Journal ArticleDOI
Solidification of an alloy from a cooled boundary
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In this article, a mathematical model for the region of dendritic or cellular growth which often forms during the solidification of alloys is presented, where the model treats the mixed phase (solid and liquid) as a continuum whose properties vary with the local volume fraction of solid.Abstract:
We Present a mathematical model for the region of dendritic or cellular growth which often forms during the solidification of alloys. The model treats the region of mixed phase (solid and liquid) as a continuum whose properties vary with the local volume fraction of solid. It is assumed that transports of heat and of solute are by diffusion alone, and the model is closed by a condition of marginal equilibrium. Results are obtained for the unidirectional solidification of an alloy from a plane wall. The spatial variations of solid fraction are highly suggestive of the types of morphology that can occur, and a wealth of different structures are found as the physical parameters are varied. Although the model ignores gravity entirely, the results can be applied to the solidification from below of an alloy which is initially less dense than its eutectic. Predictions for the growth rate of the mixed-phase region agree well with existing experimental measurements of ice growing from aqueous salt solutions.read more
Citations
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Geochemical consequences of in situ crystallization
TL;DR: In situ crystallization of a magma chamber in a transition zone between solidus and liquidus may cause the magma to evolve along a chemical path that differs markedly from that produced by fractional crystallization in closed or periodically replenished magma chambers as discussed by the authors.
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Convection in mushy layers
TL;DR: In this paper, the authors present an account of various studies of buoyancy-driven convection in mushy layers, paying particular attention to the complex interactions between solidification and flow that lead to novel styles of convective behavior, including focusing of the flow to produce chimneys.
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Instabilities of the liquid and mushy regions during solidification of alloys
TL;DR: In this article, two modes of compositional convection during solidification from below are uncovered using a linear-stability analysis: one is driven by buoyant residual fluid within a mushy layer, or porous medium, of dendritic crystals; the other, which we shall call the " boundary-layer mode " is associated with a narrow compositional boundary layer in the melt just above the mush-liquid interface.
Journal ArticleDOI
Compositional convection in a reactive crystalline mush and melt differentiation
Stephen Tait,Claude Jaupart +1 more
TL;DR: In this paper, the authors describe experiments on the directional solidification of aqueous ammonium chloride solutions, where the addition of small amounts of a polymerizing agent permits variation of the solution viscosity independently of thermal conditions, phase diagram, and permeability.
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The fluid mechanics of solidification
TL;DR: In this article, a review of the concepts involved in the fluid mechanics of solidification is presented, as well as quantitative calculations for the fluid motion, the rate of growth of solid and the evolution of both the thermal and the compositional fields in various geometries.
References
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Handbook of Mathematical Functions
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Stability of a Planar Interface During Solidification of a Dilute Binary Alloy
W. W. Mullins,R. F. Sekerka +1 more
TL;DR: In this article, the stability of a moving planar liquid-solid interface during unidirectional freezing of a dilute binary alloy is theoretically investigated by calculating the time dependence of the amplitude of a sinusoidal perturbation of infinitesimal amplitude introduced into the planar shape.
Journal ArticleDOI
Instabilities and pattern formation in crystal growth
TL;DR: In this article, the authors examined several common modes of crystal growth and identified a few new theoretical ideas and a larger number of outstanding problems, including sidebranching and tip-splitting instabilities.
Journal ArticleDOI
A prismatic substructure formed during solidification of metals
J. W. Rutter,B. Chalmers +1 more
TL;DR: In this article, single crystals of tin grown from the melt under a wide range of conditions are shown to exhibit a fibrous structure which manifests itself as parallel ridges ("corrugations") on the free surface o...