Progress Towards a Gas-Flow Standard using Microwave and Acoustic Resonances

We describe our progress in developing a novel gas flow standard that utilizes 1) microwave resonances to measure the volume, and 2) acoustic resonances to measure the average gas density of a collection tank / pressure vessel. The collection tank is a 1.85 m3, nearly-spherical, steel vessel used at pressures up to 7 MPa. Previously, using the cavity's microwave resonance frequencies, we determined the cavity's pressure- and temperature-dependent volume V BBB with the expanded uncertainty of 0.022 % (coverage factor k = 2, corresponding to 95 % confidence level). This was the first step in developing a pressure, volume, speed of sound, and time (PVwt) primary standard. In the present work, when the shell was filled with argon, measurements of pressure and acoustic resonance frequencies determined the "acoustic mass" M acst that agreed with gravimetric measurements within 0.04 %, even when temperature gradients were present. Most of these differences were a linear function of pressure; therefore, they can be reduced by further research. We designed and implemented a novel positive feedback system to measure the acoustic resonance frequencies. Using the measurements of V BBB, pressure, and acoustic resonance frequencies of the enclosed gas (nitrogen or argon), we calibrated 3 critical flow venturis that NIST has used as working standards for over 10 years. The two independent flow calibrations agreed within the long-term reproducibility of each CFV, which is less than 0.053 %. Furthermore, the feasibility of a dynamic tracking technique using this feedback loop was tested by comparing ΔM acst computed under no-flow conditions and ΔM acst computed by the rate of fall or rise during a flow. This was done for flows ranging from 0.11 g/s to 3.9 g/s.

Determination of the Boltzmann constant with cylindrical acoustic gas thermometry: new and previous results combined

We report a new determination of the Boltzmann constant kB using a cylindrical acoustic gas thermometer. We determined the length of the copper cavity from measurements of its microwave resonance frequencies. This contrasts with our previous work (Zhang et al 2011 Int. J. Thermophys.32 1297, Lin et al 2013 Metrologia50 417, Feng et al 2015 Metrologia52 S343) that determined the length of a different cavity using two-color optical interferometry. In this new study, the half-widths of the acoustic resonances are closer to their theoretical values than in our previous work. Despite significant changes in resonator design and the way in which the cylinder length is determined, the value of kB is substantially unchanged. We combined this result with our four previous results to calculate a global weighted mean of our kB determinations. The calculation follows CODATA's method (Mohr and Taylor 2000 Rev. Mod. Phys. 72 351) for obtaining the weighted mean value of kB that accounts for the correlations among the measured quantities in this work and in our four previous determinations of kB. The weighted mean k̂B is 1.380 6484(28) × 10-23 J K-1 with the relative standard uncertainty of 2.0 × 10-6. The corresponding value of the universal gas constant is 8.314 459(17) J K-1 mol-1 with the relative standard uncertainty of 2.0 × 10-6.

Onset of Casimir-Polder retardation in a long-range molecular quantum state

Two 4He atoms form a diatomic molecule with a significant vibrational wave function amplitude at interatomic separations R>100  Å, where the retardation switches the London R(-6) decay of the potential to the Casimir-Polder R(-7) form. It has been assumed that this effect of retardation on the long-range part of the potential is responsible for the 2 Å (4%) increase of the bond length <R> of 4He2. We show that <R> is, unexpectedly, insensitive to the potential at R>20  Å and its increase is due to quantum electrodynamics effects computed by us from expressions valid at short R--beyond the validity range of Casimir-Polder theory--that seamlessly extend this theory to distances relevant for properties of long molecules.

