SOLIDIFICATION OF BINARY MIXTURE IN A FINITE PLANAR MEDIUM
Doctor of Philosophy
A model describing the one-dimensional heat transfer and solute redistribution during a planar solidification of a binary mixture in a finite medium, insulated and nonpermeable at one boundary, and subject to thermal boundary conditions of the first, second, third and fourth kind at the other boundary is developed. The temperature and concentration fields were obtained by both, approximate analytical and numerical techniques. Approximate analytical solutions consist of using a modified Karman-Pohlhausen integral technique and Biot's variational method (only for the first domain of the temperature field in the liquid domain). An implicit finite difference method was employed to obtain the temperature and concentration fields numerically. The Mullins-Sekerka stability criterion was used to analyze the stability of the planar interface. The results indicate that the solute concentration at the interface is not constant but increases with time due to increased solute rejection from the ice matrix as the nonpermeable wall slows the interface motion, and the fusion temperature will be depressed because of the solute build-up at the interface. Application of the stability criterion to the freezing of saline water indicates that almost for any practical freezing rate the planar interface was unstable. This represents an indictment of the planar freezing model and indicates the tendency for aqueous solutions to freeze dendritically. It was found that for lower initial solute concentrations and/or heat fluxes, the instability will be reached in longer times.