Clustering and collision of Brownian particles in homogeneous and isotropic turbulence

The collision rate between primary nanoparticles in the turbulent flow is of significance for accurately predicting the growth rate of agglomerates during the flame synthesis process. In this work, the clustering and the collision of Brownian particles in the free-molecular regime in ho-mogeneous isotropic turbulence are investigated using the direct numerical simulation and the Langevin dynamics. It is found that the Brownian motion can distribute the particles more uni-formly, leading to the formation of a plateau on the curve of the radial distribution function (RDF). This anti-clustering effect is significant only at a small separation distance of particle pairs and cannot be observed when the separation is larger than a critical value. The radial relative velocity (RRV) is significantly enhanced, especially at the small separation distance, when the Brownian motion is taken into account. A velocity superposition analysis shows that the statistics of RRV of Brownian particles can be obtained by adding a random variable onto the RRV of non -Brownian particles with the same Stokes number. The increased radial relative velocity coun-teracts the anti-clustering effect of the Brownian motion and leads to the increase of the geometric collision kernel. Finally, the collision kernel of Brownian particles is formulated as a function of asymptotic values of RDF and RRV at a vanishing separation. The proposed collision kernel en-ables us to estimate the collision rate between nanoparticles that are much smaller than the Kolmogorov length scale.