Non-stationary dendrite shape in the case of a high growth rate

Abstract

In the limit of infinite Peclet number, the shape of the solid/liquid interface is defined by the Gibbs-Thomson thermodynamic balance condition which contains the mean curvature and kinetic term in the general undercooling at the phase transition interface. Expressing the time derivative of the surface function from the kinetic contribution we have found the shape of the phase transition surface in the two-dimensional case for non-stationary solidification. The analytical solution was found in the form of a time-dependent correction factor to the spherical surface. It is shown that the dendritic surface quickly approaches the steady-state spherical shape in the course of time. In addition, the time of non-stationary period approximately equals 10−14 sec. The theory under consideration can be applied in analyzing more complex problems met in the dendritic growth theory (for instance, the growth of crystals in undercooled binary melts, the growth of dendrites in the presence of forced convection, local-nonequilibrium (rapid) solidification, and so on).