Correlated collisions and history filtering: unraveling and reproducing the statistics of coalescing particles in turbulence from the ghost-particle framework

Abstract

This is the first in a series of papers aimed at understanding the statistics of coalescing particles in turbulent flow and their relation to collisionless ghost particles. We perform three families of Direct Numerical Simulations (DNS) under identical flow conditions: ghost particles without mutual interactions; particles that coalesce upon collision with lost monomers replenished at random positions (CR); and particles with the same collision-coalescence kinetics without replenishment (CN). All analyses are monodisperse and concern only monomers. Across $St=0.01\text{-}3.0$, the ghost-particle system has higher collision kernels ($K$) and radial distribution functions (RDFs, $g(r)$) near contact than the coalescing systems. A velocity-filtered RDF, $g_{\mathrm{G}}^{(-)}(r)$, provides a reasonable estimate of the CR contact RDF, $g_{\mathrm{CR}}(d)$. We show that the residual discrepancy between $g_{\mathrm{G}}^{(-)}(d)$ and $g_{\mathrm{CR}}(d)$, and between the corresponding kernels, arises from correlations among successive collisions in the ghost-particle system. A history-filtered ghost-particle kernel, excluding such correlations, reproduces the coalescing-system kernel. We introduce a collision-correlation time $τ_{\mathrm{cc}}$ that quantifies how long current collisions influence future events and find that it has a finite, narrow range across the studied $St$. Filtering particles with collisions within a period comparable to $τ_{\mathrm{cc}}$ yields a history-filtered RDF that reproduces those of both coalescing systems. Finally, the fraction of repeated collisions involving identical particles decays exponentially with $St$. These results unify the coalescing and ghost-particle systems as a history-filtered framework.