Detailed characterization of extreme clustering at near-contact scales in isotropic turbulence

Abstract

Recent measurements of inertial particles in isotropic turbulence (Hammond & Meng, J. Fluid Mech., vol. 921, 2021, A16) revealed surprising extreme clustering of particles at near-contact separations $(r)$ , whereby the radial distribution function, $g(r)$ , grows from $O(10)$ to $O(10^3)$ with a $(r/a)^{-6}$ scaling (where $a$ is the particle radius), and a surprising upturn of the mean inward particle-pair relative velocity (MIRV). Hydrodynamic interactions (HIs) were proposed to explain the extreme clustering, but despite predicting the correct scaling $(r/a)^{-6}$ , the HI theory underpredicted $g(r)$ by at least two orders of magnitude (Bragg et al., J. Fluid Mech., vol. 933, 2022, A31). To further understand the extreme clustering phenomenon and the relevance of HI, we characterize $g(r)$ and particle-pair kinematics for Stokes numbers $0.07 \leq St \leq 3.68$ in a homogeneous isotropic turbulence chamber using three-dimensional (3-D) particle tracking resolved to near–contact. A drift–diffusion equation governing $g(r)$ is presented to investigate the kinematic mechanisms of particle pairs. Measurements in all 24 conditions show that when $r/a\lessapprox 20$ , extreme clustering consistently occurs, scaling as $g(r) \sim (r/a)^{-k}$ with $4.5 \leq k \leq 7.6$ , which increases with $St$ . Here $g(r)$ varies with $St$ , particle size, density and polydispersity in ways that HI cannot explain. The extreme clustering region features an inward drift contributed by particle-pair turbophoresis and an inward radial relative acceleration. The latter indicates an interparticle attractive force at these separations that HI also cannot explain. The MIRV turns upward when approaching the extreme clustering region, opposite to direct numerical simulation predictions. These observations further support our previous assessment that extreme clustering arises from particle–particle interactions, but HI is not the main mechanism.