On the Long-Wave Nonlinear Instability in Directional Solidification

Jin-Yuan Hsieh；Chi-Chuan Hwang

Chinese Journal of Physics

33卷3期（1995 / 06 / 01）

263 - 269

英文

In the present work, we undertake a fully nonlinear analysis of an evolution equation which describes the behavior of a solid-liquid interface in the directional solidification of a dilute binary mixture. The steady-state solutions, together with their stability analyses, and the locations of regular turning points in cases of subcritical bifurcation are evaluated. In the supercritical bifurcation, the stable finite amplitude to which a small perturbation to the planar interface will grow is also obtained. Some 2-D cellular patterns are also shown.