Polydisperse collision kernels in droplet-laden turbulence with implications for rain formation

The collision kernel of droplets in warm clouds is a crucially important quantity for the parameterization of precipitation in weather and climate models. Nevertheless, its accurate representation remains a challenge, specifically in the bottleneck range $15\,\mu\text{m}<r<40\,\mu\text{m}$ within which turbulence is believed to substantially contribute to droplet growth. In this work, we address this problem by performing direct numerical simulations of polydisperse inertial particles suspended in three-dimensional turbulence at Reynolds number up to $Re_\lambda=418$. Collision statistics are compiled for droplet pairs across the Stokes number range $St\in[0.02,2]$, yielding comprehensive bidisperse maps of collision kernels, radial relative velocities, and radial distribution functions at contact. Our analysis reveals that polydispersity enhances collisions between light droplets through differential sampling, but attenuates collisions at larger Stokes numbers by rapidly reducing the spatial overlap of droplet clusters. By benchmarking existing models, we show that dominant bidisperse errors arise from overpredicted cross-species clustering. In light of these results, we propose an adapted model for the bidisperse radial distribution function, as well as a novel parameterization for the associated collision kernel, applicable to the smallest droplets in the bottleneck range with small settling velocities. Finally, we study the broadening of the droplet size distribution due to collision-coalescence and demonstrate that droplet growth is markedly accelerated in parcels of large local dissipation rate, supporting the hypothesis that turbulent intermittency may help overcome the bottleneck barrier.