Viscosity of GaseousHe3andHe4between 1.3°K and 4.2°K

Abstract

W E have recently shown 1 that the symmetry effects calculated by Halpern and Gwathmey 2 which should occur with the gaskinetic collisions of ortho-para-T&i and ortho-para-T> 2 cannot be observed with even an approximately right order of magnitude. The reliability of the calculations, however, is not very high, because they are based on the hard-elastic-sphere model which is not suitable for the nonspherical potential of H2 and D 2 . Halpern 3 has therefore suggested that the influence of the statistics on the gaskinetic cross sections be reinvestigated by measuring the viscosity-difference of gaseous He 3 and He 4 at very low temperatures. In the case of He no difficulties with respect to the potential are to be expected. Since He 3 obeys Fermi statistics while He 4 obeys Bose statistics, the viscosity of gaseous He 3 should appreciably exceed the viscosity of He 4 at low temperatures. Somewhat later, de Boer and Cohen 4 have explicitly calculated the temperature-dependence of the viscosities between 0 and 5°K using a Lennard-Jones potential of the form 4e[(o-/r) 12 -(er/f) 6 ].To investigate the extremely small viscosities, we have developed a measuring device based on the principle of the oscillating cylinder. The amplitudes of the oscillations are recorded by 1S\ 9 (MP)\ 10\ f ° 0 He 3 ^^ X 0 X He* O O O O < ; 3 T(°K) i FIG. 1. The temperature dependence of the viscosity coefficient 17 (micropoise) of gaseous He 3 and He 4 . Circles and crosses represent the experimental results obtained with decreasing and increasing temperature, respectively. Continuous lines represent theoretical curves of de Boer and Cohen.11 1 (MP)\ 70 U5°K 2M°K 25 50 75 %He 3 FIG. 2. Concentration dependence of the viscosity coefficient t\ (micropoise) of gaseous He 3 -He 4 mixtures at temperatures 4.15°K and 2.64°K.high-frequency circuits using a change in capacity connected with the oscillation. At 4.2°K the relaxation time of the oscillating system filled with He 4 amounts to 2.7 min while it exceeds 3 hr with the highest obtainable vacuum. The period of the oscillating cylinder is 1.3 sec. At a viscosity of 5 micropoise the accuracy of the measurements was better than ±1 percent. The viscosities of pure He 3 and He 4 were measured between 1.3° and 4.2 °K (Fig. 1). The results for pure He 4 agree perfectly with the calculations of de Boer and Cohen. For He 3 the figure shows a small deviation between theory and experiment at low temperatures. In any case, we^may presume that the results obtained confirm the predicted^symmetry effect of the helium isotopes.Furthermore, the concentration dependence of the viscosity of gaseous He 3 -He 4 mixtures was determined at 4.2° and 2.6°K as shown in Fig. 2. The absolute values of 77 are derived from the well-known viscosity of He 4 at 77.3°K (83.68 micropoise). 5 The pure He 3 was supplied by the U. S. Atomic Energy Commission. Details will be published in the Zeitschrift fur Physik.

Elastic molecular collision models for quantum mechanical scattering in the Monte Carlo simulation of rarefied gas flow at low temperatures

“…The quantum mechanical viscosity coefficients of a first approximation for 4 He atoms, which are indistinguishable particles obeying BoseEinstein statistics at low temperatures, were calculated using Q BE ͑2͒ * and compared to experimental data. The quantum mechanical viscosity of the first approximation was in good agreement with experimental data, [14][15][16] as shown in Fig. 3.…”

Non-perturbative temperature instabilities in N = 4 strings

“…Local supersymmetry in three-dimensional space-time is notoriously difficult to establish in the presence of massive states. This is because [30,31] masses induce asymptotically a conical geometry [32], making Noether supercharges hard to define. Supersymmetry of the vacuum does not necessarily imply supersymmetry of the massive spectrum.…”

Accommodation Coefficient of Unsaturated He I Films

“…where A is the geometrical constant and rj is the viscosity of He 4 gas. 3,4 The value of a versus the film thickness in the temperature range 2.174-3.991 °K is given in Fig. 1.…”