The viscosity of gaseous propane and its initial density dependence

Results of five series of high-precision viscosity measurements on gaseous propane, each differing in density, are reported. The measurements were performed in a quartz oscillating-disk viscometer with small gaps from room temperature up to about 625 K and for densities between 0.01 and 0.05 mol · L^–1. The experimental data were evaluated with a first-order expansion, in terms of density, for the viscosity. Reduced values of the second viscosity virial coefficients deduced from the zero-density and initial-density viscosity coefficients for propane and for furthern-alkanes are in close agreement with the theoretical representation of the Rainwater-Friend theory for the potential parameter ratios by Bich and Vogel. A new representation of the viscosity of propane in the limit of zero density is provided using the new experimental data and some data sets from literature. The universal correlation based on the extended principle of corresponding states extends over the temperature range 293 to 625 K with an uncertainty of ±0.5 % and deviates from earlier representations by about 1 % at the upper temperature limit.     

The Viscosity of Gaseous Isobutane and Its Initial Density Dependence1

Results of new relative high-precision measurements on gaseous isobutane are reported. Six series, each differing in density, were performed in a quartz oscillating-disk viscometer from 297 to 627 K and for densities between 0.010 to 0.048 mol·L^–1. Isothermal values recalculated from the original experimental data were evaluated with a first-order expansion, in terms of density, for the viscosity. Reduced values of the second viscosity virial coefficient derived from the zero-density and initial-density viscosity coefficients agree with the representation of the Rainwater–Friend theory when using energy and length scaling factors specific for the interactions of the isobutane molecules. With the same scaling factors an individual correlation in the limit of zero density was developed including only a few values from the literature. The uncertainty of the zero-density viscosity correlation is estimated to be ±0.4%.     

The initial density dependence of transport properties: Noble gases

The usual procedure that the transport properties at atmospheric pressure are identified with values in the limit of zero density cannot be accepted for all reduced temperatures T ^*. It is shown in the framework of the Rainwater-Friend theory for noble gases, as a good example, that for T ^*<1 the effect of the initial density dependence has different signs for viscosity and thermal conductivity and amounts to a few percent, when data at atmospheric pressure are compared with zero-density values. An improved representation of the monomer-dimer contribution to the second transport virial coefficients of the Rainwater-Friend theory is presented in the paper. This is based, among others, on the author's own experimental data of the initial density dependence of viscosity of polytomic gases.     

Dilute-gas mixture properties from pure-component data

The second virial coefficient, dilute-gas viscosity, and binary diffusion coefficients of some binary-gas mixtures are predicted from potentials which have been fitted to the properties of the pure components. It has been noted that the SSR-MPA potential for polyatomic and the MSK potential for monatomic molecules together with a suitable set of universal combination rules are adequate to make predictions essentially within the inaccuracy of the data.     

The Viscosity of Gaseous n-Butane and Its Initial Density Dependence

New relative high-precision measurements of the viscosity of gaseous n-butane were carried out in an oscillating-disk viscometer. Seven series of measurements were performed between 298 and 627 K. in the density range from 0.01 to 0.05 mol·L^–1. Isotherms recalculated from the original experimental data were analyzed with a first-order expansion, in terms of density, for the viscosity. Reduced values of the second viscosity virial coefficient deduced from the zero-density and initial-density viscosity coefficients for n-butane are in good agreement with the representation of the Rainwater–Friend theory. The new experimental data and some data sets from the literature were used to develop a representation for the viscosity of n-butane in the limit of zero density on the basis of the extended principle of corresponding states. It has been shown that an individual correlation is needed to represent the experimental data between 293 and 627 K with an uncertainty of ±0.4%.     

Ab Initio Values of the Thermophysical Properties of Helium as Standards

Recent quantum mechanical calculations of the interaction energy of pairs of helium atoms are accurate and some include reliable estimates of their uncertainty. We combined these ab initio results with earlier published results to obtain a helium-helium interatomic potential that includes relativistic retardation effects over all ranges of interaction. From this potential, we calculated the thermophysical properties of helium, i.e., the second virial coefficients, the dilute-gas viscosities, and the dilute-gas thermal conductivities of ³He, ⁴He, and their equimolar mixture from 1 K to 10⁴ K. We also calculated the diffusion and thermal diffusion coefficients of mixtures of ³He and ⁴He. For the pure fluids, the uncertainties of the calculated values are dominated by the uncertainties of the potential; for the mixtures, the uncertainties of the transport properties also include contributions from approximations in the transport theory. In all cases, the uncertainties are smaller than the corresponding experimental uncertainties; therefore, we recommend the ab initio results be used as standards for calibrating instruments relying on these thermophysical properties. We present the calculated thermophysical properties in easy-to-use tabular form.     

