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In this two--part study, we present the development and analysis of astochastic theory for characterizing the relative positions of monodisperse,low-inertia particle pairs that are settling rapidly in homogeneous isotropicturbulence. In the limits of small Stokes number and Froude number such that$Fr \ll St_\eta \ll 1$, closures are developed for the drift and diffusionfluxes in the probability density function (PDF) equation for the pair relativepositions. The theory focuses on the relative motion of particle pairs in thedissipation regime of turbulence, i.e., for pair separations smaller than theKolmogorov length scale. In this regime, the theory approximates the fluidvelocity field in a reference frame following the primary particle as locallylinear.

Clustering of Rapidly Settling, Low-Inertia Particle Pairs in Isotropic Turbulence. I. Drift and Diffusion Flux Closures