Melt flow effect on interface stability during directional solidification

Abstract

In the framework of the phenomenological macroscopic continuum theory using the approximation of a flat frontier layer the stability of solid-liquid interface at the directional solidification under melt motion along the interface is studied. The stability conditions are reduced to determination of eigenvalues of boundary value problem for infinitesimal disturbances of stationary process. In case of stagnant melt it is shown that in the plane “wave number-pulling rate” there are two areas of instability for low and large pulling rates divided by the area of steady-steady growth. Neutral stability curve calculated for rather large pulling rates for succinonitrile-acetone (SCN-Ac) system is close to the relevant values received by Mullins and Sekerka, while the absolute values of critical growth rates are of the same order of magnitude as the experimental ones. Melt flow along the interface leads to emergence of the third area of instability which is characterized by small values of wave numbers. When increasing the melt flow rate the area of instability extends towards great values of wave numbers.