When is settling important for particle concentrations in wall-bounded turbulent flows?

The role of settling on inertial particle concentrations in a wall-bounded turbulence is explored. While it may be thought that settling can be ignored when the Stokes settling velocity $v_s$ is small compared with the fluid friction velocity $u_\tau$, we show that even in this regime the settling may make a leading order contribution to the concentration profiles. This is because the importance of settling is determined by the size of $v_s$ compared with the turbophoretic velocity, not compared with $u_\tau$. We explain this in the context of the particle mean-momentum equation, and show that in general, there always exists a region in the boundary layer where settling cannot be neglected, no matter how small $v_s/u_\tau$ is (provided it is finite). Direct numerical simulations confirm the arguments, and show that even for $v_s/u_\tau = O(10^−2)$, the near wall particle concentration can be orders of magnitude larger than for the case where $v_s/u_\tau= 0$, and for $v_s/u_\tau = O(10^−3)$ enhancements of up to a factor of two are observed. It is also found that even for $v_s/u_\tau = O(10^−2)$, the preferential sampling of ejection events in the boundary layer by the inertial particles is profoundly modified compared with the $v_s/u_\tau=0$ case.