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.