Morphological stability during directional solidification into an oscillatory molten zone

We study the morphological instabilities of a dilute binary alloy during directional solidification into a time-periodic, oscillatory molten zone by modulating the solute field. The basic state, in which the flat melt–solid interface advances in a sinusoidal way, is solved analytically by expanding the governing equations in terms of the assumed-small amplitude of modulation. A linear stability analysis is then performed on the interface considering two specific instability modes: synchronous and subharmonic modes. We find the original Mullins–Sekerka instability can be stabilized synchronously by the imposed modulation. The subharmonic mode occurs with smaller wave numbers and is less critical than the synchronous Mullins–Sekerka mode.