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

We investigate the role of turbulence in enhancing cloud droplet collisions within the size bottleneck range using direct numerical simulations (DNS) of polydisperse particles in high-Reynolds-number turbulence. Our findings reveal a dual role for polydispersity: it enhances collisions at small Stokes numbers (St ≤ 0.5) through differential sampling, but attenuates them at larger Stokes numbers by weakening preferential concentration and the sling effect, which are the dominant collision mechanisms in this regime. A novel, physically transparent parameterization for the bidisperse collision kernel is introduced which blends inertial effects with differential sampling. This model accurately reproduces the DNS data. Furthermore, simulations with coalescence demonstrate that turbulence alone is effective in broadening the droplet size distribution of typical cloud droplets (St ≈ 0.2). We also show that turbulent intermittency dramatically accelerates droplet growth, providing a viable pathway for fast activation of rain showers in warm clouds. These results highlight the complex interplay of inertia, polydispersity, and intermittency in rain initiation and provide a foundation for refinement of microphysics schemes in large-scale cloud simulations.