Tuning Fork Viscometry in Liquid Helium

Matt JachowskiAJ KumarNaveen SinhaAaron LigonJohn RutherfordEd Fei

TA: Charis Quay

Physics 108, Group 4

Outline

Motivation Experimental Setup Results Discussion

Why Liquid Helium?

Superfluid transition Viscosity goes to zero

Existing LHe viscometers Vibrating wire Torsional oscillator MEMS cantilever

Why Tuning Forks?

Advantages of tuning forks Crystal acts as both

actuator and sensor No optical

measurements necessary

Crystals are inexpensive and easy to obtain

Study properties of piezoelectric crystals at low temperatures

5 mm

Design and Construction

Three environments Open in LHe Sealed in LHe Open in vacuum

Two stages One stick

The Stick and Vacuum Chamber

The Inner Stage

The Outer Stage

Design and Construction

Three open forks Thermal contact to

walls of can Si diode thermometer In vacuum

Mixture of open and sealed forks

DIP socket for modularity

In direct contact with LHe

Electronics

Excite tuning fork crystal with random noise

Measure tuning fork spectral response

Preamp

Circuit Diagram

Tuning Fork

Adjustable Capacitor

Output

White noise

Transformer

Pre-amp

Data Collection

Tuning Fork Resonance: The Movie

Open Tuning Fork

Resonant Frequency

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

32695.2

32695.6

32696.0

32696.4

32696.8

Sealed Tuning Fork

Reso

nan

t F

req

uen

cy [

Hz]

Temperature [K]

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

32695.2

32695.6

32696.0

32696.4

32696.8

Sealed Tuning Fork

Reso

nan

t F

req

uen

cy [

Hz]

Temperature [K] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

31920

31940

31960

31980

32000

Open Tuning Fork

Reso

nan

t F

req

uen

cy [

Hz]

Temperature [K]

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

31920

31940

31960

31980

32000

Open Tuning Fork

Reso

nan

t F

req

uen

cy [

Hz]

Temperature [K]

Resonance Width

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

5

10

15

20

25

30

Open Tuning Fork

Reso

nan

ce W

idth

[H

z]Temperature [K]

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

5

10

15

20

25

30

Open Tuning Fork

Reso

nan

ce W

idth

[H

z]Temperature [K]

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Sealed Tuning Fork

Reso

nance

Wid

th [H

z]

Temperature [K]

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Sealed Tuning Fork

Reso

nance

Wid

th [H

z]

Temperature [K]

Quality Factor

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.520000

30000

40000

50000

60000

70000

Sealed Tuning Fork

Qu

ality

Facto

r

Temperature [K]

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.520000

30000

40000

50000

60000

70000

Sealed Tuning Fork

Qu

ality

Facto

r

Temperature [K]1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

Sealed Tuning Fork

Qu

ality

Facto

rTemperature [K]

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

Sealed Tuning Fork

Qu

ality

Facto

rTemperature [K]

Applications

Already shown to be an indicator for passing Tλ

2.175 +/- 0.04 K Viscometry and density measurement Several theories

Kanazawa and Gordon (1985): Zhang (2001):

f 2

0f f

Applications (cont’d)

There are (complicated) functional forms for density of liquid helium: Donnelly and Barenghi (1998):

Practicality of tuning fork viscometry 2

ln ma T T b T T T T P T T

DensityViscosity

Conclusions

Demonstration of novel LHe viscometry technique

Clear indicator of lambda transition Future work:

Closer examination of lambda transition regime

Determination of proper theoretical model

Real-time extraction of resonance characteristics

The End