  In a seminal article, \citet[J. Fluid Mech., 174:441-465]{maxey87} presented
a theoretical analysis showing that enhanced particle settling speeds in
turbulence occur through the preferential sweeping mechanism, which depends on
the preferential sampling of the fluid velocity gradient field by the inertial
particles. However, recent Direct Numerical Simulation (DNS) results in
\citet[J. Fluid Mech., 796:659--711]{ireland16b} show that even in a portion of
the parameter space where this preferential sampling is absent, the particles
nevertheless exhibit enhanced settling velocities. Further, there are several
outstanding questions concerning the role of different turbulent flow scales on
the enhanced settling, and the role of the Taylor Reynolds number $R_\lambda$.
The analysis of Maxey does not explain these issues, partly since it was
restricted to particle Stokes numbers $St\ll1$. To address these issues, we
have developed a new theoretical result, valid for arbitrary $St$, that reveals
the multiscale nature of the mechanism generating the enhanced settling speeds.
In particular, it shows how the range of scales at which the preferential
sweeping mechanism operates depends on $St$. This analysis is complemented by
results from DNS where we examine the role of different flow scales on the
particle settling speeds by coarse-graining the underlying flow. The results
show how the flow scales that contribute to the enhanced settling depend on
$St$, and that contrary to previous claims, there can be no single turbulent
velocity scale that characterizes the enhanced settling speed. The results
explain the dependence of the particle settling speeds on $R_\lambda$, and show
how the saturation of this dependence at sufficiently large $R_\lambda$ depends
upon $St$. The results also show ...
