  The collision rate of particles suspended in turbulent flow is critical to
particle agglomeration and droplet coalescence. The collision kernel can be
evaluated by the radial distribution function (RDF) and radial relative
velocity (RV) between particles at small separations $r$. Previously, the
smallest $r$ was limited to roughly the Kolmogorov length $\eta$ due to
particle position uncertainty and image overlap. We report a new approach to
measure RDF and RV near contact ($r/a\: \approx$ 2.07, $a$ particle radius)
overcoming these limitations. Three-dimensional particle tracking velocimetry
using four-pulse Shake-the-Box algorithm recorded short particle tracks with
the interpolated midpoints registered as particle positions to avoid image
overlap. This strategy further allows removal of mismatched tracks using their
characteristic false RV. We measured RDF and RV in a one-meter-diameter
isotropic turbulence chamber with Taylor Reynolds number $Re_\lambda=324$ with
particles of 12-16 $\mu$m radius and Stokes number $\approx$ 0.7. While at
large $r$ the measured RV agrees with the literature, when $r<20\eta$ the first
moment of negative RV is 10 times higher than direct numerical simulations of
non-interacting particles. Likewise, when $r>\eta$, RDF scales as $r^{-0.39}$
reflecting RDF scaling for polydisperse particles in the literature , but when
$r\lessapprox\eta$ RDF scales as $r^{-6}$, yielding 1000 times higher
near-contact RDF than simulations. Such extreme clustering and relative
velocity enhancement can be attributed to particle-particle interactions.
Uncertainty analysis substantiates the observed trends. This first-ever
simultaneous RDF and RV measurement at small separations provides a clear
glimpse into the clustering and relative velocities of particles in turbulence
near-contact.
