Crossover scaling of wavelength selection in directional solidification of binary alloys

A phase-field model solved with adaptive-mesh refinement was used to simulate cellular and dendritic growth in directional solidification in dilute binary alloys. The spacing of primary branches was examined for a wide range of thermal gradients and alloy compositions. It was found to undergo a maximum as a function of pulling velocity. The sharp-interface model was used to describe solidification of a dilute binary alloy with a partition coefficient k. The result confirm that the selected wavelength displays nonmonotonic behavior as a function of pulling speed.