Nonlinear Three Dimensional Morphological Instability inDirectional Solidification --- An Integral Approximation

Abstract

In this article, we derive a strongly nonlinear evolution equation by usingthe integral method to study the instabilities in a directionallysolidified binary mixture. This equation not only can describe the interfacialbehaviors of all the long-wave limits, but also can provide the possibility ofstrongly nonlinear instability analysis.Three-dimensional weakly nonlinear analysis proceeded from the criticalcondition is undertaken to investigate the two-dimensional bend-like cells andthe three-dimensional hexagonal structures.