Nonequilibrium thermodynamics of kinetic metamorphism in snow: Fid-Bau Portal

Nonequilibrium thermodynamics of kinetic metamorphism in snow

Staron, Patrick J. / Adams, Edward E. / Miller, Daniel A.

Abstract Entropy production rates derived from nonequilibrium thermodynamics are used to show that depth hoar develops from the natural progression of snow toward thermal equilibrium. Laboratory experiments were undertaken to examine the evolution of snow microstructure under nonequilibrium thermal conditions. Snow samples with similar initial microstructure were subjected to either a fixed temperature gradient or fixed heat input. The metamorphism for both sets of boundary conditions produced similar depth hoar chains with comparable increases in effective thermal conductivity. Examination of the entropy production rates showed that the microstructural changes resulted from the snow or the surroundings moving toward a stationary state under the given non-equilibrium constraints imposed by the boundary conditions. This behavior is dictated by the second law of thermodynamics. A numerical model applied nonequilibrium thermodynamics to depth hoar formation at the grain scale. Entropy production rate relations were developed for an open system of ice and water vapor subjected to heat and mass flow. Heat conduction in the bonds had the highest specific entropy production rate, indicating it was the most inefficient part of the snow system at transferring heat. As the metamorphism advanced, the bond sizes grew to enhance the conduction pathways through the snow and increase the heat transfer. This spontaneous microstructural evolution moved the system and the surroundings toward equilibrium by reducing the local temperature gradients across the bonds and increasing the entropy production rate density.

Highlights • Depth hoar chain formation increases thermal conductivity in heat flow direction. • Second law of thermodynamics dictates system evolution toward equilibrium. • Equilibrium described by reduced temperature gradient or increased entropy production • Boundary conditions determine reduced gradient vs. increased entropy production. • Microstructural changes result from system evolution toward equilibrium.