Global Asymptotic Solution for Axisymmetric Dendrite Growth with Small Undercooling

Abstract

Stationary non-isothermal growth of a needle-like crystal is considered. When the undercooling parameter is very small, the dendrite will always be slender. Hence slender body theory is applicable. We obtain a self consistent uniformly valid asymptotic solution to the problems. Our results show that as long as the surface tension parameter is small enough there always exists a smooth needle like solution for a given undercooling temperature. This non-isothermal needle is close to the Ivantsov parabaloid.