Examination of binary alloy free dendritic growth theories with a phase-field model

Two-dimensional phase-field simulations are used to test standard theories for free dendritic growth of alloys. While the transport of heat and solute in the melt is predicted well by the theories, the selection criterion for the operating state of the dendrite tip is found to break down in several respects. The selection parameter, σ*, computed from the phase-field simulations varies strongly with alloy composition, Lewis number, and imposed undercooling, whereas the theories assume σ* to be independent of these parameters. While the computed σ* is the same for purely thermal and solutal dendrites, it experiences a minimum at a small but finite solute concentration where thermal and solutal effects are both important. A pronounced growth velocity maximum at this composition is therefore not found in the simulations. The high Péclet number corrections of the LKT theory are found to be ineffective for the present range of undercoolings.