Stability and selection of dendritic growth with anisotropic kinetic attachment

Abstract

In the investigations of free dendritic growth, the effect of kinetic attachment at the interface on pattern formation and selection has been an important issue attracting a great deal attention of researchers in the field of dynamics of pattern formation during the last decade. Particularly, the role of the effect of anisotropic kinetics played in the stability mechanisms and the selection of dendrite tip's velocity has become a crucial element for further understanding of the behaviors of dendritic growth of many important materials. In this paper, we attempt to study this subject. We assume that the system has both anisotropic interfacial energy and kinetic attachment at interface. In terms of the approach developed in the interfacial wave theory, we explore the effect of kinetic attachment on the stability mechanisms and the selection criterion of the limiting state of dendritic growth, by solving the related eigenvalue problem. It is found that the effect of kinetic attachment may render a significant effect on the global travelling wave (GTW) instability mechanism, as well as the low-frequency (LF) instability mechanism. The kinetic attachment may considerably stabilize the GTW mechanism by reducing the corresponding stability criterion ε ∗ . However, the kinetic attachment some times stabilizes, and some times destabilizes the LF instability mechanism. On this aspect, the ratio of anisotropy parameters of kinetic attachment and surface tension, r 4, plays the important role.