4He Thermophysical Properties: New Ab Initio Calculations

Since 2000, atomic physicists have reduced the uncertainty of the helium-helium “ab initio” potential; for example, from approximately 0.6 % to 0.1 % at 4 bohr, and from 0.8 % to 0.1 % at 5.6 bohr. These results led us to: (1) construct a new inter-atomic potential ϕ₀₇, (2) recalculate values of the second virial coefficient, the viscosity, and the thermal conductivity of ⁴He from 1 K to 10,000 K, and (3), analyze the uncertainties of the thermophysical properties that propagate from the uncertainty of ϕ₀₇ and from the Born-Oppenheimer approximation of the electron-nucleon quantum mechanical system. We correct minor errors in a previous publication [J. J. Hurly and M. R. Moldover, J. Res. Nat. Inst. Standards Technol. 105, 667 (2000)] and compare our results with selected data published after 2000. The ab initio results tabulated here can serve as standards for the measurement of thermophysical properties.     

New Correlation Functions for Viscosity Calculation of Gases Over Wide Temperature and Pressure Ranges

The viscosity of 14 supercritical gases over a wide temperature–pressure range is calculated with a new correlation scheme. Highly accurate realistic interatomic potentials of the noble gases are used in the Chapman–Enskog calculation of the zero-density viscosity and in the Rainwater–Friend theory to determine the initial density dependence of the viscosity. At densities beyond the range of the theory, a variant of the residual viscosity is developed. It is shown that the temperature dependence of the residual viscosity function increases with the number of atoms in the molecule. By including this temperature dependence, the accuracy of the predicted results improves significantly. The accuracy of this method is within the experimental uncertainties.     

Second virial coefficients in closed form for a Kihara (2m-m)-potential

In the literature second virial coefficients are calculated by series expansions or by direct numerical integration. For thermodynamic quantities such as thermodynamic functions, analytical expressions are wanted. This paper gives closed formulas for the second virial coefficient for a convex-body Kihara potential of the type U()= U ₀[( ₀/)_2m -2( ₀/) ^m ], where m can be a rational number n>3. Furthermore, a number of related problems such as dielectric virial coefficients and Buckingham-Pople integrals are reduced to the same Laplace-transformation-type technique.     

Thermophysical Properties of Nitrogen from a New Potential Energy Surface Using the Mason–Monchick Approximation

A recent N₂–N₂ potential has been used to calculate the second virial, viscosity, and diffusion coefficients. Calculations have been done up to the first quantum correction for virial coefficients and the second-order kinetic theory approximation for transport coefficients. The Mason–Monchick approximation (MMA) has been used for the calculation of collision integrals and, via a numerical analysis, a common intersection point has been found for reduced cross sections and collision integrals of different orientations. This regularity has been interpreted with the aim of the orientation dependence of the potential energy and different types of collisions between molecules. The overall agreement of the calculated second virial coefficient with experiment is reasonable but suggests that a slight re-scaling of the potential would be beneficial. In the case of transport properties, calculated and experimental results show an average deviation of about 1.6% and 0.7% for viscosity and relative diffusion coefficients, respectively.     

First-Principles Calculation of the Air–Water Second Virial Coefficient

Recent theoretical work has produced quantitatively accurate potential-energy surfaces for water with common gases. These pair potentials have been used to calculate second interaction virial coefficients with an accuracy superior to that obtained by most experiments. In this work, results for water–nitrogen, water–oxygen, and water–argon are combined to calculate an effective second virial coefficient for water with air. The results are in agreement with the existing experimental data, but they cover a wide range of temperatures while the experimental data extend only from 253 to 348 K. These results will be useful for humidity standards and other applications requiring thermodynamic properties of moist air.     

The thermal conductivity and viscosity of acetic acid-water mixtures

The viscosity and thermal conductivity of acetic acid water mixtures were measured over the entire composition range and at temperatures ranging from 293 to 453 K. Viscosity measurements were performed with a high-pressure viscometer and thermal conductivity was measured using a modified transient hot-wire technique. A mercury filled. glass capillary was used as the insulated hot wire in the measurements. The l iscosity data showed unusual trends with respect to composition. At it given temperature. the viscosity was seen to increase with increasing acid concentration, attain a maximum. and then decrease. The thermal conductivity, on the other hand, decreased monotonically with acid concentration. A generalized corresponding-states principle using water and acetic acid as the reference fluids was used to predict both viscosity and thermal conductivity with considerable sucres.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–34, 1994, Boulder. Colorado, U.S.A.     

