NONLINEAR MORPHOLOGICAL INSTABILITIES IN DIRECTIONAL SOLIDIFICATION - AN INTEGRAL APPROXIMATION

In this article, we derive a strongly nonlinear evolution equation by using the integral method to study the instabilities in a directionally solidified binary mixture. This equation can not only describe the interfacial behaviors of all the long-wave limits, but can also provide the possibility of strongly nonlinear instability analyses. Weakly nonlinear analyses proceeded from the critical conditions are undertaken to investigate the two-dimensional bifurcation types and a transition curve separating subcritical and supercritical ranges is obtained.