Particle extreme clustering and inward drifts measured at small separations in an isotropic turbulent flow*

Recent experiments have shown explosive growth of the radial distribution function g(r) of particles in isotropic turbulence with r ^-6 scaling when r/η < 1 (r is particle-pair separation; η is Kolmogorov length scale), characteristic of hydrodynamic interaction. Using high-resolution particle tracking we measure g(r), inward radial relative velocities, and kinematic quantities for varying particle radius a and Stokes number at r down to near-contact (r/a = 2.07). A kinematic relation governing g(r) shows particles cluster when inward drift 〈w_r'(t)〉_r - ▽_rS₂ is < 0 (〈w_r'(t)〉_r is the mean particle-pair radial acceleration, -▽_rS₂ is the gradient of 2^nd-order velocity structure function). Extreme clustering regime statistics scale with r/a, indicating particle interactions. At the onset of extreme clustering,〈w_r'(t)〉_r turns strongly negative, indicative of inward-driving forces and increases magnitude as r decreases. After〈w_r'(t)〉_r magnitude peaks, -▽_rS₂ dominates. The experimental collision kernel estimate is O(10³)-O(10⁵) higher than simulations assuming non-interacting particles. Our study highlights the need to understand particle interactions responsible for extreme clustering.