Modelling the collision kernel of fractal nanoparticle agglomerates in homogeneous isotropic turbulence

Agglomeration dynamics of nano-sized particles in aerosol flame reactors are dominated by the effects of Brownian diffusion and turbulent shear. In this study, we perform population balance calculations to predict the evolution of an initially monodisperse nanoparticle population in a turbulent carrier gas. To evaluate the required coagulation rate coefficients for the resulting agglomerates, we extend a recently developed model for spherical particles by a suitable expression for the effective collision cross-section. Population balance calculations are validated by detailed particle simulations where trajectories of all primary particles and agglomerates are directly resolved and the structure of the agglomerates is preserved. The primary particle sizes considered here range from 50 to $100\mathrm{nm}$, corresponding to Knudsen numbers between 2.3 and 4.6.

Our results show that collision rates measured from detailed particle simulations are in good agreement with predictions by the extended collision kernel model. In contrast, comparisons with a standard model from the literature reveal systematic differences which can be as large as an order of magnitude and more depending on the conditions. In addition, the effect of morphology on the measured collision rates is found to be rather small due to an opposing effect of the effective collision diameter and the particle inertia.

An a posteriori comparison between direct numerical simulations and population balance calculations suggests that the extended collision kernel model is able to correctly reproduce the evolution of the agglomerate population. The standard model, on the contrary, yields slower agglomeration rates compared to the direct simulation as it neglects particle inertia effects and thus underestimates turbulence-driven collision rates between large nanoparticle agglomerates.