The Quarterly Journal of Mechanics and Applied Mathematics · 1983 · 295 citations · 0 references
Natural SciencesMathematicsPhysicsFluid DynamicsStochastic ProcessesThermodynamicsEntropyPhase TransitionsSecond Law Of ThermodynamicsStatistical MechanicsThermodynamic StabilityMushy Zone DynamicsMushy Zone EvolutionMushy Zone FormationMushy Zone Heat TransferMushy Zone MechanicsMushy Zone ModelingThermodynamic Modeling
A thermodynamically consistent theory is developed capable of modelling a mushy zone, that is a region of mixed solid phase and liquid phase that can occur during the cooling of a binary alloy. The solid phase forms as a matrix of crystals—often dendrites—which resembles a porous medium of spatially varying permeability. This permeability diminishes in time as further solid freezes out of the liquid phase as it percolates through the matrix. The theory developed here is general enough to incorporate these and other ingredients essential to a proper theoretical treatment of a mushy zone. A simple one-dimensional freezing problem is formulated and solved.