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The collision rate of particles suspended in turbulent flow is critical toparticle agglomeration and droplet coalescence. The collision kernel can beevaluated by the radial distribution function (RDF) and radial relativevelocity (RV) between particles at small separations $r$. Previously, thesmallest $r$ was limited to roughly the Kolmogorov length $\eta$ due toparticle position uncertainty and image overlap. We report a new approach tomeasure RDF and RV near contact ($r/a\: \approx$ 2.07, $a$ particle radius)overcoming these limitations. Three-dimensional particle tracking velocimetryusing four-pulse Shake-the-Box algorithm recorded short particle tracks withthe interpolated midpoints registered as particle positions to avoid imageoverlap. This strategy further allows removal of mismatched tracks using theircharacteristic false RV. We measured RDF and RV in a one-meter-diameterisotropic turbulence chamber with Taylor Reynolds number $Re_\lambda=324$ withparticles of 12-16 $\mu$m radius and Stokes number $\approx$ 0.7. While atlarge $r$ the measured RV agrees with the literature, when $r<20\eta$ the firstmoment of negative RV is 10 times higher than direct numerical simulations ofnon-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 highernear-contact RDF than simulations. Such extreme clustering and relativevelocity enhancement can be attributed to particle-particle interactions.Uncertainty analysis substantiates the observed trends. This first-eversimultaneous RDF and RV measurement at small separations provides a clearglimpse into the clustering and relative velocities of particles in turbulencenear-contact.

Particle Radial Distribution Function and Relative Velocity Measurement in Turbulence at Small Particle-Pair Separations