Evolution and Instability of the Dendrite Growth Line in a Supercooled Melt
The growth of a dendrite in a unicomponent overcooled melt is studied. The phase boundary is considered as a strong rupture surface complying the conditions of dynamical compatibility subjected to the integral conservation laws. We studied the class of movements with the phase boundary velocity depending on the angle between the normal and the growth line. The time evolution of the two-dimensional contour of the phase boundary was studied both analytically and numerically. The shape of the growth line, its curvature, velocity and heat flux in the solid phase were studied as well. With respect to the problem of the vibration effect on the crystallization process, the influence of phase boundary velocity fluctuations on the heat transfer intensification is considered. The calculations showed strong sensitivity of the heat flux to changes in the vibration amplitude. The uniform (with account to the special time coordinate) growth of a two-dimensional axially symmetric contour of dendrite is considered. The case when the original line suffers a perturbation localized at a final distance from the vertex is analyzed. It is established that the perturbation of the growth line curvature (a protrusion or a dent) induces a harbinger of a side branches of an axon. Its geometrical image is the point of intersection of the time-evolving the contour line. The applied aspects of the report refer to the methods of high-speed solidification of melts and obtaining new functional materials.