A kinematical model of liquid-drop solidification due to multiple surface-nucleation events

An analysis of the kinematics of liquid-drop solidification is developed using a nucleation/growth model consisting of multiple nucleation events, occurring simultaneously on the drop surface, followed by progression of solidification fronts from each of these nuclei into the drop interior. The rate at which the fronts move may vary with time, but at any given instant it is the same for every point on every front. On this basis, closed-form expressions are derived for the time-dependent average volume-fraction that has solidified both as a function of position within the drop and for the drop as a whole. Some specific examples are considered; among these are certain limiting cases, the results for which are shown to be consistent with studies reported by other investigators.