Concluding Remark

Abstract

In this monograph, I reviewed some recent research works on dynamics of dendritic growth interacting with convective flow. My attention is focused on the results obtained by a systematic, analytical approach in the framework of the IFW theory, some relevant numerical simulation works on this subject are left out. Moreover, as mentioned at the beginning of the book, dendritic growth is a complex nonlinear phenomenon occurring in a variety of crystal growth systems, hence, the studies presented in this book can only reveal a portion of the nature of this phenomenon. Many significant problems in this field are open. Among these unsolved issues, in my opinion, the following are particularly of interest and should be further explored in the near future:

• Dendritic growth interacting with more complicated flow field in melt;

• Non-axi-symmetric dendritic growth, caused by anisotropic surface tension, or non-axi-symmetric buoyancy effect.

• Dendritic growth affected by external forces other than gravity.

• Dendritic growth with the effect of anisotropic kinetic attachment.

• Stability, selection and formation of an array of dendritic growth under various growth conditions. Especially, the stability and transition of cellular growth to an array of dendritic growth in directional solidification. This long-standing, challenging problem in the area of materials science is still not well resolved.