Theory and experiments on the ice-water front propagation in droplets\n freezing on a subzero surface

An approximate theory is presented describing the propagation of the\nice-water front that develops in droplets of water that are deposited on a\nplanar surface at a temperature below the melting point of ice. A calculation\nbased on this theory is compared with our experimental observations of the time\nevolution of this front. The results of calculations of this front by Schultz\net al7, obtained by integrating numerically the exact differential equations\nfor this problem, were published graphically, but only for the time-dependent\nvelocity of this front. Unfortunately, these theoretical results cannot be\ncompared directly with our experimental observations. Our experiments were\nperformed by freezing water droplets directly on a block of dry ice, and in\norder to examine the effects of the heat conductivity of a substrate during the\nfreezing process, such droplets were also deposited on a glass plate and on a\ncopper plate placed on dry ice. The temperature at the base of these droplets,\nand the dependence of the freezing time on their size was also investigated ex\nperimentally, and compared with our analytic approximation of the theory. Such\nexperiment have not been published previously, and reveal that the usual\nassumption that the temperature at the base of the droplets is a constant, made\nin all previous theoretical papers on this subject, cannot be implemented in\npractice.\n