Long-wave morphological instabilities in directional solidification of a dulite binary mixture are investigated. We present a new nonlinear evolution equation of the solid-liquid interface for lage surface energy. This evolution equation contains not only quadratic and cubic nonlinearity terms, but also terms whose nonlinearites are higher than cubic and terms which are nonlinear and with time derivatives. It is shown that, in the weakly nonlinear instability analysis, when surface energy is very large, the cubic nonlinearity terms can be neglected. However, as surface energy is only finite, these terms may become significant for instability effects. If the bifurcation is supercritical, the cubic terms tends to enlarge the steady-state amplitudes of disturbances. On the other hand, for subcritical bifurcation, the cubic terms will diminish the threshold amplitudes which should not be exceeded by the amplitudes of the initial disturbances in the linearly stable region if a stable solidification system is wanted.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Inorganic Chemistry
- Materials Chemistry