Visualization of Two-Fluid Flows of Superfluid Helium-4 SPECIAL FEATURE
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Visualization of two-fluid flows of superfluid helium-4 SPECIAL FEATURE Wei Guoa,b, Marco La Mantiac, Daniel P. Lathropd, and Steven W. Van Scivera,b,1 aMechanical Engineering Department, Florida State University, Tallahassee, FL 32303; bNational High Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32310; cDepartment of Low Temperature Physics, Faculty of Mathematics and Physics, Charles University, 180 00 Prague, Czech Republic; and dDepartments of Physics and Geology, Institute for Research in Electronics and Applied Physics, and Institute for Physics Science and Technology, University of Maryland, College Park, MD 20742 Edited by Katepalli R. Sreenivasan, New York University, New York, NY, and approved December 13, 2013 (received for review July 17, 2013) Cryogenic flow visualization techniques have been proved in not kept pace, in part due to the extremely low temperature and recent years to be a very powerful experimental method to study low density of the fluid. A number of early efforts were devoted superfluid turbulence. Micron-sized solid particles and metastable to producing macroscopic particles for qualitative investigations helium molecules are specifically being used to investigate in (10–12) and the challenge of producing neutrally buoyant par- detail the dynamics of quantum flows. These studies belong to ticles that faithfully follow the complex flow fields has been the a well-established, interdisciplinary line of inquiry that focuses on main impediment to quantitative advancement. In addition, sev- the deeper understanding of turbulence, one of the open problem eral attempts have been made to visualize fluid dynamics in su- of modern physics, relevant to many research fields, ranging from perfluid helium with microscopic tracers, which include neutron fluid mechanics to cosmology. Progress made to date is discussed, absorption tomography, using 3He particles (13), and acoustic to highlight its relevance to a wider scientific community, and cavitation imaging, using electron bubbles (14). These small par- future directions are outlined. The latter include, e.g., detailed ticles are expected to follow the fluid motion, because Stokes drag, studies of normal-fluid turbulence, dissipative mechanisms, and from the normal-fluid flow, is deemed to dominate other forces. unsteady/oscillatory flows. However, these methods have specific challenges. Neutron ab- sorption tomography requires a finely collimated neutron beam uantum fluids have been studied experimentally for many and the ability to raster the neutron beam through the region of years and have by now become a major focus of low-tem- interest. The electron-bubble cavitation method relies on the Q PHYSICS perature physics (ref. 1 and references therein). Applications of generation of strong ultrasonic sound waves in helium that in- the subject are widely ranged, from engineering, where super- evitably disturb the flow to be studied. Recently, the groups rep- fluid 4He is used as a coolant for superconducting magnets and resented by the present authors have successfully developed a infrared detectors (2), to astrophysics, where superfluidity is in- number of liquid helium flow-visualization techniques: particle voked to explain glitches in the rotation of neutron stars (3, 4) image velocimetry (PIV) and particle tracking velocimetry (PTV) and the formation of cosmic strings (5, 6). More recently, su- techniques, using micron-sized solid particles (15–21), and a laser- perfluidity has been used to describe the collective behavior of induced fluorescence imaging technique, using angstrom-sized p birds (7) and a cosmological model has been used to obtain He2 excited molecules (22, 23). results relevant to superfluid turbulence (8). The latter form of turbulence, occurring in quantum fluids, is indeed an especially PIV and PTV Techniques. PIV and PTV are valuable, quantitative interesting topic because of its quantum peculiarities and its tools that have been applied to study many scientific and in- similarity to classical turbulence. Superfluids, in which turbu- dustrial problems (24). PIV can estimate the fluid velocity in lence can be directly visualized and studied, include superfluid a section of the flow field, by assuming a single, smoothly varying 4He and atomic Bose–Einstein condensates (9). Due to the limit velocity field, whereas PTV allows the measurement of La- of small sample volumes, the experimental study of turbulence in grangian quantities, i.e., the local velocity and its derivatives. Bose–Einstein condensates has hardly begun. The development With both techniques the particles are suspended in the fluid and of visualization techniques applicable to superfluid 4He is thus reflect the light from a laser sheet that illuminates the flow field essential, if our understanding of quantum turbulence is to make of interest. The time-dependent positions of the particles are significant progress in the near future. thus captured