Moving Phase Boundary Problems and Thermal Modeling

Moving phase boundary problems (MPBP) are a special class of problems where the position of the contact between two phases is not known a-priori but is determined as a function of space and time once the equilibrium state at the contact is perturbed by changing pressure/temperature conditions. A simple example of MPBP is the classical Stefan problem of freezing of material, initially in liquid state, in a half-space under stepwise change in the surface temperature ( Stefan, 1889 ). As a result of phase transformation and movement of phase boundary heat is either liberated or absorbed depending on the nature of the transformation across the boundary. Phase boundaries occur in the interior of the earth in the form of solid-solid, solid-partial melt, and solid-melt boundaries. In the lithosphere, these boundaries occur in the form of contacts between metamorphic grades, solidification fronts of magma chambers/lava lakes, and lithosphere- asthenosphere boundary (LAB). These boundaries respond to any perturbation in the equilibrium temperature/pressure state of the lithosphere and act as heat source/ sink. Therefore, these are vital in understanding the thermal and tectonic evolution of the lithosphere.