Prof Ryuji Nomura (Hokkaido University) gives a webinar on ‘Dripping Superfluid 4He’ at 10AM UK time.

We visualized the dripping of superfluid 4He from a cup due to film flow and the oscillation of the pendant droplet that forms on the underside of the cup, using a high-speed video camera. We discovered that the oscillation period of the pendant droplet is anomalously independent of volume [1]. Because the surface of the cup was coated with a superfluid film, the droplet’s edge was not pinned to the surface, but the entire droplet, including its edge, oscillated simultaneously with a high amplitude and negligible damping. The volume-independent oscillation contradicts the widely accepted belief in classical fluid dynamics that larger droplets should oscillate more slowly. Our research shows that the free movement of the droplet’s edge allows the superfluid pendant droplet to stably exist only within a specific volume range, which is defined by two instabilities: the pinch-off instability that occurs at large volumes and the Rayleigh-Taylor instability that arises at small volumes. These two instabilities create a broad minimum in the oscillation period within this stable volume range, resulting in only marginally volume-dependent oscillations around this minimum. Moreover, we found that the dripping periods were consistently discretized and determined by the number of oscillations, even when the flow rate was gradually changing [2]. This anomalous behavior resembles that of a continuous time crystal, which spontaneously breaks time translation symmetry. This is in stark contrast to the chaotic dripping behavior of classical fluids, which exhibit widely varying dripping periods even under a fixed flow rate. To further investigate the role of the edge mobility of the droplets, we attached a narrow cylinder to the undersurface of the cup, restricting the edge movement. This modification effectively pinned the droplet’s edge at the cylinder’s corner, causing the previously observed anomalous behaviors to disappear. As a result, the droplets began to oscillate with periods that depended on their volume, and their dripping periods became widely distributed, resembling behaviors seen in classical fluids [1]. In conclusion, the anomalous oscillations and dripping behaviors are attributed to the free movement of the droplet’s edge across the cup’s surface, which is a phenomenon specific to superfluids.

[1] K. Onodera, R. Nagatomo, K. Miyake, R. Yamane, S. Takamatsu, Y. Aoki, and R. Nomura, Phys. Rev. Lett. 133, 216001 (2024).

[2] S. Takamatsu, R. Yamane, T. Tani, Y. Ishimoto, K. Miyake, Y. Aoki, and R. Nomura, New J. Phys. 27, 123503 (2025).