Title: Collisions of cloud droplets: non-continuum lubrication and the warm-rain size gap
Speaker: Anubhab Roy (IIT Madras)
Abstract: The growth of cloud droplets into raindrops hinges on collisions, yet classical microphysics leaves a stubborn “size gap”: above ~15 microns, condensation is slow, while gravitational coalescence becomes efficient only beyond ~40 microns. A central obstacle is hydrodynamic: as two droplets approach, the air between them must drain, and continuum lubrication predicts a resistance that diverges, so droplets on a collision course never actually touch. I will show that this singularity is an artefact of the continuum approximation: once the gap falls below the air’s mean free path (~70 nm), the gas flow becomes rarefied, and the resistance grows far more slowly, allowing coalescence in finite time without invoking van der Waals attraction. Building on the kinetic-theory analysis of Sundararajakumar & Koch (1996), we construct uniformly valid resistance and mobility functions spanning the far-field continuum and near-contact non-continuum regimes, and use them to compute collision rates and efficiencies for droplet pairs settling in quiescent, sheared and turbulent flows. The collision efficiency depends systematically on the size ratio, the Knudsen number, and droplet inertia; turbulence is found to augment differential sedimentation; and the results condense into compact, closed-form collision kernels suited to cloud and aerosol models. I will close with the effect of atmospheric electric fields on droplet collisions and the open questions these raise for rain initiation.
A few references to our work that the talk draws on:
1. Dhanasekaran, Roy & Koch, Collision rate of bidisperse spheres settling in a compressional non-continuum gas flow, J. Fluid Mech. 910, A10 (2021).
2. Dhanasekaran, Roy & Koch, Collision rate of bidisperse, hydrodynamically interacting spheres settling in a turbulent flow, J. Fluid Mech. 912, A5 (2021).
3. Patra, Koch & Roy, Collision efficiency of non-Brownian spheres in a simple shear flow – the role of non-continuum hydrodynamic interactions, J. Fluid Mech. 950, A18 (2022).
4. Patra & Roy, Gravity-induced collisions of uncharged cloud droplets in an electric field, J. Atmos. Sci. 82, 11 (2025).