Selected Abstracts (Experimental Techniques)
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Reentrant radio-frequency resonator
for automated phase-equilibria and dielectric measurements in fluids
Anthony R.H. Goodwin
Center for Applied Thermodynamic Studies, Department of Mechanical Engineering,
University of Idaho, Moscow, ID 83844-0902 USA
James B. Mehl and Michael R. Moldover
Physical and Chemical Properties Division, Chemical Science and Technology
Laboratory, National Institute of Standards and Technology, Gaithersburg,
MD 20899 USA
A reentrant radio-frequency (rf) cavity resonator has
been developed for automated detection of phase separation of fluid mixtures
contained within the cavity. Successful operation was demonstrated by re-determining
the phase boundaries of a CO2+C2H6 mixture
in the vicinity of its critical point. We developed an accurate electrical
model for the resonator and used helium to determine the deformation of
the resonator under pressure. With the model and pressure-compensation,
the resonator was capable of very accurate dielectric measurements. We
confirmed this by re-measuring the molar dielectric polarizability 
of argon and obtained the result
= (4.140 ± 0.006) cm3/mol (standard uncertainty) in excellent
agreement with published values. We exploited the capability for accurate
dielectric measurements to determine the densities of the CO2+C2H6
mixture at the phase boundaries and to determine the dipole moment of 1,1,1,2,3,3-hexafluoropropane,
a candidate replacement refrigerant. Near the operating frequency of 375
MHz the capacitor in the resonator has an impedance near 14
.
This low-impedance is more tolerant of electrical conductivity within the
test fluid and in parallel paths in the support structures than comparable
capacitors operating at audio frequencies. This will be an advantage for
operation at high temperatures where some conductivity must be expected
in all fluids. Of further value for high-temperature applications, the
present rf resonator has only two metal-insulator joints. These joints
seal coaxial cables; neither joint is subjected to large mechanical stresses
and neither joint is required to maintain precise dimensional tolerances.
The resonator is rugged and may be operated with inexpensive electronics.
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Accurate acoustic measurements in gases under difficult conditions
K. A. Gillis, M. R. Moldover, and A. R. H. Goodwin
Physical and Chemical Properties Division, Chemical
Science and Technology Laboratory, National Institute of Standards and
Technology, Gaithersburg, MD 20899, U.S.A.
Accurate measurements of the speed of sound in gases are
often made using metal resonators with small transducers that perturb the
resonance frequencies in minor and predictable ways. We extend this method
to gases that may be corrosive and/or at high temperatures by using remote
transducers coupled to a resonator by acoustic waveguides. Thin metal diaphragms
separate the waveguides from the resonator. Thus, only metal parts come
into contact with the test gas. In the present apparatus, any gas compatible
with gold and stainless steel can be studied.
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An all-metal collection system for gas chromatography: purification of low boiling point compounds
T.J. Buckley and K.A. Gillis
Physical and Chemical Properties Division, Chemical
Science and Technology Laboratory, National Institute of Standards and
Technology, Gaithersburg, MD 20899, U.S.A.
We describe a purification system based on a commercial
preparative-scale gas chromatograph with a custom-designed condenser, collector,
and fraction handling system. In our fraction collector design, all the
wetted surfaces were either 316 stainless-steel or nickel. The collectors
and the integrated gas-handling manifold were designed to be used down
to liquid nitrogen temperature and up to 7 MPa of pressure to accomodate
low-boiling-point compounds, such as refrigerants. The design, operation,
and performance of this apparatus are presented.
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Greenspan acoustic viscometer for gases
K.A. Gillis, J.B. Mehl, and M.R. Moldover
Physical and Chemical Properties Division, Chemical
Science and Technology Laboratory, National Institute of Standards and
Technology, Gaithersburg, MD 20899, U.S.A.
Double Helmholtz acoustic resonators, first proposed by
Greenspan for measuring the viscosity of gases, were tested with helium,
argon, and propane. Two different resonators were tested extensively with
all three gases. For each of these instruments, the results for the viscosities
of the three gases were consistent within ± 0.5% at pressures spanning
the range 25 kPa - 1000 kPa. Without calibration, the viscosities deduced
from one viscometer were systematically 1% larger than data from the literature;
the viscosities from the second viscometer were systematically 3% larger
than data from the literature. If systematic differences were removed for
each viscometer by calibration with a single gas at a single temperature
and pressure, then nearly all the results for both instruments would have
fallen within ± 0.5% of the data from the literature. In these viscometers,
test gases are in contact with robust metal parts only; thus, these instruments
are applicable to a very wide variety of gases over a very wide range of
temperatures.
