Mechanism for ice growth on the surface of a spherical water droplet

The formation and growth of ice particles, particularly on the surfaces of spherical water droplets, bear profound implications for localized weather systems and global climate. Herein, we develop a theoretical framework for ice nucleation on minuscule water droplets, establishing that $10--5000\phantom{\rule{4pt}{0ex}}\mathrm{nm}$ droplets can considerably increase in volume, making a substantial contribution to ice formation within mist, fog, or even cloud systems. We reveal that the Casimir-Lifshitz (van der Waals) interaction within these systems is robust enough to stimulate both water and ice growth on the surfaces of ice-cold spherical water droplets. The significant impacts and possible detectable phenomena from the curvature are demonstrated.