TY - JOUR
T1 - Three-dimensional cellular instabilities in directional solidification considering interfacial kinetics
AU - Yang, Hwei Yen
AU - Hwang, Chi Chuan
AU - Luo, Yong Yuan
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1997
Y1 - 1997
N2 - In this work, three-dimensional cellular instabilities in directional solidification are investigated. Local thermodynamic nonequilibrium at the solid-liquid interface is taken into account by applying a model of velocity-dependent segregation coefficient and attachment kinetics developed by Boettinger, Aziz, and Jackson et al. The infinitely one-sided model and the frozen-temperature approximation are adopted in the analysis. An evolution equation was first derived by an integral technique. Then the Segel-Stuart method was used to determine the solvability constants of the amplitude equations. The equilibrium solutions associated with different morphologies were evaluated and the stability analysis of them to three-dimensional disturbances was studied. Finally, five stability basins of bifurcation were addressed. The result shows that the interface morphologies depend on which basin the chosen critical condition is located in and how far the operating point is exceeded from the critical condition. The presence of disequilibrium can stabilize the steady cellular mode, cause the wave number to be smaller, and affect the location of the chosen critical condition in the basin of bifurcation.
AB - In this work, three-dimensional cellular instabilities in directional solidification are investigated. Local thermodynamic nonequilibrium at the solid-liquid interface is taken into account by applying a model of velocity-dependent segregation coefficient and attachment kinetics developed by Boettinger, Aziz, and Jackson et al. The infinitely one-sided model and the frozen-temperature approximation are adopted in the analysis. An evolution equation was first derived by an integral technique. Then the Segel-Stuart method was used to determine the solvability constants of the amplitude equations. The equilibrium solutions associated with different morphologies were evaluated and the stability analysis of them to three-dimensional disturbances was studied. Finally, five stability basins of bifurcation were addressed. The result shows that the interface morphologies depend on which basin the chosen critical condition is located in and how far the operating point is exceeded from the critical condition. The presence of disequilibrium can stabilize the steady cellular mode, cause the wave number to be smaller, and affect the location of the chosen critical condition in the basin of bifurcation.
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U2 - 10.1103/PhysRevB.55.824
DO - 10.1103/PhysRevB.55.824
M3 - Article
AN - SCOPUS:0345726436
SN - 1098-0121
VL - 55
SP - 824
EP - 836
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 2
ER -