Interplay of NonQuantum And Quantum TurbulenceProbes Gary Ihas

Interplay of Non-Quantum And Quantum Turbulence-Probes Gary Ihas

Good and Bad of Low Temperatures Good • 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 Bad • Difficulty of refrigeration • Room temperature sensors don’t work or need modifications • Size restrictions

A look at the 4 He phase diagram superfluidity breaks down due to production of quantized vortices Superfluid is irrotational, but can have finite circulation about a line singularity (vortex core):

Two Fluid Model– Landau in 1941 (oscillating disc viscometer) Viscosity ( P) 4 He Two Fluid model density viscosity entropy Two fluids s s =0 Ss =0 normal n fluid = n Sn=SHe Superfluid irrotational [J. Wilks, 1987] Fluid density Two-fluid equations for He II: = n + s 0. 14 g/cm 3 s 56 % n T (K) 0 2. 0 T stress tensor total mass flow [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. 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 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) [Yarmchuk, 1979] 3. n 0=2 m/h=2 /

Simple Superfluids Re-cap q 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. (Consequences of Bose or BCS condensation. ) q Quantization of rotational motion: , except on quantized vortex lines, each with one quantum of circulation round a core of radius equal to the coherence length ( ~0. 05 nm for 4 He; ~80 nm for 3 He-B; larger for Bose gases). q 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.

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. ws= L = total rms superfluid vorticity l= L-1/2 = average inter-vortex line spacing. (~10 -7 erg cm-1, a 0~0. 1 nm, reff ~ l)

Stalp Apparatus

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

Need Probe of Vorticity-- requirements q 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. ØE. g. turbulence in 4 He above 1 K has energy-containing eddies of 1 cm and characteristic velocity 1 cm s-1. Below 1 K Kelvin wave cascade (Vinen) to dissipate energy may take smallest scale to 10 nm. q. Time scales: ranges from 1 s to a few milliseconds. q. 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). q. Do not underestimate the importance of visualizing the flow.

Localized probes q 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 k. Hz. q Hot wire anemometers do not work in 4 He owing to the high thermal conductivity. Could they work in 3 He? q 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. q. We have made a nano-scale flow measuring device seems to not detect super flow!

Acoustic Probe in TSF for ref. : Baudet, Gagne (LEGI) • Refrigerator-vibrations proof (tested in -situ) • Operation checked at room temperature • Should work both in He. I and He. II

Hot wire for the TSF experiment Température Tc T 3 2 1 2 for ref. : P. Diribarne Ph. D (Inst. Neel) • Stripped Nb-Ti wire • velocity-dependent quenched length -> velocity dep. resistance • Focused ion beam machining

Hot wire anemometer (He-I) & 2 nd sound probe (He-II) • Hot wire • 2 nd sound open cavity (next part of the talk)

Axis propeller 80 g/s flow T. Didelot (ex. Ph. D) local probes Pitot tube (mean velocity) Screens pipe 2. 3 cm Honeycomb • T = 1. 6 K superfluid ratio = 84% • V = 0. 3 -1. 3 m/s Re = V. F/k 0 up to 3. 105

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

Calorimetry Probe Development Thermistor Characteristics § Operating temperature: 10 – 100 m. K § Sensitivity: T ~ 10 -4 m. K § Short response time: ~ 1 ms § Small mass & good thermal contact. § Ease of manufacture

Use computer chip fabrication technique: V. Mitin http: //microsensor. com. ua/products. html Sensor Package Construction § Ge/Ga. As thermistors 300 m square by 150 m thick. Ge/Ga. As Thin Film Element 1 and 5: copper discs; 2: gold strip; 3: corundum cylinder; 4: Ge/Ga. As sensitive element; 6: copper wire; 7 - tin.

Advantages of Thin Film Technology Mass Production/Consistency § Each wafer will generate sensors with very similar properties § Resistance measurements made on a single batch over the range 10 K – 150 K § A single fixed point measurement at 4. 2 K will approximate the sensors properties if the entire curve for any one sensor from the batch is known

Conduction in a doped semiconductor

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

Another Probe or two or three Pressure Transducer Requirements § sampling on micron scale § sensitivity: 0. 1 Pascal § fast: 1 msec § function at low temperatures (20 – 100 m. K) § transduction: as simple as possible MEMS Technology Pressure Sensors § Piezo-resistive § Capacitive § Optical

MEMS Technology Perfect size range blockkkkkk

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 SM 5108 Semiconductor resistors joined by aluminum conductors in bridge configuration Resistors placed on diaphragm Two strained parallel to I Two strained perpendicular to I Manufactured by Silicon Microstructures, Inc.

Piezo-resistive Pressure Sensor SM 5108

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

Nanotube Film Flow Sensor Test Helium liquid or gas flow Tinned Copper 4 -terminal Resistance Measurement G 10 (fiberglas)

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

Visualizing Flow Requirements of PIV in quantum turbulence at low T q 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 q A new candidate: triplet state He 2 excimer molecules (Mc. Kinsey et al, PRL 95, 111101 (2005)) lifetime of about 13 s -- radius 0. 53 nm -- Production ~ 13000 per Mev.

How does it work? • 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. • ~ 4 x 107 photons/s at 640 nm.

Re-Cap q Probing quantum turbulence has pluses and minuses q Possible to make almost micron-size probes q Visualization possible q All depends on much preparatory word = stable budgets for period of years

Sreenivasan Einstein

Some quotes on the study of turbulent fluids… “Simple fluids are easier to drink than understand. ” --A. C. Newell and V. E. Zakharov, Turbulence: A Tentative Dictionary ( Plenum Press, NY 1994) “Simple fluids are easier to understand if you drink. ” --G. Ihas and J. Niemela, Tiny’s Bar, Santa Fe, NM 2003