# Dependence of homogeneous crystal nucleation in water droplets on their radii and its implication for modeling the formation of ice particles in cirrus clouds

## TL;DR

This paper models ice nucleation rates in supercooled water droplets, considering both volume and surface-stimulated modes, revealing how droplet size and temperature influence ice formation in cirrus clouds.

## Contribution

It introduces a new approximation for ice nucleation rates that accounts for surface-stimulated nucleation in small droplets, a mode previously neglected.

## Key findings

- Crossover radius for nucleation mode transition varies nonmonotonically with temperature.
- Ice-air interfacial tension increases slightly with decreasing temperature.
- Surface-stimulated nucleation dominates in droplets smaller than a few microns.

## Abstract

We propose an approximation for the total ice nucleation rate J=J(T,R) in supercooled water droplets as a function of both droplet radius R and temperature T, taking account of both volume-based and surface-stimulated nucleation modes. Its crucial idea is that, even in the surface-stimulated mode crystal nuclei initially emerge (as sub-critical clusters) homogeneously in the sub-surface layer, not "pseudo-heterogeneously" at the surface. This mode is negligible in large droplets, but becomes increasingly important with decreasing droplet size and is dominant in small droplets. The crossover droplet radius for the transition of homogeneous ice nucleation from the volume-based mode to the surface-stimulated mode nonmonotonically depends on T from 233 K to 239.5 K, ranging there from about 2 microns to about 100 microns. Using experimental data on ice nucleation rates in small droplets, we determine that the ice-air interfacial tension of basal facets of ice crystals monotonically increases from about 89 dyn/cm at T=234.8 K to about 91 dyn/cm at T=236.2 K.