Gary Ihas

Interplay of Non-QuantumAnd

Quantum Turbulence-Probes

• Controlled temperature environment-regulated heat flows

• Low Heat Capacities-Sensitive energy measurements

• Size-can be much smaller

• New materials and properties-e.g. superconductivity

• New techniques—e.g. NMR

Good and Bad of Low TemperaturesGood

Bad

•Difficulty of refrigeration

•Room temperature sensors don’t work or need modifications

•Size restrictions

A look at the 4He phase diagram

(r) = 0

(r)e iSv Ss

m4

4 4

hd

m msv l S n

vs 0

Superfluid is irrotational, but can have finite circulation about a line singularity (vortex core):

superfluidity breaks down due to production of quantized vortices

Two Fluid Model– Landau in 1941

[J. Wilks, 1987]

Viscosity (P)

4He

(oscillating disc viscometer)

56 %

Fluid density

0 2.0 T

T (K)

n

s

=n +s 0.14g/cm3

Sn=SHe = n nnormal fluid

Ss =0s =0

irrotational

sSuper-fluid

Two fluids

entropyviscositydensityTwo Fluid model

0 s

on)conservati (momentum 0

)(

on)conservati(entropy 0

on)conservati (mass 0

r

P

t

JtDt

D

st

st

ii

sssss

n

Two-fluid equations for He II:

total mass flow ssnnJ

jsissjninnijij pP ,,,, stress tensor

[S.J. Putterman, 1974]

Quantization of Superfluid Circulation

Quantization of superfluid circulation:

scmnm

nhds / 1097.9 24

(postulated separately in 1955 by Onsager and Feynman)

The angular velocity is

(a) 0.30 /s, (b) 0.30 /s,

(c) 0.40 /s, (d) 0.37 /s,

(e) 0.45 /s, (f) 0.47 /s,

(g) 0.47 /s, (h) 0.45 /s,

(i) 0.86 /s, (j) 0.55 /s,

(k) 0.58 /s, (l) 0.59 /s.

[Yarmchuk, 1979]

1. Circulation round any circular path of radius r concentric with the axis of rotation=2r2

2. Total circulation=r2n0h/m (n0: # of lines per unit area)

3. n0=2 m/h=2 /

All superfluid vortex lines align along the rotation axis with ordered array of areal density= length of quantized vortex line per unit volume=

2000 lines/cm2

s

2

Superfluids (4He; 3He-B; cold atoms) exhibit

• Two fluid behaviour: a viscous normal component + an “inviscid” superfluid component. Normal component disappears at lowest temps.

• Quantization of rotational motion in the superfluid component.

Quantization of rotational motion: , except on quantized vortex lines, each with one quantum of circulation

0svcurl

34 2mhmhds or rv

(Consequences of Bose or BCS condensation.)

Kinematic viscosity of normal fluid: 4He very small; 3He-B very large. Turbulence in normal fluid? 4He: YES; 3He-B: NO.

( ~0.05 nm for 4He; ~80nm for 3He-B; larger for Bose gases).

round a core of radius equal to the coherence length

Simple Superfluids Re-cap

Grid Turbulence

quantum of circulation:h/m4~10-3cm2 s-1 (n=1)

L = length of quantized vortex line per unit volume.

s= L = total rms superfluid vorticity

= L-1/2 = average inter-vortex line spacing.

H e II

Er

aveff

0

FHG

IKJ

s

2

4ln (~10-7erg cm-1, a0~0.1 nm, reff ~ )

Stalp Apparatus

Second Sound and NMR

Second sound, used successfully to measure vortex line density in 4He, does not propagate below 1 K in 4He or in superfluid 3He.

However, NMR signals can be used to measure vortex densities in 3He, with very high sensitivity.

Second Sound and NMR

Length scales: wide range of scales from the size of the flow obstacle or channel giving rise to the turbulence to the (small) scale on which dissipation occurs.

