A mechanism for ice growth on the surface of a spherical water droplet

Abstract

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 $10\sim5000\rm\ nm$ 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.

Figures (3)

• Figure 1: (a) The schematic illustration on the configuration studied, i.e., the water-ice-vapor spherical system, with the inner and outer radius of the ice layer being $a$ and $b$. (b) The Casimir-Lifshitz free energy per unit area as a function of the thickness of the ice layer, i.e., the difference between the outer $b$ and inner $a$ radius of the intervening layer in the water-ice-vapor concentric configuration.
• Figure 2: (a) The thickness of the ice layer (solid line) minimizing the CL free energy per unit area as a function of droplet's inner radius $a$. The global minimum thickness is about $1020\rm\ nm$ located near $a=2642\rm\ nm$ (red dot). The minimum thickness of the ice layer in the corresponding planar configuration is also shown (dotted line) as a reference. The minimum CL free energy per unit area for each $a$, scaled by the absolute value of that for the planar case, are plotted as the red line, with the black dot being the minimum. (b) With small ice layer thicknesses, the CL free energy per unit area of the concentric configuration, scaled by their corresponding planar cases with the same ice layer thicknesses, as the function of $a$. (c) The plot is in the same manner as (b) except for the relatively large ice layer thicknesses.
• Figure 3: The factor $\gamma(a,d)$ defined in Eq. \ref{['eq.Hamaker1']} as a function of $d/a$ for each given inner radius $a=100{\rm nm}$ (black), $a=200{\rm nm}$ (red), $a=500{\rm nm}$ (blue), and $a=1000{\rm nm}$ (green).