TY - JOUR
T1 - Hydrodynamic stability of the melt during the solidification of a binary alloy with small segregation coefficient
AU - Riley, D. S.
AU - Davis, S. H.
N1 - Funding Information:
The authors wish to thank T. Erneux for producing fig. 2. The work was supportedi n part by the National Aeronauticsa nd SpaceA dministra-tion, Microgravity Sciencea nd Applications Program and in part by the Sciencea nd Engineering ResearchC ouncil.
PY - 1989/10/2
Y1 - 1989/10/2
N2 - We consider the convective flow present during the directional solidification of a dilute binary alloy having small segregation coefficient k. The constitutional undercooling is set to zero, so that morphological instabilities of the melt-crystal interface are suppressed and the interface is planar. In the linearized stability theory, the critical wave number of the convective mode ac is found to behave like ac ≈ k 1 4 as k → 0, which is identical in behavior to the morphological mode. The weakly nonlinear theory gives rise to a Sivashinsky equation governing the spatial structure of the convection. Unlike previous long-wave evolution equations governing convective processes, this one arises in a geometrically unbounded domain with system boundaries that are neither fixed heat flux nor small Biot number; here the equivalent Biot number is of unit order.
AB - We consider the convective flow present during the directional solidification of a dilute binary alloy having small segregation coefficient k. The constitutional undercooling is set to zero, so that morphological instabilities of the melt-crystal interface are suppressed and the interface is planar. In the linearized stability theory, the critical wave number of the convective mode ac is found to behave like ac ≈ k 1 4 as k → 0, which is identical in behavior to the morphological mode. The weakly nonlinear theory gives rise to a Sivashinsky equation governing the spatial structure of the convection. Unlike previous long-wave evolution equations governing convective processes, this one arises in a geometrically unbounded domain with system boundaries that are neither fixed heat flux nor small Biot number; here the equivalent Biot number is of unit order.
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U2 - 10.1016/0167-2789(89)90006-7
DO - 10.1016/0167-2789(89)90006-7
M3 - Article
AN - SCOPUS:0024752952
SN - 0167-2789
VL - 39
SP - 231
EP - 238
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 2-3
ER -