Thermal effects in rapid directional solidification: linear theory

We study the morphological instability of the planar solid/liquid interface for a unidirectionally-solidified dilute binary mixture. We use a model developed by Boettinger et al., Aziz, and Jackson et al., which allows for nonequilibrium effects on the interface through velocity-dependent segregation and attachment kinetics. Two types of instabilities are found in the linear stability analysis: (i) a cellular instability, and (ii) an oscillatory instability driven by disequilibrium effects. Merchant and Davis characterized these instabilities subject to the frozen-temperature approximation (FTA). The present work relaxes the FTA by including the effects of latent heat and the full temperature distribution. Thermal effects slightly postpone the onset of the cellular instability but dramatically postpone the onset of the oscillatory instability; however, the absolute-stability conditions, at which at high speed the cellular and oscillatory instabilities are suppressed, remain unchanged from the FTA. The critical wavenumber for the oscillatory instability can be zero or nonzero depending on the material parameters. The experimental observations of banding are correlated with the predictions of our theory.