Instability Formation and Directional Dendritic Growth of Ice Studied by Optical Interferometry

Abstract

Mach−Zender optical interferometry was used to measure the concentration gradient at the ice−solution interface, and the ice−solution interface morphology, during directional crystallization of ice in sucrose (disaccharide) and pullulan (polysaccharide) solutions. For sucrose, at all concentrations, the solute concentration decayed exponentially with distance from the interface. For pullulan, an exponential decay was only measured for dilute solutions, there being a substantial deviation from a single-exponential decay for concentrated, entangled solutions. Constitutional supercooling was shown to be responsible for the onset of interfacial instability in all solutions. The Mullins−Sekerka (MS) theory of interfacial instability was tested and provided a reasonable prediction of the instability wavelength for sucrose solutions over a range of velocities within which the partition coefficient varied considerably, but not for pullulan. The discrepancy for pullulan was explained in terms of the hindered diffusion mechanism caused by entanglement of the polymer chains, rendering the assumptions made in the MS theory inaccurate. Three different equations for predicting the dendrite primary spacing were tested for sucrose solutions. Reasonable agreement was obtained with two expressions at low solute concentrations but, owing to invalidity of the assumptions made in its formulation, one of the expressions (the Hunt and Lu model) became increasingly inaccurate at higher concentrations.