Structure and Dynamics of Partially Solidified Systems

1. Front Matter

   Pages i-ix

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2. Experimental Evidence

   1. Front Matter

      Pages 1-1

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   2. Local Convective Flows in Partly Solidified Alloys

      • A. Hellawell

      Pages 3-22

   3. Evolution of Lengthscales in Partially Solidified Systems

      • S. P. Marsh, M. E. Glicksman

      Pages 23-35

   4. Various Aqueous Solutions Crystallizing from the Side

      • A. M. Leitch

      Pages 37-57

   5. Double Diffusive Convection during Solidification at a Vertical Wall

      • M. E. Thompson, J. Szekely

      Pages 59-77

3. Phase Change and Crystal Growth

   1. Front Matter

      Pages 79-79

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   2. Nonlinear Analyses of Phase Change and Crystal Growth Phenomena

      • D. J. Wollkind

      Pages 81-94

   3. Global Asymptotic Solution for Axisymmetric Dendrite Growth with Small Undercooling

      • Jian-Jun Xu

      Pages 95-109

   4. Some Aspects of the Stefan Model for Phase Transitions

      • S. D. Howison

      Pages 111-119

   5. Some Aspects of the Weakly Nonlinear Theory of the Morphological Instability

      • A. A. Wheeler

      Pages 121-129

   6. Phase Field Models of Free Boundary Problems: Exterior Boundaries Higher Order Equations and Anisotropy

      • Gunduz Caginalp, Paul Fife

      Pages 131-139

   7. The Numerical Solution of Phase Change Problems

      • Gunter H. Meyer

      Pages 141-156

4. Theories of Slurries and Mushy Zones

   1. Front Matter

      Pages 157-157

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   2. Theories of Mushy Zones: Applications to Alloy Solidification, Magma Transport, Frost Heave and Igneous Intrusions

      • A. C. Fowler

      Pages 159-199

   3. On Crystalization of a Binary Alloy Capable of Forming a Eutectic Mixture

      • Lev Rubinstein, Abraham Levy

      Pages 201-228

   4. Dynamical Processes in Slurries

      • Paul H. Roberts, David E. Loper

      Pages 229-290

   5. A Boussinesq Model of a Slurry

      • David E. Loper, Paul H. Roberts

      Pages 291-323

5. Application to Magmatic and Aqueous Systems

   1. Front Matter

      Pages 325-325

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   2. Towards Scaling Laws for the Interpretation of Igneous Structures

      • Geneviève Brandeis, Claude Jaupart

      Pages 327-347

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.

• convection
• dynamics
• growth
• mechanics
• stability
• surgical oncology

• Florida State University, Tallahassee, USA

  David E. Loper

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