Structure and Dynamics of Partially Solidified Systems

This volume contains papers presented at the NATO Advanced Research Workshop on the Structure and Dynamics of Partially Solidified Systems held at Stanford Sierra Lodge, Tahoe, California, May 12-16, 1986. This work shop grew out of a realization that there was a significant amount of interest and activity in this topic in several unrelated disciplines, and that it would be mutually beneficial to bring together those mathemati' cians, scientists and engineers interested in this subject to share their knowledge and ideas with each other. Partially solidified systems occur in a variety of natural and man made environments. Perhaps the most well-known occurrence involves the solidification of metallic alloys. Typically as a molten alloy is cooled, the solid phase advances from the cold boundary into the liquid as a branching forest of dendritic crystals. This creates a region of mixed solid and liquid phases, commonly referred to as a mushy zone, in which the solid forms a rigidly connected framework with the liquid occurring in the intercrystalline gaps. In addition to the casting of metallic alloys, mushy zones can occur in weld pools, the Earth's core and. mantle, magma chambers, temperate glaciers, frozen soils, frozen lakes and sea ice. A second mechanical configuration for the solid phase is as a suspension of small crystals within the liquid; this is referred to as a slurry.

Inhalt

1. Experimental Evidence.- Local Convective Flows in Partly Solidified Alloys.- Evolution of Lengthscales in Partially Solidified Systems.- Various Aqueous Solutions Crystallizing from the Side.- Double Diffusive Convection During Solidification at a Vertical Wall.- 2. Phase Change and Crystal Growth.- Nonlinear Analyses of Phase Change and Crystal Growth Phenomena.- Global Asymptotic Solution for Axisymmetric Dendrite Growth with Small Undercooling.- Some Aspects of the Stefan Model for Phase Transitions.- Some Aspects of the Weakly Nonlinear Theory of the Morphological Instability.- Phase Field Models of Free Boundary Problems: Exterior Boundaries Higher Order Equations and Anisotropy.- The Numerical Solution of Phase Change Problems.- 3. Theories of Slurries and Mushy Zones.- Theories of Mushy Zones: Applications to Alloy Solidification, Magma Transport, Frost Heave and Igneous Intrusions.- On Crystalization of a Binary Alloy Capable of Forming a Eutectic Mixture.- Dynamical Processes in Slurries.- A Boussinesq Model of a Slurry.- 4. Application to Magmatic and Aqueous Systems.- Towards Scaling Laws for the Interpretation of Igneous Structures.- Constitutional Zone Refining of Magmatic Intrusions.- The Role of Conjugate Convection in Magmatic Heat and Mass Transfer.- Melt Stability and Compaction in a Partially MoltenSilicate Layer Heated from Below.- Melt Migration in Deformable Media.- Crystallization Shrinkage in the Region of Partial Solidification: Implications for Silicate Melts.- Morphology, Microstructure and Micromechanics of Ice Fields.- Slush on Lakes.- A Bibliography of Partially Solidified Systems.