Gary Ihas Interplay of Non-Quantum And 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 Temperatures Good Bad Difficulty of refrigeration Room temperature sensors don’t work or need modifications Size restrictions

A look at the 4 He phase diagram 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) 4 He (oscillating disc viscometer) 56 %  Fluid density T T (K)  nn ss  =  n +  s  0.14g/cm 3 S n =S He  =  n nn normal fluid S s =0  s =0 irrotational ss Super- fluid Two fluids entropyviscositydensityTwo Fluid model Two-fluid equations for He II: total mass flow stress tensor [S.J. Putterman, 1974]

Quantization of Superfluid Circulation Quantization of superfluid circulation: (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=2  r 2  2. Total circulation=  r 2 n 0 h/m (n 0 : # of lines per unit area) 3.  n 0 =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/cm 2

 Superfluids ( 4 He; 3 He-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 (Consequences of Bose or BCS condensation.)  Kinematic viscosity of normal fluid: 4 He very small; 3 He-B very large. Turbulence in normal fluid? 4 He: YES; 3 He-B: NO. (  ~0.05 nm for 4 He; ~80nm for 3 He-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/m 4 ~10 -3 cm 2 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. (~10 -7 erg cm -1, a 0 ~0.1 nm, r eff ~ )

Stalp Apparatus

Second Sound and NMR  Second sound, used successfully to measure vortex line density in 4 He, does not propagate below 1 K in 4 He or in superfluid 3 He.  However, NMR signals can be used to measure vortex densities in 3 He, 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 4 He 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 4 He owing to the high thermal conductivity. Could they work in 3 He?  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 Tc Température TT for ref. : P. Diribarne PhD (Inst. Neel)

Hot wire anemometer (He-I) & 2 nd 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 = m/s  Re = V.  /   up to T. Didelot (ex. PhD) Axis propeller local probes pipe Pitot tube (mean velocity) Screens Honeycomb 2.3 cm

Assembly of the 2 nd sound sensor Cavity size : 1mm*1mm*250  m Thickness ~ 15  m Gap ~ 250  m Design/micromachining of both beams : H. Willaime, P. Tabeling, Microfluidic group, ESPCI O. Français, L. Rousseau, Micromachining center, ESIEE

Thermistor Characteristics  Operating temperature: 10 – 100 mK  Sensitivity:  T ~ 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

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 Advantages of Thin Film Technology

Conduction in a doped semiconductor

Thermistor R vs. T Development Work Tune characteristics by heat treatment

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 diaphragm Two strained parallel to I Two 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

Nanotube/Film Technology Small Strong Conducting But not too conducting Elastic Stick to some surfaces Can be used for Thermometers Heaters Strain gauges Capacitor plates Flow meters Turbulence detectors

Nanotube film AFM Image 1 micron

Nanotube Film R vs. T measurements

Nanotube Flow Meter

Helium liquid or gas flow Tinned Copper G10 (fiberglas) 4-terminal Resistance Measurement Nanotube Film Flow Sensor Test

Nanotube film “rope” test jig

Nanotube Flow Meter

Nanofilm Capacitive Flow/Pressure Fluctuation Sensor AFM of Nanofilm Flow

Optically Transduced Pressure Sensors microsensor 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 Flow Requirements of PIV in quantum turbulence at low T  A new candidate: triplet state He 2 excimer molecules lifetime of about 13 s -- radius 0.53 nm -- Production ~ per Mev. (McKinsey et al, PRL 95, (2005))

Illuminate with crossed pulsed lasers at 910 nm and 1040 nm(modest power). Only molecules in crossed beams react OObserve decay of d 3  + u to b 3  g with emission at 640 nm (lifetime 25 ns). The b 3  g returns to a 3  + u by non-radiative processes (may need to be accelerated by optical means) Process recycles.  ~ 4x10 7 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

SreenivasanEinstein

“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