  The growth of a single needle of succinonitrile (SCN) is studied in three
dimensional space by using a phase field model. For realistic physical
parameters, namely, the large differences in the length scales, i.e., the
capillarity length (10^{-8}cm - 10^{-6}cm), the radius of the curvature at the
tip of the interface (10^{-3}cm - 10^{-2}cm) and the diffusion length
(10^{-3}cm - 10^{-1}cm), resolution of the large differences in length scale
necessitates a 500^{3} grid points on the supercomputer. The parameters,
initial and boundary conditions used are identical to those of the microgravity
experiments of Glicksman et al for SCN. The numerical results for the tip
velocity are (i) largely consistent with the Space Shuttle experiments; (ii)
compatible with the experimental conclusion that tip velocity does not increase
with increased anisotropy; (iii) different for 2D versus 3D by a factor of
approximately 1.9; (iv) essentially identical for fully versus rotationally
symmetric 3D.
