Journal of Low Temperature Physics

, Volume 196, Issue 1–2, pp 52–59 | Cite as

The Role of Substrate Roughness in Superfluid Film Flow Velocity

  • Jun UsamiEmail author
  • Nobuyuki Kato
  • Tomohiro Matsui
  • Hiroshi Fukuyama


It is known that the apparent film flow rate \(j_0\) of superfluid \(^4\)He increases significantly when the container wall is contaminated by a thin layer of solid air. However, its microscopic mechanism has not yet been clarified enough. We have measured \(j_0\) under largely different conditions for the container wall in terms of surface area (0.77–6.15 m\(^2\)) and surface morphology using sintered silver fine powders (particle size: 0.10 \({\upmu }\)m) and porous glass (pore size: 0.5, 1 \({\upmu }\)m). We could increase \(j_0\) by more than two orders of magnitude compared to non-treated smooth glass walls, where liquid helium flows down from the bottom of the container as a continuous stream rather than discrete drips. By modeling the surface morphology, we estimated the effective perimeter of the container \(L_{\mathrm {eff}}\) and calculated the flow rate \(j~(= j_0L_0/L_{\mathrm {eff}})\), where \(L_0\) is the apparent perimeter without considering the microscopic surface structures. The resultant j values for the various containers are constant within a factor of four, suggesting that the enhancement of \(L_{\mathrm {eff}}\) plays a major role to change \(j_0\) to such a huge extent and that the superfluid critical velocity, \(v_{\mathrm {c}}\), does not change appreciably. The measured temperature dependence of j revealed that \(v_{\mathrm {c}}\) values in our experiments are determined by the vortex depinning model of Schwarz (Phys Rev B 31(9):5782, 1985. with several nm size pinning sites.


Superfluid Film flow Vortex pinning Critical velocity Porous glass 



The authors thank Akagawa Glass Co., Ltd., for providing us the porous glass containers. We are also grateful to the late Tadao Imai for processing the Pyrex glass containers. JU was supported by Japan Society for the Promotion of Science through Program for Leading Graduate Schools (MERIT).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsThe University of TokyoTokyoJapan

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