Experimental investigation of the dynamics of spontaneous pattern formation during dendritic ice crystal growth

Abstract

The dynamics of spontaneous pattern formation are studied experimentally by observing and recording the evolution of ice crystal patterns which grow freely in a supercooled melt. The sequence of evolution to dendrites is recorded in real time using cine-micrography. In the range of subcoolings from 0.06 to 0.29°C, all the patterns evolved as follows: Smooth disk → Perturbed disk → Disk dendrite → Partially developed dendrite → Fully developed dendrite. The initial smooth disk, the main branch and the side branches all developed perturbations beyond a critical size which depends on the subcooling. The combined effect of the destabilizing thermal gradients ahead of the growing crystal and the stabilizing Gibbs-Thompson capillarity effect dictates the critical size of the unstable structures in terms of the mean curvature of the interface. Detailed analysis of the evolving patterns was done using digital image analysis on the PRIME computer to determine both the manner in which the dendritic growth process replicates itself and the role which the shape and the movement of the interface play in the pattern formation process. Total arc length S T, total area A and the complexity ratio ξ = S T ⧸√ A of evolving patterns were computed as a function of time and undercooling for each crystal image. These results permitted us to make some comparisons with theoretical models on pattern evolution. Three distinct phases of evolution were identified: the initial phase when the crystal structure is smooth and free of any perturbations and the complexity ratio is almost a constant, an intermediate phase when the crystal structure develops perturbations which grow quickly in number and in size and the complexity ratio increases rapidly and a final phase when the pattern approaches that of a fully developed dendrite which, on a global scale grows in a shape-perserving manner and has a slowly increasing complexity ratio which seems to approach an asymptote. Two factors were found to be responsible for the symmetric dendritic patterns. These are: first, hexagonal symmetry due to the hexagonal closed packed structure, leads to strong anisotropy in molecular attachment kinetics and in surface free energy; second, the competition among side branches causes smaller side branches to melt when they are trapped between larger ones which generate latent heat and prevent the small branches from gaining access to the fresh cold fluid ahead of them. These two factors lead to a channelling effect which prevents the growth of perturbations from occurring randomly and thus directs the evolving crystal structure into patterns which are regular and reproducible. Theoretical models which are local in nature fail to take into account side branch competition, and this is one of their major weaknesses.