An Absolute Viscometer-Densimeter and Measurements of the Viscosity of Nitrogen, Methane, Helium, Neon, Argon, and Krypton over a Wide Range of Density and Temperature

An apparatus for the simultaneous measurement of viscosity and density of fluids is presented. The viscometer-densimeter covers a viscosity range up to 150 µPas and a density range up to 2000 kgm^–3 at temperatures from 233 to 523 K and pressures up to 30 MPa. Very accurate density measurements with uncertainties of ±0.02 to ±0.05% have always been carried out with this apparatus, although in its first version it was necessary to calibrate the viscosity measuring system on a reference fluid in order to achieve uncertainties of ±0.6 to ±1.0% in viscosity. After significant improvements, the apparatus now achieves uncertainties in viscosity of less than ±0.15% in the dilute gas region and less than ±0.4% for higher densities. Moreover, the viscosity measuring system can be described in an absolute way; calibration is no longer necessary. In order to test the advanced apparatus and to determine viscosity-density values of very high quality, comprehensive measurements on nitrogen, argon, and methane were carried out in the entire working range of the viscometer-densimeter. In addition, viscosity-density measurements on helium, neon, and krypton were made on two selected isotherms each. All measurements show that the estimated total uncertainty of ±0.15 to ±0.4% in viscosity and of ±0.02 to ±0.05% in density is clearly met. In order to verify the results of the combined viscometer-densimeter, a new apparatus for very accurate viscosity measurements was designed. While the working range of this apparatus is restricted to the dilute gas region, it yields uncertainties of less than ±0.07% in viscosity. Measurements carried out with this apparatus confirmed the previously measured values of the combined viscometer-densimeter within ±0.03%.     

A new,accurate single-sinker densitometer for temperatures from 233 to 523 K at pressures up to 30 MPa

A new apparatus for density measurements of fluids in the entire range from gas to liquid densities is presented. The instrument is a single-sinker buoyancy densitometer designed in a completely new way. The buoyancy force exerted by the sample fluid on an immersed sinker (buoy) is transferred by a new type of magnetic suspension coupling to an analytical balance. In order to reduce drastically the linearity error of the (commercial) balance. a special basic load compensation is applied which also avoids any buoyancy ellèct of the laboratory air on the balance. The new single-sinker densitometer covers a density range from 10 to 200(1 kg - m ' at temperatures from 233 to 523 K and pressures up to 30 MPa. A special compact version of such a single-sinker densitometer can even he used at temperatures from 80 to 523 K at pressures up to 100 MPa. Test measurements on densities of carbon dioxide at 233, 360, and 523 K at pressures up to 30 MPa show that the estimated total uncertainty of ±0.02% to ±0.03% in density is clearly met.Invited paper presented at the Twellth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado. U.S.A.Author to whom correspondence should be addressed.     

Simultaneous Measurement of the Density and Viscosity of Compressed Liquid Toluene

A vibrating-wire densimeter described previously has been used to perform simultaneous measurements of the density and viscosity of toluene at temperatures from 222 to 348 K and pressures up to 80 MPa. The density measurements are essentially based on the hydrostatic weighing principle, using a vibrating-wire device operated in forced mode of oscillation, as a sensor of the apparent weight of a cylindrical sinker immersed in the test fluid. The resonance characteristics for the transverse oscillations of the wire, which is also immersed in the fluid, are described by a rigorous theoretical model, which includes both the buoyancy and the hydrodynamic effects, owing to the presence of the fluid, on the wire motion. It is thus possible, from the working equations, to determine simultaneously, both the density and the viscosity of the fluid from the analysis of the resonance curve of the wire oscillation, the density being related essentially to the position of the maximum and the viscosity to its width. New results of measurements of the density and viscosity of toluene in the compressed liquid region are presented, and compared with literature data. The density results extend over a temperature range 222 KT348 K, and pressures up to 80 MPa. The viscosity results cover a temperature range of 248 KT348 K and pressures up to 80 MPa. The uncertainty of the present density data is estimated to be within ±0.1% at temperatures 298 KT350 K, and ±0.15% at 222 KT273 K. The corresponding overall uncertainty of the viscosity measurements is estimated to be ±2% for temperatures 298 KT350 K, and ±3% for 248 KT273 K.     

