抄録
We give an historical perspective of efforts to model the growth of an ice disk from pure supercooled water. A disk shape occurs essentially because growth along the c axis is strongly limited by interfacialkinetics but growth in the basal plane is relatively isotropic and limited by heat flow. Thus, although the growth is predominantly two-dimensional, the heat flow problem is three dimensional and practically that of heat liberated by a hot expanding ring whose thickness increases very slowly. Quantitative modeling of this heat flow by Fujioka in his doctoral work of 1978 will be presented. Morphological stability analysis of the ice disk also turns out to be an interesting three dimensional problem, even though early attempts to model it by Williamson and Chalmers were strictly two dimensional. Indeed, the mean curvature, K=1/R1 + 1/R2 where R1 and R2 are principal radii of curvature, is known to provide the stabilizing effect that offsets the destabilizing effect of heat flow into supercooled water. One of these radii, R1, is the order of the disk radius, R, while the other, R2, is of the order of the disk thickness, h Since h << R, the stabilizing effect is mostly related to the disk thickness, not its radius, even though both increase together This is in agreement with two experimental observations: First, discs of the same radius R can be either thick or thin depending on initial conditions; the thin ones are stable and the thick ones are unstable. Second, the len<gth scale of an instability, when it occurs, is comparable to h, not R In order to quantify these phenomena, some simultaneous measurements of disk thickness and radius by optical techniques were made by El Zayyat, but the work was never completed. Now, years later, beautiful work under by Professor Furukawa and his collaborators is yieldinga detailed experimental knowledge of the complex surface morphology of lce disks and dendrites as well as theoretical understanding of the origin of growth anisotropies and instabilities. Yet some mysteries remain to be explored.
