Morphological instabilities in rapid directional solidifications under local nonequilibrium conditions

We perform the linear morphological instability analysis in rapid directional solidifications of dilute binary alloys considering the local nonequilibriums both in the bulk liquid and at the solid/liquid front. The generalized Fick's law for mass transport in the melt and the velocity dependence of the segregation coefficient modified by Sobolev and coworkers are employed for the analysis. The result shows that, compared to the situation where nonequilibrium effects at the interface only are considered, the effect of the local nonequilibrium in the bulk postpones the onset of the steady cellular instability but quickens the onset of the oscillatory cellular instability. Consequently, smaller surface-energy and larger attachment kinetics are expected for the absolute-stability boundaries of the steady and oscillatory cellular instabilities, respectively.