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Marginally volume-dependent oscillation modes of superfluid pendant droplets in an intervening stability region

Ryota Yamane1, Shota Takamatsu1, Yuri Ishimoto1, Keito Miyake1, Tomoyuki Tani1, Yuki Aoki2, and Ryuji Nomura1,*

  • 1Department of Applied Physics, Hokkaido University, Kita 13 Nishi 8, Kitaku, Sapporo, Hokkaido 060-8628, Japan
  • 2Center for Mathematics and Data Science, Gunma University, 4-2 Aramaki-machi, Maebashi, Gunma 371-8510, Japan

  • *Contact author: nomuraryuji@eng.hokudai.ac.jp
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Phys. Rev. Research 8, 033255 – Published 1 September, 2026

DOI: https://doi.org/10.1103/qjzn-l6yj

Abstract

Droplets are ubiquitous in nature and industry, yet their behavior is not yet fully understood, particularly for extreme conditions not typically encountered in viscous classical fluids. In this study, we investigated the oscillations of a superfluid He4 pendant droplet formed beneath a cup by superfluid film flow. We controlled the mobility of the droplet's edge by attaching cylinders of varying diameter to the underside of the cup, so that the droplet was suspended from the bottom of the cylinder. For wide cylinders or in the absence of a cylinder, the lowest point of the droplet oscillated vertically, while the edge oscillated along the surface, with only a slight dependence of the oscillation period on the droplet volume, which contradicts the common assumption in classical fluids that larger droplets oscillate with a longer period. For narrow cylinders, the droplet oscillated vertically, while the edge remained fixed at the cylinder's edge, and the oscillation period increased monotonically with increasing droplet volume, displaying the expected behavior. These observations demonstrate that free motion of the droplet's edge contributes to anomalous volume-independent oscillation of pendant droplets. We propose that the marginal volume dependence arises from the stability of superfluid pendant droplets in a region between two instabilities. This behavior is significant only for fluids that completely wet the substrate and possess a mobile edge, a condition rarely observed in classical fluids but naturally occurring in superfluids. Hence, these findings reveal unique properties of droplets in superfluid He4 not seen in classical fluids.

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Phys. Rev. Research 8, 033255– Published 1 September, 2026
  • Received 9 February 2026
  • Accepted 23 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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