Dendritic Growth tip velocities and radii of curvature in microgravity
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. INTRODUCTION
DENDRITES are ramified, treelike crystals formed from a solidifying melt, occurring in many pure materials and alloy systems. Dendritic growth also provides an archetypal problem in morphogenesis, where a complex pattern evolves from simple starting conditions. As one of the simplest nontrivial examples of spontaneous pattern formation, the physical understanding and mathematical description of dendrites remains of interest to mathematicians, scientists, and engineers. The growth of dendrites is known to be controlled by the transport of latent heat (and for alloys, solute) from the moving crystal–melt interface into the supercooled (supersaturated) melt. The transport of heat and solute combine with the interplay of weaker effects like surface tension, interface attachment kinetics, and ambient noise. Gradients of the melt’s density near the solid–liquid interface, caused by the release of solute or latent heat, are acted upon by gravity. The gravitational body force results in buoyancyinduced melt flows affecting the overall transport conditions. Gravity-induced convection complicates how dendrites grow. A series of microgravity experiments in dendritic solidification, the IDGE, first flew in low-Earth orbit aboard the space shuttle Columbia (STS-62) in March 1994, and again in February 1996 and November 1997. The experiments involved growing thermal dendrites in a pure material at precisely measured supercoolings, and photographing them M.B. KOSS, Research Assistant Professor, J.C. LaCOMBE, Postdoctoral Research Associate, L.A. TENNENHOUSE, Graduate Research Assistant, and M.E. GLICKSMAN, John Tod Horton Professor, are with the Materials Science and Engineering Department, Rensselaer Polytechnic Institute, Troy, NY 12180-3590. E.A. WINSA, Project Manager, is with the Fluids and Combustion Facility, Microgravity Science Division, NASA-Glenn Research Center at Lewis Field, Cleveland, OH 44135. Manuscript submitted June 23, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
as they solidified. The local quasi-static acceleration field that promotes convection may be reduced on orbit to about one-millionth of its terrestrial value. The scientific objective of the experiments was to produce data sets of dendritic tip velocities and radii as benchmarks for critically testing theories of diffusion-limited dendritic growth. This article presents the final results and conclusions reached mainly from the first flight experiment. These experiments reveal for the first time large differences between dendritic growth occurring under terrestrial and microgravity conditions, as well as some disparities between the microgravity experiments and predictions based on theory.
II. BACKGROUND ON DENDRITIC GROWTH The quantitative study of dendrites began with the heattransport analysis of Ivantsov in 1947.[1] Ivantsov’s analysis only incorporates the conduction of latent heat from a dendrite, assumed to be paraboloidal and branchless. Over the past 50 years, a number of theories of steady-state dendritic crystal growth h
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