Effects of gravitational settling on the collision rate of monodisperse particles in turbulence*

Numerical simulations have been widely employed to study the collision rate of particles in turbulent flows. While most studies have focused on quantifying the rate of particle collision in homogeneous, isotropic turbulence (HIT), the additional effects of gravitational settling are still not fully understood. In this study, we investigate the collision rate of settling microparticles in HIT using direct numerical simulations (DNS) and Lagrangian tracking of point particles. The properties of the fluid and particles were selected based on suspended marine microparticles in the upper ocean. The problem setup covers a range of relatively small Stokes numbers: $1\times 10^{-3}<St<4\times 10^{-3}$ and moderate settling numbers: $1<Sv<30$. To study the effects of gravity, we compare the motion and collision of particles in three different flow conditions: HIT without gravity, HIT with gravity, and gravitational settling in quiescent fluid. The results show that gravity decreases the collision rate of monodispersed particles in HIT as it significantly reduces the horizontal velocity fluctuations of the particles. By examining the relative radial and tangential velocity components between pair particles, we propose corrections to existing theoretical models and significantly improve the predictions of the rates of collisions.