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Hydrodynamic similarity in an oscillating-body viscometer
R.F. Berg
Physical and Chemical Properties Division, Chemical
Science and Technology Laboratory, National Institute of Standards and
Technology, Gaithersburg, MD 20899 U.S.A.
Hydrodynamic similarity can be used to simply and accurately
calibrate an oscillating-body viscometer of arbitrarily complicated geometry.
Usually, an explicit hydrodynamic model based on a simple geometry is required
to deduce viscosity from the transfer function of an oscillating body such
as a vibrating wire or a quartz torsion crystal. However, at low Reynolds
numbers the transfer function of any immersed oscillator depends on the
fluid's viscosity only through the viscous penetration depth 
.
(Here, 
and 
are the fluid's viscosity and density and 
is the oscillator's frequency.) This hydrodynamic similarity can be exploited
if the oscillator is over damped and thus is sensitive to viscosity in
a broad frequency range. Even an oscillator of poorly known geometry can
be characterized over a range of penetration depths by measurements in
a fluid of known
and
over the corresponding range of frequencies. The viscosity of another fluid
can then be compared to that of the calibrating fluid with high accuracy
by varying the frequency so that the penetration depth falls within the
characterized range. In the present work, hydrodynamic similarity was demonstrated
with a highly damped viscometer comprised of an oscillating screen immersed
in carbon dioxide. The fluid's density was varied between 2 and 295 kg/m3
and the fluid's temperature was varied between 25 and 60ºC. The corresponding
variation of the viscosity was 50%.
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Temperature and frequency dependence of anelasticity in a nickel oscillator
R.F. Berg
Physical and Chemical Properties Division, Chemical
Science and Technology Laboratory, National Institute of Standards and
Technology, Gaithersburg, MD 20899 U.S.A.
The frequency dependence of the real and imaginary parts
of a nickel oscillator's transfer function is described over 3 decades
in frequency by the use of simple expressions. These expressions incorporate
only the resonance frequency 
,
the quality factor Q, and a characteristic exponent 
determined by a single measurement of creep. They are based on the ansatz
.gif)
= 
/Q,
where 
is the imaginary part of the spring constant. Over a 100 K range of temperature
T, the exponent
= 0.18 was constant even though Q(T) changed by a factor of 8. These
expressions are potentially useful for accurately describing a mechanical
oscillator whose transfer function must be modeled at frequencies far below
.
Examples include accelerometers based on a flexure element and suspensions
for interferometric gravitational wave detectors.
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High-temperature high-pressure oscillating tube densimeter
R.F. Chang and M.R. Moldover
National Institute of Standards and Technology
We describe an oscillating tube densimeter for use at
temperatures up to at least 575 K and at pressures up to 20 MPa. After
the densimeter was calibrated under vacuum and filled with water, it was
used to measure the density of toluene from 298 to 575 K at 13.8 MPa. The
results agree (0.1% rms deviation) with those obtained using other techniques.
In the present densimeter, an alternating current is passed through the
tube containing the sample to force the tube to oscillate in the field
of a permanent magnet. The design avoids the use of electromagnets (with
their attendant polymer or ceramic insulations) and does not require attachment
of appendages to the oscillating tube. This densimeter oscillates in an
overtone rather than in its fundamental mode, thereby achieving improved
isolation from environmental noise and a shorter response time. The densimeter
is small, weighing 370 g. If transformers are used to couple electrical
signals to the oscillating tube, the densimeter itself may be constructed
entirely out of metal.
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Greenspan acoustic viscometer: Numerical calculations of
fields and duct end effects
James B. Mehl
Physical and Chemical Properties Division,
National Institute of Standards and Technology,
Gaithersburg MD 20899,
and
Department of Physics and Astronomy, University of Delaware,
Newark, DE 19711-2570
Inertial and resistive end corrections for the Greenspan
acoustic viscometer were computed using a
boundary-integral-equation technique for determination of the acoustic field.
Viscous effects were estimated using a boundary layer approximation.
The results apply to a circular duct coupling two concentric
chambers and to ducts terminated by infinite plane baffles.
The effects of rounding the sharp edge at the duct end
were investigated and found to be described by simple
scaling relations.
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Resonators for accurate dielectric measurements in conducting liquids
Jean Hamelin, James B. Mehl, and Michael R. Moldover
Physical and Chemical Properties Division,
National Institute of Standards and Technology,
Gaithersburg MD 20899
The compact, rugged, reentrant radio-frequency resonator
[A.R.H. Goodwin, J.B. Mehl, and M.R. Moldover, Rev Sci.
Instrum. 67, 4294 (1996)] was modified for accurate
measurements of the zero-frequency dielectric constant
(relative electric permittivity) 
of
moderately conducting liquids such as impure water.
