The collision kernel of nanoparticles in homogeneous isotropic turbulence: Direct simulations and modelling

An accurate model for the collision kernel is essential to predict the growth dynamics of agglomerates in both, natural and industrial processes. In many cases, including the gas-phase synthesis of functional nanoparticles in flames, the model development is hampered by the coupled effects of turbulent shear and Brownian diffusion on the relative particle motion. In the present work, we perform detailed numerical simulations of spherical Brownian particles in homogeneous isotropic turbulence where their individual trajectories are directly resolved. In this way, particle pair statistics such as relative velocities, clustering profiles and, most importantly, the geometric collision rate are deduced for mono- and bidisperse systems.

Our results show that Brownian diffusion inhibits particle clustering by distributing particles more uniformly, resulting in an effective reduction of the radial distribution function. This behaviour is also observed in bidisperse particle populations where the reduction is shown to be controlled by the harmonic mean of both Peclet numbers. In addition, mean radial relative velocities are significantly enhanced when Brownian motion is considered and this increase is most evident at low Stokes and Peclet numbers. We further develop a semi-empirical model to predict the binary collision kernel by fitting suitable expressions to the simulation data. Lastly, an a posteriori analysis is carried out to demonstrate the model’s accuracy by comparing the results of the population balance calculations against independent simulations of coalescing particles. Using the present model, the error in the predicted particle number density could be reduced to around 23% while existing models from the literature deviate from the detailed simulation by a factor of 2.1 and more.