Classical mixture models for polythermal ice

Abstract

In this work, cold ice is treated as a heat conducting, viscous fluid, and temperate ice as a saturated mixture of a nearly density preserving, viscous heat conducting fluid (ice) and a nearly incompressible, ideal heat-conducting fluid (water) which exchange mass via phase change. Cold and temperate ice are separated by a singular surface, i.e., the cold-temperate transition surface (CTS), across which Stefan-type energy transfer occurs.

With the help of a general thermodynamic theory for binary mixtures, we derive an approximate formulation for polythermal ice accurate to linear orders in the volume fraction of the water. We show that the standard polythermal ice models are straightforward reductions of this formulation and we derive explicit expressions for the volumetric and surfacial melting rates using approximate energy balances.