TY - JOUR
T1 - Directional solidification near minimum c
T2 - Two-dimensional isolas and multiple solutions
AU - Merchant, G. J.
AU - Davis, S. H.
N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 1989
Y1 - 1989
N2 - Mullins and Sekerka showed, using linear-stability theory, that for fixed temperature gradient, the planar interface is stable for all pulling speeds V when the solute concentration cc*, there is a low-speed instability when the melt is constitutionally undercooled and a high-speed stabilization due to surface energy when the absolute-stability criterion is reached. The two branches meet at c*. In this paper two-dimensional weakly nonlinear instabilities are studied for small -c-c*- so both the low- and high-speed bifurcations can be simultaneously described. When the thermal-conductivity ratio n=kS/kL is small (large), both bifurcations are supercritical (subcritical) and shallow (deep) cells emerge. For intermediate n there is complex behavior exhibiting multiple transitions, separated branches (isolas), and multiple cellular states.
AB - Mullins and Sekerka showed, using linear-stability theory, that for fixed temperature gradient, the planar interface is stable for all pulling speeds V when the solute concentration cc*, there is a low-speed instability when the melt is constitutionally undercooled and a high-speed stabilization due to surface energy when the absolute-stability criterion is reached. The two branches meet at c*. In this paper two-dimensional weakly nonlinear instabilities are studied for small -c-c*- so both the low- and high-speed bifurcations can be simultaneously described. When the thermal-conductivity ratio n=kS/kL is small (large), both bifurcations are supercritical (subcritical) and shallow (deep) cells emerge. For intermediate n there is complex behavior exhibiting multiple transitions, separated branches (isolas), and multiple cellular states.
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U2 - 10.1103/PhysRevB.40.11140
DO - 10.1103/PhysRevB.40.11140
M3 - Article
AN - SCOPUS:33746458769
VL - 40
SP - 11140
EP - 11152
JO - Physical Review B
JF - Physical Review B
SN - 0163-1829
IS - 16
ER -