Measurement of Inertial Particle Collision Statistics in Isotropic Turbulence Using 3D Particle Tracking Velocimetry*

We experimentally investigate the effects of turbulence and particle inertia on three particle collision statistics in particle-laden isotropic turbulence: radial distribution function (RDF), radial particle-pair relative velocity (RV), and for the first time, geometric collision kernel for which RDF and RV are factors. Experimentally obtaining these statistics has been difficult in the past especially as particle separation distance $r$ decreases below the Kolmogorov length scale $\eta $ to near-contact, where the physics becomes obscure and theoretical models may not hold. Using Shake-the-Box 3D particle tracking, we are able to resolve particle positions and velocities at $r$\textless $\eta $, which enables estimations of RDF and RV at near-contact and calculation of the collision kernel. Experiments are performed in a truncated icosahedron isotropic turbulence chamber at ten Stokes numbers 0.2\textless \textit{St}\textless 2.3. The \textit{St} was changed by varying the fan speed (which also changes 246$\le $\textit{Re}$_{\lambda }\le $357) and particle diameter d between 15$\mu $m and 45$\mu $m. RDF increases as $r$/$\eta $ decreases to $O$(1), and increases with \textit{St}. RV decreases as $r$/$\eta $ decreases until $r$/$\eta =$1, recapitulating previous DNS and experimental results (Dou et al, 2018, DOI: 10.1017/jfm.2017.813); however, as $r$/$\eta $ \textless 1, RV exhibits a sharp upturn. This first simultaneous near-contact estimation of RDF, RV, and collision kernel calculated from real turbulence enables examination of theory and DNS, and may reveal new phenomena not previously accounted for in prior models.