  `Preferential concentration' (\emph{Phys. Fluids} \textbf{A3}:1169--78, 1991)
refers to the clustering of inertial particles in the high-strain, low-rotation
regions of turbulence. The `centrifuge mechanism' of Maxey (\emph{J. Fluid
Mech.} \textbf{174}:441--65, 1987) appears to explain this phenomenon. In a
recent paper, Bragg \& Collins (\emph{New J. Phys.} \textbf{16}:055013, 2014)
showed that the centrifuge mechanism is dominant only in the regime ${St\ll1}$,
where $St$ is the Stokes number based on the Kolmogorov time scale. Outside
this regime, the centrifuge mechanism gives way to a non-local, path-history
symmetry breaking mechanism. However, despite the change in the clustering
mechanism, the instantaneous particle positions continue to correlate with
high-strain, low-rotation regions of the turbulence. In this paper, we analyze
the exact equation governing the radial distribution function and show how the
non-local clustering mechanism is influenced by, but not dependent upon, the
preferential sampling of the fluid velocity gradient tensor along the particle
path-histories in such a way as to generate a bias for clustering in
high-strain regions of the turbulence. We also show how the non-local mechanism
still generates clustering, but without preferential concentration, in the
limit where the timescales of the fluid velocity gradient tensor measured along
the inertial particle trajectories approaches zero (such as white-noise flows
or for particles in turbulence settling under strong gravity). Finally, we use
data from a direct numerical simulation of inertial particles suspended in
Navier-Stokes turbulence to validate the arguments presented in this study.
