Solvability condition for 3-D axisymmetric needle crystals at large undercooling

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Abstract
We extend the analytical method developed in a recent paper to investigate the existence of axisymmetric 3-D needle-crystals in a realistic non-local model of diffusion-controlled growth of a pure solid in the limit of large undercooling. As in 2-D systems, the breaking of the Ivantsov degeneracy by the singular capillary perturbation results in a solvability condition to be satisfied by needle-crystal solutions. In the limit of very small surface tension, we find that no axisymmetric needle crystal exists in the 3-D isotropic system