Mechanisms governing the settling velocities and spatial distributions of inertial particles in wall-bounded turbulence

We use theory and direct numerical simulations (DNSs) coupled with point particles to explore the average vertical velocities and spatial distributions of inertial particles settling in a wall-bounded turbulent flow. The theory is based on the exact phase-space equation for the probability density function describing particle positions and velocities. This allows us to identify the distinct physical mechanisms governing the particle transport, which we then examine using the DNS data and relate them to the well-known preferential sweeping mechanism in homogeneous isotropic turbulence. When the average vertical particle mass flux is zero, the averaged vertical particle velocity is zero away from the wall due to the particles preferentially sampling regions where the fluid velocity is positive, which balances with the downward Stokes settling velocity. When the average mass flux is negative, the combined effects of turbulence and particle inertia lead to average vertical particle velocities that can significantly exceed the Stokes settling velocity by as much as ten times. Sufficiently far from the wall, the enhanced vertical velocities are due to the preferential sweeping mechanism. However, as the particles approach the wall, the contribution from the preferential sweeping mechanism becomes small, and a downward contribution from the turbophoretic velocity dominates the behavior. Close to the wall, the particle concentration grows dramatically, and the behavior is directly related to the behavior of the mechanisms governing the particle settling velocity. Finally, our results highlight how the Rouse model of particle concentration is to be modified for particles with finite inertia by identifying particular mechanisms missing from that model due to its assumption of vanishing inertia.