Towards a Thermodynamically Consistent Phase-Field Model for Snow Metamorphism

The microstructure of snow undergoes continuous transformation in a process known as snow metamorphism. This evolving microstructure determines meso- and macroscopic optical, mechanical and thermal properties of the snowpack. Therefore, understanding the microstructural evolution on the pore scale is essential to forecast large-scale behavior.
By modeling phase transitions between ice and water vapor, we can treat fully coupled heat and mass transport on an arbitrary microstructure, allowing us to model dry snow metamorphism under temperature gradients and isothermal conditions alike. For this, a multi-phase-field model is used, by which we implicitly track the evolving microscopic ice-air interface. Compared to previous phase field models for dry snow metamorphism, a grand potential formulation is used to simplify the simulation of ice-vapor interfaces, as well as increasing the thermodynamic consistency. Thereby, we can treat various cross couplings between heat and mass transport like the Soret effect as well as surface diffusion and crystal growth dynamics. In this new model, near isothermal snow metamorphism is interpreted as sintering of ice grains. The thermodynamic properties of ice are modeled using CALPHAD data and humid air is modeled as a mixture of ideal gases.
We present our novel phase field model and validate it against semi-analytical solutions of the Stefan-problem and recently published experiments on simple geometries.