The modified resonator has two modes with frequencies near
216/
MHz and
566/ MHz. The results for
at both frequencies were consistent
within 0.0002 , verifying that the
low-frequency limit had been
attained with water samples with conductivities in the
range 100-2500 µS/m. The results for water and for
the insulating liquid cyclohexane were within
0.0005 of literature values. The
present analysis is based on a simplified equivalent
circuit that accounts for the loading of the resonator
by the external instrumentation. This circuit can easily
be generalized for a resonator with three or more modes.
The present resonator has a thick gold plating on its
interior surfaces. With the plating, the quality factors
Q of the resonances varied in a predictable way with
frequency and temperature. Predictable Qs were essential
for obtaining accurate values of
.
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Measurement of microkelvin temperature differences in a critical point thermostat
Robert F. Berg1, Gregory A. Zimmerli2, and Michael R. Moldover1
1Physical and Chemical Properties Division, NIST
2Engineering Services Division, NYMA, Incorporated, Brook Park, OH 44142
The density of a pure fluid near its critical point is extremely sensitive to temperature
gradients. In the absence of gravity, this effect limits the fluid's homogeneity. For example,
at 0.6 mK above the critical temperature, the microgravity experiment Critical Viscosity of
Xenon (CVX) can allow temperature differences no larger than 0.2 µK, corresponding to a gradient
of 10-5 K/m. The CVX thermostat, which consists of a thick-walled copper cell
contained within three concentric aluminum shells, was designed to achieve such a small
temperature gradient. However, asymmetries not included in the thermostat's model could degrade
the thermostat's performance. Therefore we measured the temperature gradient directly with a
miniature commercial thermoelectric cooler consisting of 66 semiconductor thermocouples. We
checked the results with a half bridge consisting of two matched thermistors. The measurement
was made along a thin-walled stainless steel cell whose conductance was much lower than that of
the copper cell, thus "amplifying" the temperature differences by a factor of 60. When the
thermostat was controlled at constant temperature, the steel cell's static temperature
difference was 5±1 µK. (The value inferred for the copper cell is 0.08 µK.) Ramping the
thermostat's temperature at the rate of 1 × 10-5 K/s increased the temperature
difference to 0.36 mK. These results demonstrate the feasibility of achieving extremely low
temperature gradients.
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An Improved Greenspan Acoustic Viscometer
J. Wilhelm,1,2 K. A. Gillis,1 J. B. Mehl,1 and M. R. Moldover1,3
1 Process Measurements Division, NIST, Gaithersburg, Maryland 20899-8360, U.S.A.
2 Guest Scientist from Fachbereich Chemie, Universität Rostock, D-18051 Rostock, Germany.
3 To whom correspondence should be addressed.
An improved Greenspan acoustic viscometer (double Helmholtz
resonator) was used to measure the viscosity of gases at
temperatures from 250 to 400 K and at pressures up to
3.4 MPa. The improvements include a vibration damping
suspension and the relocation of the fill duct. The fill
duct, which is needed to supply gas to the resonator, was
connected to the center of the resonator to eliminate
acoustic coupling between the resonator and the manifold.
In anticipation of handling corrosive gases, all surfaces
of the apparatus that are exposed to the test gas are made
of metal. The viscometer was tested with argon, helium,
xenon, nitrogen, and methane. Isothermal measurements were
carried out at 298.15 and 348.15 K and at pressures up to
3.2 MPa. Without calibration, the results differed from
published viscosity data by -0.8 % to +0.3 %
(0.47 % r.m.s.). These results are significantly better
than previous results from Greenspan viscometers. The
measurements also yielded the speed of sound, which
differed from literature data by +0.16 % to +0.20 %
(0.18 % r.m.s.). Adding empirical effective-area and
effective-volume corrections to the data analysis
decreased the r.m.s. deviations to 0.12 % for the
viscosity and to 0.006 % for the speed of sound. No
unusual phenomena were encountered when the viscometer was
tested with a helium-xenon mixture between 250 and 375 K.
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Toroidal cross capacitor for measuring the dielectric constant of gases
Thomas J. Buckley1, Jean Hamelin2, and M. R. Moldover3
1 Physical and Chemical Properties Division, NIST, Gaithersburg, MD 20899-8380
2 Present address: Institut de recherche sur l'hydrogène, Université du Québec à Trois-Rivières, 3351 Boul. Des Forges, C.P. 500, Trois-Rivières, Québec, Canada G9A 5H7
3 Corresponding author; Process Measurements Division, NIST, Gaithersburg, MD 20899-8360;
electronic mail: michael.moldover@nist.gov
We describe toroidal cross capacitors built to accurately
measure the dielectric constant of gases. We tested the
capacitors by measuring the dielectric polarizability of
helium and argon at 7 °C and 50 °C at pressures up to 3 MPa.
