  Three-dimensional Voronoi analysis is used to quantify the clustering of
inertial particles in homogeneous isotropic turbulence using data from numerics
and experiments. We study the clustering behavior at different density ratios
and particle response times (i.e. Stokes numbers St). The Probability Density
Functions (PDFs) of the Voronoi cell volumes of light and heavy particles show
a different behavior from that of randomly distributed particles -i.e. fluid
tracers-implying that clustering is present. The standard deviation of the PDF
normalized by that of randomly distributed particles is used to quantify the
clustering. Light particles show maximum clustering for St around 1-2. The
results are consistent with previous investigations employing other approaches
to quantify the clustering. We also present the joint PDFs of enstrophy and
Voronoi volumes and their Lagrangian autocorrelations. The small Voronoi
volumes of light particles correspond to regions of higher enstrophy than those
of heavy particles, indicating that light particles cluster in higher vorticity
regions. The Lagrangian temporal autocorrelation function of Voronoi volumes
shows that the clustering of light particles lasts much longer than that of
heavy or neutrally buoyant particles. Due to inertial effects, the Lagrangian
autocorrelation time-scale of clustered light particles is even longer than
that of the enstrophy of the flow itself.
