Rocket drops: The self-propulsion of supercooled freezing drops

Isolated supercooled water drops have been observed to move spontaneously while freezing in vacuum. This motion is caused by an increase of the evaporation rate during the early stages of freezing, which transfers momentum to the drops, similar to rocket propulsion. As in other cases of self-propulsion, symmetry breaking is necessary, and occurs when ice nucleation occurs away from the center of the drop. The self-propulsion velocity was modeled analytically for a simplified case, and numerically for two experiments. The model predicts peak velocities on the order of 1 m/s in vacuum, and a drop kinematics similar to that observed experimentally. In air, the self-propulsion velocity is expected to be much smaller but may be detectable for micron-sized drops.

Figure 1

Observation and modeling of the reactive self-propulsion of freezing drops. (a) Spreading of a train of drops after they froze. The images are averages of multiple drop stream images synchronized with the generation of drops, and cover the range of flight distances over which the drops nucleate ice and start to freeze. (b) A simplified physical model of the reactive force due to enhanced evaporation during freezing. (c) Additional mechanisms that impact the reactive force. (d) The evolution of the self-propulsion speed from ice nucleation until complete solidification, for a 40.9-µm-diameter drop supercooled to 234 K.

Figure 2

Comparison of the reactive self-propulsion model with experimental data. (a) Comparison between the trajectory of a 62-µm freezing drop observed by Ando et al. [18], and the trajectory predicted by the model. (b) The experimental distributions of vertical velocities of liquid drops at 69 mm and of frozen drops at 74 mm, and the distribution predicted by the self-propulsion model at 74 mm.