E.g. turbulence in 4He above 1K has energy-containing eddies of 1 cm and characteristic velocity 1 cm s-1. Below 1K Kelvin wave cascade (Vinen) to dissipate energy may take smallest scale to 10 nm.

Time scales: ranges from 1 s to a few milliseconds.

Velocity correlation functions: play an important role in classical turbulence (structure functions). We could derive energy spectra from them and look for deviations from Kolmogorov scaling (higher-order structure functions).

Do not underestimate the importance of visualizing the flow.

Need Probe of Vorticity-- requirements

We shall wish to discuss probes (other than PIV and LDV) that measure local properties (such as pressure, velocity). Remember that ideally we need a spatial resolution of at least 30 microns and a frequency response to at least 1 kHz.

Hot wire anemometers do not work in 4He owing to the high thermal conductivity. Could they work in 3He?

A pressure transducer with a spatial resolution of about 1 mm and good frequency response was used in an important experiment by Maurer and Tabeling. We are pursuing smaller pressure transducers based on nano-fabrication techniques.

We have made a nano-scale flow measuring device seems to not detect super flow!

Localized probes

Acoustic Probe in TSF

• Refrigerator-vibrations proof (tested in -situ)

• Operation checked at room temperature

• Should work both in HeI and HeII

for ref. : Baudet, Gagne (LEGI)

Hot wire for the TSF experiment

• Stripped Nb-Ti wire• velocity-dependent quenched length -> velocity dep. resistance • Focused ion beam machining

13 2 2

Tc

Température

T

for ref. : P. Diribarne PhD (Inst. Neel)

Hot wire anemometer (He-I) & 2nd sound probe (He-II)

• Hot wire

• 2nd sound open cavity

(next part of the talk)

80 g/s flow

• T = 1.6 K superfluid ratio = 84%

• V = 0.3-1.3 m/s Re = V./ up to 3.105

T. Didelot (ex. PhD)

He II

Conduite=2,5cm

Hélice

Axe

Mesures

Axis

propeller

local probes

pipe

Pitot tube(mean velocity)

Screens

Honeycomb2.3 cm

Assembly of the 2nd sound sensor

• Cavity size :1mm*1mm*250m

Thickness ~ 15m

Gap ~ 250m

QuickTime™ et undécompresseur TIFF (LZW)

sont requis pour visionner cette image.

Design/micromachining of both beams :H. Willaime, P. Tabeling, Microfluidic group, ESPCIO. Français, L. Rousseau, Micromachining center, ESIEE

Thermistor Characteristics

Operating temperature: 10 – 100 mK

Sensitivity: T ~ 10-4 mK

Short response time: ~ 1 ms

Small mass & good thermal contact.

Ease of manufacture

Calorimetry Probe Development

Sensor Package Construction Ge/GaAs thermistors 300 m square by 150 m thick.

1 and 5: copper discs; 2: gold strip; 3: corundum cylinder; 4: Ge/GaAs sensitive element; 6: copper wire; 7- tin.

Ge/GaAs Thin Film Element

Use computer chip fabrication technique: V. Mitin

http://microsensor.com.ua/products.html

Mass Production/Consistency Each wafer will generate sensors with very similar properties Resistance measurements made on a single batch over the range 10K – 150K A single fixed point measurement at 4.2K will approximate the sensors properties if the entire curve for any one sensor from the batch is known

1 10 10010

1

102

103

104

Re

sis

tan

ce,

Oh

ms

Tem p erature, K

Advantages of Thin Film Technology

Conduction in a doped semiconductor

1 10 10010

100

1000

10000

100000

1000000

Electron Collisions

(R~T-1)

Phonon Collisions

(R~T-1/2}

Variable Range Hopping

(R~exp{T-1/4})

Coulomb Interaction

(R~exp{T-1/2})

Re

sist

an

ce ()

Temperature (K)

Thermistor R vs. T Development WorkTune characteristics by heat treatment

25 50 75 100

10

100

1000

#2

#3 #1

R(k)

T (mK)

Pressure Transducer Requirements

sampling on micron scale sensitivity: 0.1 Pascal fast: 1 msec function at low temperatures (20 – 100 mK) transduction: as simple as possible

