Snowflake growth in three dimensions using phase field modelling

TL;DR

This paper introduces a modified phase field model that accurately reproduces the complex three-dimensional growth patterns of snowflakes, linking model parameters to thermodynamic processes and matching experimental growth dynamics.

Contribution

A novel phase field model that captures 3D snowflake morphologies, including anisotropy, faceting, and dendritic growth, with validated growth dynamics matching experimental observations.

Findings

Model reproduces diverse snowflake forms in 3D

Growth dynamics align with selection theory

Successfully simulates Nakaya diagram morphologies

Abstract

Snowflake growth provides us with a fascinating example of spontaneous pattern formation in nature. Attempts to understand this phenomenon have led to important insights in non-equilibrium dynamics observed in various active scientific fields, ranging from pattern formation in physical and chemical systems, to self-assembly problems in biology. Yet, very few models currently succeed in reproducing the diversity of snowflake forms in three dimensions, and the link between model parameters and thermodynamic quantities is not established. Here, we report a modified phase field model that describes the subtlety of the ice vapour phase transition, through anisotropic water molecules attachment and condensation, surface diffusion, and strong anisotropic surface tension, that guarantee the anisotropy, faceting and dendritic growth of snowflakes. We demonstrate that this model reproduces the growth dynamics of the most challenging morphologies of snowflakes from the Nakaya diagram. We find that the growth dynamics of snow crystals matches the selection theory, consistently with previous experimental observations.