Fluid Dynamics: Modeling and Analysis

This chapter summarizes the numerical modeling and analysis of mass transport processes, especially the fluid dynamics of crystal growth systems. It begins with a general description of diffusion in fluids, followed by a discussion of forced and natural convection. The second part relates these phenomena to external forces and flow instability. The chapter closes with a discussion of impurity transfer, including transfer in gaseous phase and at liquid-gas interfaces. Through impurity transfer, we can better understand the effect of the melt surface on convection in crystal growth systems such as Czochralski and directional silicon solidification.