analytical expression for the u_{s} of agglomerates consisting of polydisperse PPs is then derived, us=1-ρfρpg3πμmdm (ρ_{f} is the density of the fluid, ρ_{p} 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_{s} by a fraction depending on σ_{p,g} and agglomerate mass mobility exponent. Simulations are in excellent agreement with deposition rate measurements of fumed SiO_{2} agglomerates in water.

Original language | English (US) |
---|---|

Article number | 064703 |

Journal | Journal of Chemical Physics |

Volume | 148 |

Issue number | 6 |

DOIs | |

State | Published - Feb 14 2018 |

### Fingerprint

### Cite this

*Journal of Chemical Physics*,

*148*(6), [064703]. https://doi.org/10.1063/1.5012037

**Mobility and settling rate of agglomerates of polydisperse nanoparticles.** / Spyrogianni, Anastasia; Karadima, Katerina S.; Goudeli, Eirini; Mavrantzas, Vlasis G.; Pratsinis, Sotiris E.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 148, no. 6, 064703. https://doi.org/10.1063/1.5012037

}

TY - JOUR

T1 - Mobility and settling rate of agglomerates of polydisperse nanoparticles

AU - Spyrogianni, Anastasia

AU - Karadima, Katerina S.

AU - Goudeli, Eirini

AU - Mavrantzas, Vlasis G.

AU - Pratsinis, Sotiris E.

PY - 2018/2/14

Y1 - 2018/2/14

N2 - Agglomerate settling impacts nanotoxicology and nanomedicine as well as the stability of engineered nanofluids. Here, the mobility of nanostructured fractal-like SiO2 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 dm and is compared with that from scaling laws for fractal-like agglomerates. The ratio dm/dg of the mobility diameter to the gyration diameter of the agglomerate decreases with increasing relative shape anisotropy. For constant dm and mean dp, the agglomerate settling rate, us, increases with increasing PP geometric standard deviation σp,g (polydispersity). A linear relationship between us and agglomerate mass to dm ratio, m/dm, is revealed and attributed to the fast Brownian rotation of such small and light nanoparticle agglomerates. An analytical expression for the us of agglomerates consisting of polydisperse PPs is then derived, us=1-ρfρpg3πμmdm (ρf is the density of the fluid, ρp 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 us by a fraction depending on σp,g and agglomerate mass mobility exponent. Simulations are in excellent agreement with deposition rate measurements of fumed SiO2 agglomerates in water.

AB - Agglomerate settling impacts nanotoxicology and nanomedicine as well as the stability of engineered nanofluids. Here, the mobility of nanostructured fractal-like SiO2 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 dm and is compared with that from scaling laws for fractal-like agglomerates. The ratio dm/dg of the mobility diameter to the gyration diameter of the agglomerate decreases with increasing relative shape anisotropy. For constant dm and mean dp, the agglomerate settling rate, us, increases with increasing PP geometric standard deviation σp,g (polydispersity). A linear relationship between us and agglomerate mass to dm ratio, m/dm, is revealed and attributed to the fast Brownian rotation of such small and light nanoparticle agglomerates. An analytical expression for the us of agglomerates consisting of polydisperse PPs is then derived, us=1-ρfρpg3πμmdm (ρf is the density of the fluid, ρp 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 us by a fraction depending on σp,g and agglomerate mass mobility exponent. Simulations are in excellent agreement with deposition rate measurements of fumed SiO2 agglomerates in water.

UR - http://www.scopus.com/inward/record.url?scp=85041713991&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041713991&partnerID=8YFLogxK

U2 - 10.1063/1.5012037

DO - 10.1063/1.5012037

M3 - Article

C2 - 29448768

AN - SCOPUS:85041713991

VL - 148

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 6

M1 - 064703

ER -