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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A

Studies of superfluid 4 He using vibrating resonators. Viktor Tsepelin. Porvoo , 11 th September 2013. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A. Lancaster Quantum Fluids Ian Bradley Shaun Fisher Tony Guénault

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TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A

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  1. Studies of superfluid 4He using vibrating resonators Viktor Tsepelin Porvoo, 11th September 2013 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAA

  2. Lancaster Quantum Fluids Ian Bradley Shaun Fisher Tony Guénault Richard Haley Viktor Tsepelin George Pickett Peter McClintock MarcelCloveckoMark Giltrow Chris Lawson Malcolm Poole RochSchanen Sean Ahlstrom Ed Guise MukeshKumar Lydia Munday Matt Sarsby MarosSkyba Paul Williams Andrew Woods Alan Stokes Martin Ward TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA

  3. Custom made quartz tuning forks W = 50, 75mm T = 90mm L = 700 - 3500mm 42 117 227 kHz 21.9 36.0 54.2 95.4 155 6.5 8.3 12.X 16.3 kHz

  4. Fork (cantilever) flexure modes

  5. Optical measurements of prong velocity profile 50 micron fork 6.7 kHz 41.9 kHz 117 kHz 227 kHz

  6. Electromechanical measurements Driven by Piezoelectric Force from applied Voltage, Resulting Velocity produces a Current. DrivingForceF = a V/2 Velocity v = I / a Optical and electromechanical detection agree within 10% for all modes PHYSICAL REVIEW B 85, 014501 (2012)

  7. Frequency sweeps for 6.5kHz fork at 450mK in 4He 6.5 kHz 40.5 kHz 219 kHz 113 kHz

  8. Amplitude sweeps for 6.5kHz fork at 450mK in 4He `Turbulent’ damping F v2 Intrinsic damping (approx. linear)

  9. TF damping at 4.2K and 1.5K Hydrodynamic damping Sound emission PHYSICAL REVIEW B 85, 014501 (2012)

  10. TF acoustic damping at 4.2K and 1.5K Hydrodynamic damping Sound emission PHYSICAL REVIEW B 85, 014501 (2012)

  11. Amplitude sweeps for 6.5kHz fork at 450mK in 4He `Turbulent’ damping F v2 Intrinsic damping (approx. linear)

  12. Amplitude sweeps for 6.5kHz fork

  13. Drag coefficient 6.5kHz fork 1.6K

  14. Turbulent drag for the fundamental mode of 6.5kHz fork Critical velocity and superfluid turbulent drag are temperature independent

  15. Turbulent drag for the fundamental mode of various forks

  16. Frequency dependence of critical velocity consistent with expected powerlaw dependence R. Hänninen et al. , J Low Temp Phys (2011) 164:1–4

  17. Frequency dependence of critical velocity Vc=2.6(kw)1/2 R. Hänninen et al. , J Low Temp Phys (2011) 164:1–4

  18. Drag coefficient 6.5kHz fork 1.6K

  19. Normal fluid Drag vs KC b1/2 2pa v KC= = D Df Stokes drag Stokes number Keulegan-Carpenter Number

  20. Normal fluid Drag vs KC b1/2 Drag is governed by a normal fluid component

  21. “Floppy Wire” Resonator f=57Hz For the floppy wire, we write the total force as: We use L= leg spacing + ¼ of leg length to define an effective drag coefficient for more direct comparison with straight wires

  22. Stokes Drag:

  23. Summary • Quartz tuning forks support up to 4 flexure modes with high Q values. Velocity of the tip of the fork can be easily obtained using experimental fork constant for any of these modes. • Fork damping is governed by Stocks drag at low frequencies, and acoustic emission at high frequencies. • Frequency dependence of the critical velocity for turbulence nucleation using quartz tuning forks is consistent with expected ½ powerlaw dependence. • The drag in superfluid He4 at high temperatures and moderate velocities can be accounted for by the normal fluid alone [no drag from the superfluid]

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