For helium, the results are consistent with the ab initio
calculation of the molar polarizability and are limited by
the uncertainties of the capacitance measurements. For
argon, the results are consistent with the best previously
published measurements of the polarizability and are
limited by the uncertainties of the pressure measurements.
Lessons learned are provided.
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Theory of the Greenspan Viscometer
Keith A. Gillis, James B. Mehl, and Michael R. Moldover
Process Measurements Division, NIST, Gaithersburg, MD 20899-8360
We present an acoustic model of the Greenspan acoustic viscometer,
a practical instrument for accurately measuring the viscosity
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,
= 
f(rd/Q)2,
where f and Q are the frequency and quality
factor of the isolated Greenspan
mode, and
is the gas density. Thus the viscosity can be determined
without calibration 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 judiciously-
located 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
that were within ± 0.8% of published reference values
throughout the pressure range 0.2-3.2 MPa.
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Quasi-spherical resonators for metrology based on the relative dielectric permittivity of gases
Eric F. May, Laurent Pitre, James B. Mehl, Michael R. Moldover, and James W. Schmidt
Process Measurements Division, NIST, Gaithersburg, MD 20899-8360
We evaluate a quasi-spherical, copper, microwave cavity resonator for accurately measuring the relative dielectric
permittivity εr(p,T) of helium and argon. In a simple, crude approximation
the cavity’s shape is a triaxial ellipsoid with axes of length a, 1.001a and 1.005a, with
a = 5 cm. The unequal axes of the quasi-sphere separated the triply-degenerate microwave resonance frequencies
of a sphere (f11TM, f12TM, ..., f11TE,
f12TE, ...) into three non-overlapping, easily measured, frequencies. The frequency
splittings are consistent with the cavity’s shape, as determined from dimensional measurements. We deduced
εr(p,T) of helium and of argon at 289 K and up to 7 MPa from the resonance
frequencies flnσ,
the resonance half-widths glnσ, and the compressibility of copper. Simultaneous
measurements of εr(p,T) with the quasi-spherical resonator and a cross
capacitor agreed within 1 × 10 −6 for helium, and for argon they differed by an
average of only 1.4 × 10 −6. This small difference is within the stated uncertainty of
the capacitance measurements. For helium, the resonator results for εr(p,T)
were reproducible over intervals of days with a standard uncertainty of 0.2 × 10 −6,
consistent with a temperature irreproducibility of 5 mK. We demonstrate that several properties of
quasi-spherical cavity resonators make them well suited to εr(p,T)
determinations. Ultimately, a quasi-spherical resonator may improve dielectric constant gas thermometry and realize a
proposed pressure standard based on εr(p,T).
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Re-entrant Radio-Frequency Resonator Hygrometer for Fuel Cell Research and Development
P. H. Huang, D. Ripple, M. R. Moldover, and G. E. Scace
Process Measurements Division, NIST, Gaithersburg, MD 20899-8360
Standardized mixtures of {CO2-free air + water vapor} were generated at ambient
pressure and then flowed through a reentrant, radio-frequency (RF), cavity resonator operating at
frequencies near 370 MHz. As the generator increased the mole fraction of water vapor
xw in the mixture, the dielectric constant (relative electric permittivity) εr
of the gas in the cavity
increased and the resonance frequency decreased. For example, the resonance frequency decreased
0.2 % as the relative humidity increased from 0 % to 100 % at 90 °C. The repeatability of the
frequency measurements was, fractionally, 4×10−7, or better. This repeatability corresponds to
humidity changes of 0.04 % at 90 °C. Because the resonator is robust, mechanically simple,
moderately-sized (7 cm outside diameter, 7 cm high), and constructed from corrosion-resistant
materials (Inconel with gold and ceramic seals), it is a promising candidate to become a
reference standard for humidity measurements up to the highest temperatures and pressures
proposed for fuel cell operation. Similar resonators have been used at the National Institute of
Standards and Technology (NIST) to accurately measure the dielectric constant of gases and of
liquid water and also to determine the dipole moments of gases.
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Viscometer for Low Frequency, Low Shear Rate Measurements
R.F. Berg and M.R. Moldover
Thermophysics Division, National Bureau of Standards, Gaithersburg, MD 20899
We describe a torsion-oscillator viscometer whose low frequency (0.5 Hz) and very low shear rate
(0.05 s−1) are required for measurements of shear sensitive fluids such as microemulsions,
polymer melts and solutions, gels, and liquid mixtures near critical points. The viscometer has a resolution
of 0.2% when used with liquid samples and a resolution of 0.4% when used with a dense gaseous sample. The
viscometer operates under computer control and is compatible with submillikelvin temperature control.
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