Compression factor and vapor pressure of bromotrifluoromethane in the temperature range 245–393 K at pressures up to 12 MPa

The compression factors and vapor pressures have been measured on bromotrifluoromethane using a Burnett apparatus. The results on the compression factor cover the range of temperatures 263 to 393 K and of pressures 0.14 to 11.6 MPa, corresponding to a density variation from 7 to 1367 kg· m^–3. The experimental uncertainty of these 176 measurements of compression factor was estimated to be 0.2%. Thirty measurements of vapor pressure were made for temperatures 245 to 339 K, with an experimental uncertainty of 0.1%. Based on these results, the second virial coefficients were determined for temperatures 293 to 393 K.     

Determination of the interaction second virial coefficients for the carbon dioxide-ethane system from refractive index measurements

The compressibility behavior of the CO₂-C₂H₆ system was investigated experimentally. In this work, the refractive indexes of the pure gases and the mixtures were measured using an optical apparatus. On the basis of these data, density and compressibility factors were computed using the Lorentz-Lorenz law. For the pure components, carbon dioxide and ethane, the data from the optical system were slightly adjusted by a fit to Burnett apparatus data measured separately. The experiments produced very accurate virial coefficients and refraction virial coefficients. This paper reports on the effect of temperature on the second and third virial coefficients. For the first refraction virial coefficient, no influence of temperature was found with the equipment used. The interaction second virial coefficient B ₁₂ (as a function of temperature) was computed from experimental data for the CO₂-C₂H₆ binary system. The data, for which an accuracy of ±1.5 cm³ · mol^–1 was estimated, are in agreement with the data published by Holste et al.     

The viscosity and thermal conductivity of ethane in the limit of zero density

New representations of the viscosity and thermal conductivity of ethane in the limit of zero density are provided. The correlation for the viscosity extends over the temperature range 200 to 1000 K, whereas that for thermal conductivity extends from 225 to 725 K. The behavior of each property is represented by an independent correlation of the appropriate effective collision cross section as a function of temperature. The final results are compared with experimental data as well as with earlier correlations. The accuracy of the viscosity correlation is estimated to be ±0.5 % in the temperature range 300 KT600 K, increasing to ±1.5 and ±2.5% at 200 and 1000 K, respectively. The uncertainty associated with the thermal conductivity correlation is ±2 % in the temperature range 300 KT500 K, increasing to ±3% at either end. The results of this study indicate that there is an urgent need for additional high-precision measurements of thermal conductivity especially for temperatures above 400 K.     

Sound-velocity measurements for HFC-134a and HFC-152a with a spherical resonator

A spherical acoustic resonator was developed for measuring sound velocities in the gaseous phase and ideal-gas specific heats for new refrigerants. The radius of the spherical resonator, being about 5 cm, was determined by measuring sound velocities in gaseous argon at temperatures from 273 to 348 K and pressures up to 240 kPa. The measurements of 23 sound velocities in gaseous HFC-134a (1,1,1,2-tetrafluoroethane) at temperatures of 273 and 298 K and pressures from 10 to 250 kPa agree well with the measurements of Goodwin and Moldover. In addition, 92 sound velocities in gaseous HFC-152a (1,1-difluoroethane) with an accuracy of ±0.01% were measured at temperatures from 273 to 348 K and pressures up to 250 kPa. The ideal-gas specific heats as well as the second acoustic virial coefficients have been obtained for both these important alternative refrigerants. The second virial coefficients for HFC-152a derived from the present sound velocity measurements agree extremely well with the reported second virial coefficient values obtained with a Burnett apparatus.Paper dedicated to Professor Joseph Kestin.     

Correlation and extrapolation scheme for the composition and temperature dependence of viscosity of binary gaseous mixtures: Carbon dioxide + ethane

Experimental viscosity data of ethane, carbon dioxide, and three mole fractions of the binary system carbon dioxide + ethane in the temperature range 293.15<T633.15 K and in the density range 0.010.05 mol·L^–1 reported earlier were evaluated simultaneously to find out a useful correlation and extrapolation scheme for the viscosity of binary systems in the range of moderate densities. A procedure based on the ideas of the modified Enskog theory has been found to give the best results. Dependent on temperature, the collision diameters related to the equilibrium radial distribution function at contact are fitted to viscosity values of the pure substances and of at least one mixture. The results are compared with experimental data from the literature. A recommendation is given concerning the density range in which the first density contribution to the viscosity coefficient of the system carbon dioxide + ethane is sufficient to be included.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

The dilute-gas properties of some systems containing CO2

The SSR-MPA potential model is used to correlate and extrapolate the dilutegas properties of some systems containing CO₂. With parameters determined from a consistent set of second virial and Joule-Thomson data, the third virial coefficient of CO₂ as well as the second virial coefficients of various mixtures containing CO₂ can be predicted very well. The Mason-Monchik approximation fails for a complicated molecule such as CO₂, although at least a viscosity prediction of technical accuracy is obtained. If parameters fitted to the CO₂ viscosity are used, excellent predictions can be made for the viscosity of gaseous mixtures containing CO₂.