Experimental model for study of anorectal sphincter musculature by manometry and computerized tomography in piglets

There seems to be controversy on the anorectal sphincter presentation and anatomical division, as well as on its functional representation. Evaluation of the anorectal sphincter musculature has been achieved through several methods, including anorectal manometry and computerized tomography, but to date there is no experimental model allowing a detailed manometric study of this muscle complex. In this work, we have developed such a model, which should enable the manometric and radiographic study of the anatomical features and functional mechanisms of sphincteric injuries, as well as the assessment of drug effects on the anorectal musculature upon incontinence and constipation. Twenty-two piglets (aged 25-30 days, weighing 5-7 kg) were studied by anorectal manometry (rectoanal inhibitory reflex and vector volume) and computerized tomography (anorectal angle and anal canal length). The data obtained for the rectoanal inhibitory reflex, represented here as the average and standard deviation, were the following: relaxation duration = 14.75 +/- 3.62 s, sphincter basal pressure = 41.58 +/- 8.20 mmHg, relaxation index = 87.26 +/- 11.52%, speed of relaxation = 5.90 +/- 2.10 mm/s, and speed of relaxation recovery = 4.03 +/- 1.78 mm/s. As for the vector volume, results were as follows: vector volume = 2692.32 +/- 1298.12 mm Hg2 cm, sphincter length = 11.82 +/- 2.74 mm, high pressure zone length = 5.09 +/- 1.34 mm, maximum pressure = 61.50 +/- 20.58 mmHg, and asymmetry index = 43.50 +/- 10.03%. Radiographic evaluation led to the following results: anal canal length = 9.61 +/- 2.14 mm and anorectal angle = 137.91 +/- 7.75 degrees . The experimental model designed here allows both anorectal manometry and computerized tomography to be carried out in the same way it is performed in human beings, as long as animal sedation is strictly controlled.

Acoustic Eigenvalues of a Quasispherical Resonator: Second Order Shape Perturbation Theory for Arbitrary Modes

The boundary-shape formalism of Morse and Ingard is applied to the acoustic modes of a deformed spherical resonator (quasisphere) with rigid boundaries. For boundary shapes described by r = a [1 - ε ℱ(θ, ϕ)], where ε is a small scale parameter and ℱ is a function of order unity, the frequency perturbation is calculated to order ε (2). The formal results apply to acoustic modes whose angular dependence is designated by the indices ℓ and m. Specific examples are worked out for the radial (ℓ = 0) and triplet (ℓ = 1) modes, for prolate and oblate spheroids, and for triaxial ellipsoids. The exact eigenvalues for the spheroids, and eigenvalue determined with finite-element calculations, are shown to agree with perturbation theory through terms of order ε (2). This work is an extension of the author's previous papers on the acoustic eigenfrequencies of deformed spherical resonators, which were limited to the second-order perturbation for radial modes [J. Acoust. Soc. Am. 71, 1109-1113 (1982)] and the first order-perturbation for arbitrary modes [J. Acoust. Soc. Am. 79, 278-285 (1986)].

Theory of the Greenspan viscometer

We present a detailed acoustic model of the Greenspan acoustic viscometer, a practical instrument for accurately measuring the viscosity eta of gases. As conceived by Greenspan, the viscometer is a Helmholtz resonator composed of two chambers coupled by a duct of radius rd. In the lowest order, eta=pi f rho(rd/Q)2, where f and Q are the frequency and quality factor of the isolated Greenspan mode, and rho is the gas density. In this level of approximation, the viscosity can be determined by measuring the duct radius and frequency response of the resonator. In the full acoustic model of the resonator, the duct is represented by a T-equivalent circuit, the chambers as lumped impedances, and the effects of the diverging fields at the duct ends by lumped end impedances with inertial and resistive components. The model accounts for contributions to 1/Q from thermal dissipation (primarily localized in the chambers) and from a capillary used for filling and evacuating the resonator. A robust, prototype instrument is being used for measuring the viscosity of reactive gases used in semiconductor processing. For well-characterized surrogate gases, the prototype viscometer generated values of eta that were within +/-0.8% of published reference values throughout the pressure range 0.2-3.2 MPa. Remarkably, we achieved this level of agreement by only slight adjustment of the numerically calculated inertial and resistive end effect parameters to improve the agreement with helium reference values. No other parameters were adjusted.