Initial transient solute redistribution during directional solidification with liquid flow

The initial transient solute redistribution during directional solidification with liquid flow is analyzed and approximate solutions for both finite and infinite sample length are given, based on two assumptions: (1) there exists a solute transport boundary layer within which diffusion is the only solute transport mechanism, while beyond which convective mixing makes the solute distribution completely uniform; (2) the concentration profile inside the diffusion boundary layer is of exponential form and the diffusion length is a function of time during the initial transient process. The solution for infinite sample length comes back to Warren and Langer's approximate solution for pure diffusion when thickness of the boundary layer approaches infinity, and back to Burton et al.'s accurate solution for steady state when time approaches infinity. The calculation results according to the models for initial transient solute redistribution during directional solidification with liquid flow fit well with Inatomi et al.'s experimental results.