Our results demonstrate strong coupling between RDF and MRV and imply that earlier isolated studies on either RDF or MRV have limited relevance for predicting particle collision rate. We see a further shape-preserving reduction of the RDF (and MRV) when the gravitational settling parameter ( S g) is of order O(1). We uncover a paradox: the past empirical success of the differential version of the theory is theoretically unjustified. We use the model to derive a general solution of RDF. Separately, we also propose a phenomenological model that could directly predict MRV and find that it is accurate when calibrated using fourth moments of the fluid velocities. We show numerically that the theory accurately accounts for the DNS results (i.e., given an accurate RDF, the theory could produce an accurate MRV). The theory includes contributions from turbulent fluctuations absent in earlier mean-field theories. Based on a previously proposed Fokker–Planck (drift-diffusion) framework, we derive a theoretical account of the relationship among particle collision–coagulation rate, RDF and MRV. We perform direct numerical simulation (DNS) of coagulating particles in isotropic turbulent flow in the regime of small Stokes number ( St=0.001–0.54) and find that, due to collision–coagulation, the radial distribution functions (RDFs) fall off dramatically at scales r∼ d (where d is the particle diameter) to small but finite values, while the mean radial component of the particle relative velocity (MRV) increases sharply in magnitude. Considering turbulent clouds containing small inertial particles, we investigate the effect of particle collision, in particular collision–coagulation, on particle clustering and particle relative motion.
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