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Pulsatile instability in rapid directional solidification - Strongly-nonlinear analysisIn the rapid directional solidification of a dilute binary alloy, analysis reveals that, in addition to the cellular mode of Mullins and Sekerka (1964), there is an oscillatory instability. For the model analyzed by Merchant and Davis (1990), the preferred wavenumber is zero; the mode is one of pulsation. Two strongly nonlinear analyses are performed that describe this pulsatile mode. In the first case, nonequilibrium effects that alter solute rejection at the interface are taken asymptotically small. A nonlinear oscillator equation governs the position of the solid-liquid interface at leading order, and amplitude and phase evolution equations are derived for the uniformly pulsating interface. The analysis provides a uniform description of both subcritical and supercritical bifurcation and the transition between the two. In the second case, nonequilibrium effects that alter solute rejection are taken asymptotically large, and a different nonlinear oscillator equation governs the location of the interface to leading order. A similar analysis allows for the derivation of an amplitude evolution equation for the uniformly pulsating interface. In this case, the bifurcation is always supercritical. The results are used to make predictions about the characteristics of solute bands that would be frozen into the solid.
Document ID
19930026573
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Merchant, G. J.
(IBM Thomas J. Watson Research Center Yorktown Heights, NY, United States)
Braun, R. J.
(NIST Gaithersburg, MD, United States)
Brattkus, K.
(California Inst. of Technology Pasadena, United States)
Davis, S. H.
(Northwestern Univ. Evanston, IL, United States)
Date Acquired
August 15, 2013
Publication Date
October 1, 1992
Publication Information
Publication: SIAM Journal on Applied Mathematics
Volume: 52
Issue: 5
ISSN: 0036-1399
Subject Category
Materials Processing
Accession Number
93A10570
Distribution Limits
Public
Copyright
Other

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