Directional solidification near minimumc∞: Two-dimensional isolas and multiple solutions
- 1 December 1989
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 40 (16) , 11140-11152
- https://doi.org/10.1103/physrevb.40.11140
Abstract
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 . When >, 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 . In this paper two-dimensional weakly nonlinear instabilities are studied for small ‖-‖ so both the low- and high-speed bifurcations can be simultaneously described. When the thermal-conductivity ratio n=/ 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.
Keywords
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