Using a quantitative phase-field model, a systematic investigation of cellular growth in directional solidification is carried out with emphasis on the selection of cellular tip undercooling, tip radius, and cellular spacing. Previous analytical models of cellular growth are evaluated according to the phase-field simulation results. The results show that cellular tip undercooling and tip radius not only depend on the pulling velocity and thermal gradient, but also depend on the cellular interaction related to the cellular spacing. The cellular interaction results in a finite stable range of cellular spacing. The lower limit is determined by the submerging mechanism while the upper limit comes from the tip splitting instability corresponding to the absence of the cellular growth solution, both of which can be obtained from phase-field simulation. Further discussions on the phase-field results also present an analytical method to predict the lower limit. Phase-field simulations on cell elimination between cells with equal spacing validate the finite range of cellular spacing and give deep insight into the cellular doublon and oscillatory instability between cell elimination and tip splitting.

• Received 28 April 2011

DOI:https://doi.org/10.1103/PhysRevE.84.041604