A numerical study of hollow water drop breakup during freezing

We present a numerical investigation of the breakup and freezing of a pendant hollow water drop beneath a cold curved surface. The drop contains a bubble surrounded by a shell of water that forms at an outer wetting angle of θo with the surface. The freezing begins on the cold curved surface and evolves in the direction of gravity. As it freezes, the water accumulates and forms a bulbous end at the bottom of the drop. Breakup can occur, inducing a daughter water drop. As a result, the freezing process of the remaining hollow drop attached to the surface takes less time, and the frozen drop shrinks. However, this breakup has no effect on the bubble. The various parameters under consideration include the Bond number Bo, the Stefan number St, the size of the bubble, and the angle θo. It is found that the breakup of the drop during freezing takes place for increasing Bo (from 0.1 to 3.0), increasing θo (from 60° to 120°), decreasing St (in the range of 0.01–0.64), or decreasing bubble size. On the other hand, the shape of the curved surface has little influence on the breakup of the drop. Phase diagrams of θo vs Bo and of St vs Bo are also presented to provide a more general picture of the breakup and freezing of the water drop.