A phase-field model for wet snow metamorphism

The microstructure of snow determines its fundamental properties such as the mechanical strength, reflectivity, or the thermo-hydraulic properties. Snow undergoes continuous microstructural changes due to local gradients in temperature, humidity or curvature, in a process known as snow metamorphism. In this work, we focus on wet snow metamorphism, which occurs when temperature is close to the melting point and involves phase transitions amongst liquid water, water vapor, and solid ice. We propose a pore-scale phase-field model that simultaneously captures the three relevant phase-change phenomena: sublimation (deposition), evaporation (condensation), and melting (solidification). The phase-field formulation allows one to track the temperature evolution amongst the three phases and the water vapor concentration in the air. Our three-phase model recovers the corresponding two-phase transition model when one phase is not present in the system. 2D simulations of the model unveils the impact of humidity and temperature on the dynamics of wet snow metamorphism at the pore scale. We also explore the role of liquid melt content in controlling the dynamics of snow metamorphism in contrast to the dry regime, before percolation onsets. The model can be readily extended to incorporate two-phase flow and may be the basis for investigating other problems involving water phase transitions in a vapor-solid-liquid system such as airplane icing or thermal spray coating.