Instability of the Planar Freeze Front During Solidification of an Aqueous Binary Solution

A model describing the heat transfer, solute redistribution, and interface stability during the planar solidification of an aqueous binary solution has been developed. The temperature field was calculated using a modified Ka´rma´n-Pohlhausen integral technique. With this technique, the averaged heat conduction equation was solved with the full set of boundary conditions using an assumed spatial variation of the temperature profile. The concentration field was solved for analytically. The stability of the planar freezing morphology was determined using the Mullins-Sekerka stability criterion, in which the time variation of a sinusoidal perturbation of the planar interface was calculated. Application of this criterion to the freezing of saline indicates that 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.