Phase field computations and comparison with experiments

We present a phase field computation to compute the temporal evolution of the interface for solidification of a single needle crystal of Succinonitrile (SCN). The computations are done in two different settings with conditions satisfying microgravity experiments: First, we study the growth of dendrite in a cylindrical geometry by performing large scale three dimensional (3D) computations which utilizes rotational symmetry. Secondly, we perform large scale fully three dimensional (3D) computations of phase field model in a cubical region which utilizes parallel computation and makes use of super computers. We compare the computational results with the microgravity experiments.; We study the following key issues by using the three dimensional simulators: (1) We compute the growth velocities corresponding to several undercooling values for SCN. We find that the computational growth velocities are consistent with the microgravity experiments and the results confirm the theoretical and experimental findings. The undercooling values and corresponding growth velocities show a linear relation, and the growth velocities approach a constant in large time. (2) We show that the computational results are compatible with the experimental conclusion that tip velocity does not increase for larger anisotropy (e.g. for Pivalic acid). (3) Computational growth velocities for SCN in a rotational symmetric domain do not differ very much from the results in fully 3D calculations. (4) We also show that there is about a factor of 2 between the growth velocities obtained in 2D calculations and 3D calculations which also indicates that 3D calculations approximates the experimental growth velocities more accurately. (5) The effects of kinetic coefficient is studied in a 3D geometry by using different strength of anisotropy. The computational results show that dendritic growth strongly depends on physical value of the kinetic coefficient in the model.