MEMS Technology Pressure Sensors Piezo-resistive Capacitive Optical

Another Probe or two or three

MEMS Technology

blockkkkkk

Perfect size range

Design Of Piezo-resistive Pressure Sensors Typical design: 4 piezo-resistors in Wheatstone bridge on a diaphragm diaphragm deflects from applied pressure causing the deformation of the piezo-resistors mounted on the surface

Wheatstone bridge

Piezo-resistive Pressure Sensor SM5108

Manufactured by Silicon Microstructures, Inc.

Semiconductor resistors joined by aluminum conductors in bridge configuration

Resistors placed on diaphragmTwo strained parallel to ITwo strained perpendicular to I

Piezo-resistive Pressure Sensor SM5108

Drawbacks of Piezo-resistive Pressure Sensors-Results Relatively low sensitivity Large temperature dependence temperature compensation necessary

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40

5

10

15

20

25

30

35

40

45

50

55 300 K 91.2 K - 94.6 K 64.4 K - 66.0 K 49.8 K - 51.0 K 40.4 K - 43.5 K 29.9 K - 30.4 K 22.9 K - 26.0 K 26.2 K

Voltage vs Pressure for Piezoresistive Transducer at varying temperatures

Vo

ltag

e (

mV

)

Pressure (Bar)

Nanotube/Film Technology• Small• Strong• Conducting• But not too conducting• Elastic• Stick to some surfaces

Can be used forThermometersHeatersStrain gaugesCapacitor platesFlow metersTurbulence detectors

Nanotube film AFM Image

1 micron

Nanotube FilmR vs. T measurements

1 10 100100

200

300

400

500

600R

in O

hm

s

T in K

Nanotube Flow Meter

Helium liquid or gas flow

TinnedCopper

G10 (fiberglas)

4-terminal ResistanceMeasurement

Nanotube Film Flow Sensor Test

Nanotube film “rope” test jig

Nanotube Flow Meter

1 2 3 4 5 6

800

900

1000

1100

1200

1300

1400

0 Flow 10psi Flow 20psi Flow 30psi Flow 40psi Flow 50psi Flow

Resistance() vs. Temperature(K) for 1.0mm Nanotube at varying Flow Rates

Res

ista

nce()

Temperature(K)

Nanofilm CapacitiveFlow/Pressure Fluctuation Sensor

AFM of Nanofilm

Flow

Optically Transduced Pressure Sensorsmicrosensor structure that deforms under pressure

resulting in a change in an optical signal

Choice of particle: neutrally-buoyant --helium has a very low density

small < 1 m

bound to vortex line

Type of turbulence: Grid—Van Sciver got weird results with counterflow

Visualizing FlowRequirements of PIV in quantum turbulence at low T

A new candidate: triplet state He2 excimer molecules

lifetime of about 13 s -- radius 0.53 nm -- Production ~ 13000 per Mev. )(aHe 3

2u (McKinsey et al, PRL 95, 111101 (2005))

• Illuminate with crossed pulsed lasers at 910 nm and 1040 nm(modest power). Only molecules in crossed beams react

•OObserve decay of d3+u to b3g

with emission at 640 nm (lifetime 25 ns).

• The b3g returns to a3 +u by

non-radiative processes (may need to be accelerated by optical means)

• Process recycles.

• ~ 4x107 photons/s at 640 nm.

How does it work?

Probing quantum turbulence has pluses and minuses

Visualization possible

Possible to make almost micron-size probes

All depends on much preparatory word = stable budgets for period of years

Re-Cap

Sreenivasan Einstein

“Simple fluids are easier to drink than understand.” --A.C. Newell and V. E. Zakharov, Turbulence: A

Tentative Dictionary ( Plenum Press, NY 1994)

Some quotes on the study of turbulent fluids…

“Simple fluids are easier to understand if you drink.” --G. Ihas and J. Niemela, Tiny’s Bar, Santa Fe, NM 2003