and analyzed by a suitable digital imaging system. Superfluid 4He is viewed as consisting of two interpenetrating The particles for liquid helium experimentation can be broadly fluids. The gas of thermal excitations forms the normal compo- classified into two categories: solid particles, as are often used in nent, which can be considered as a viscous fluid. The superfluid classical fluid dynamics experiments, and solidified particles, component is inviscid and its rotational motion is possible only in produced by injecting gases (usually hydrogen or deuterium) into the presence of topological defects, in the form of quantized liquid helium. Micron-sized solid particles have been successfully vortex filaments. Turbulence in the superfluid component there- used in conjunction with the PIV technique to observe broad, fore takes the form of a tangle of quantized vortex lines. Turbu- average properties of the turbulent state of superfluid helium lence in the normal fluid is more conventional, although the (15, 25, 26). However, such particles have proved to be too dense interaction between the normal fluid and the vortices leads to the to explore the detailed structure of quantum turbulence. As a nonclassical force of mutual friction between the two fluids. result, most recent experiments have used solidified hydrogen (or Turbulence in such a system can exhibit a behavior that is similar deuterium) particles (16–21). To produce these particles, a gas- to that found in a classical fluid; but it may take forms that are eous mixture of helium and hydrogen in a volume ratio of ∼100:1 unknown in classical fluid mechanics: for example, forms rele- is injected directly into liquid helium. A cloud of solid particles vant to a fluid in which there is no viscous dissipation, and those with diameters typically of a few microns can be produced. that depend on the coexistence of the two fluids. Study of quan- tum turbulence can therefore enrich our knowledge of turbulence in general, as well as being interesting in its own right. Author contributions: W.G., M.L.M., D.P.L., and S.W.V.S. designed research; W.G. and M.L.M. performed research; W.G., M.L.M., and D.P.L. analyzed data; and W.G., M.L.M., D.P.L., and Visualization Techniques S.W.V.S. wrote the paper. Flow visualization techniques have been developed to a high The authors declare no conflict of interest. degree of precision and speed for classical fluid dynamics This article is a PNAS Direct Submission. investigations. However, for liquid helium, such techniques have 1To whom correspondence should be addressed. E-mail: [email protected]. www.pnas.org/cgi/doi/10.1073/pnas.1312546111 PNAS Early Edition | 1of6 Downloaded by guest on September 28, 2021 Although solids from other gases, such as argon, methane, ni- trogen, and propane, have been tested (27), hydrogen and deu- ABC terium produce particles that are close to neutrally buoyant. p He2 Fluorescence Imaging Technique. Recently, a new visualization * technique, using excited He2 triplet molecules, was developed (22, 23). These molecules can be produced in large numbers in liquid helium, following the ionization or excitation of ground state helium atoms (28, 29). The singlet state molecules radia- tively decay in a few nanoseconds (30), but the triplet state Fig. 1. Intensity inverted images showing hydrogen ice particles trapped on molecules are metastable with a radiative lifetime of about 13 s quantized vortex lines in superfluid helium (16). The concentration of hy- (31). These triplet molecules form bubbles in liquid helium with drogen ice can be varied such that (A) only isolated particles are trapped on vortices, (B) multiple particles form dotted lines on vortices, or finally (C) a radius of about 6 Å (32) and can be used as tracers. To image * solid hydrogen skeletons perturb the dynamics of the vortices and stabilize the He2 triplet molecules, a cycling-transition laser-induced branches and crossings. The natural state is for crossings to reconnect. fluorescence technique, first developed by McKinsey et al. (33) and McKinsey and coworkers ( 34), has been used. A laser pulse − at 905 nm can excite helium molecules from their triplet ground which is characterized by the predicted v 3 power-law distribu- 3Σ+ 3Σ+ state a u to the excited electronic state d u . Over 90% of the tion (17, 42). This clearly distinguishes quantum turbulence from 3 molecules in the d state quickly decay to an intermediate b Πg classical turbulent flows, as the velocity distribution of the latter state, emitting detectable fluorescent photons at 640 nm (35). A has a nearly Gaussian shape (43). Such a power-law shape of the filter can be used to block unwanted laser light, to achieve low tails of the velocity distributions was later confirmed in two-fluid 3 background. From the b Πg state, molecules quench back to the flow experiments (20, 21) and in superflow numerical simu- 3Σ+ a u state, and the process can be repeated so that each mole- lations (44–47). Note, however, that the reasons why the tails of cule produces many fluorescence photons.