High-Pressure Measurements of the Viscosity and Density of Two Polyethers and Two Dialkyl Carbonates

The viscosity and density of four pure liquid compounds (dimethyl carbonate, diethyl carbonate, triethylene glycol dimethyl ether, and tetraethylene glycol dimethyl ether) were measured at several temperatures between 283.15 and 353.15 K. The density measurements were performed up to 60 MPa with an uncertainty of 1×10^–4g·cm^–3. The viscosity at atmospheric pressure was measured with an Ubbelohde-type glass capillary tube viscometer with an uncertainty of ±1%. At pressures up to 100 MPa the viscosity was determined with a falling ball viscometer with an uncertainty of ±2%. The density (410 experimental values) and viscosity data (184 experimental values) were fitted to several correlation equations.     

High-Pressure Viscosity and Density Behavior of Ternary Mixtures: 1-Methylnaphthalene+n-Tridecane+2,2,4,4,6,8,8-Heptamethylnonane

The dynamic viscosity and the density of the ternary system, n-tridecane+1-methylnaphthalene+2,2,4,4,6,8,8-heptamethylnonane, were measured as a function of temperature from 293.15 to 353.15 K in 10 K increments at pressures up to 100 MPa. A falling body viscometer was used for measuring the dynamic viscosity above 0.1 MPa, while at 0.1 MPa the viscosity was obtained with an Ubbelohde viscometer. The overall uncertainty in the reported data is less than 1 kg·m^–3 for densities and 2% for viscosities, except at 0.1 MPa where the uncertainty is less than 1%. The experimental results correspond to 882 values of viscosity. With reference to the 126 values published previously for the pure compounds and 882 values for the three associated binaries, the system is globally described by 1890 experimental values as a function of pressure, temperature, and composition. The results for the viscosity are discussed in terms of mixing laws and the excess activation energy of viscous flow.     

High-Pressure Viscosity and Density Measurements for the Asymmetric Binary System cis-Decalin +2,2,4,4,6,8,8-Heptamethylnonane

Measurements of the viscosity and density of seven binary mixtures composed of cis-decahydronaphthalene (cis-decalin)+2,2,4,4,6,8,8-heptamethylnonane along with the pure compounds have been performed in the temperature range 293.15 to 353.15 K and at pressures up to 100 MPa. The viscosity was measured with a falling-body viscometer, except at 0.1 MPa where a classical capillary viscometer (Ubbelohde) was used. The experimental uncertainty for the measured viscosities is less than 2% at high pressures. The density was measured up to 60 MPa with a resonance densimeter and extrapolated with a Tait-type relationship up to 100 MPa. The uncertainty for the reported densities is less than 1 kgm^–3. The measured data have been used in an evaluation of the simple mixing laws of Grunberg and Nissan and of Katti and Chaudhri, which require only the density and viscosity of the pure compounds. This evaluation showed that these mixing laws can accurately represent the viscosity of this asymmetric binary system within an average absolute deviation of 1%.     

Ultrasonic speeds and densities of poly(dimethylsiloxane) (viscosity grades 30 and 50×10−4 m · s−1) at 298.15, 303.15, and 308.15 K under high pressures

The ultrasonic speeds and densities of poly(dimethylsiloxane), viscosity grades 30 and 50×10^–4 m · s^–1 at 298.15 K, were measured at 298.15, 303.15, and 308.15 K. The measurements were carried out using new apparatuses, one for measurement of the speed under pressures up to 200 MPa and another for measurement of the density under pressures up to 100 MPa. The former is constructed with a sing-around technique of the fixed-path type operated at a frequency of 2 MHz, and the latter is a dynamic bellows piezometer. The probable uncertainty in the present results is within ±0.23% for speed and ±0.19% for density for all the experimental conditions. The ultrasonic speed in these fluids at first increases rapidly with pressure and then indicates a mild rise in the highpressure region. Similar pressure effects are observed for the density. The relationship between the speed and the density satisfied a first-order function well. The isentropic compressibility, derived from the speed and density, also showed a large pressure effect. The values and its pressure effects seemed almost independent of the viscosity of poly(dimethylsiloxane).     

Viscosity and Density Measurements of Binary Mixtures Composed of Methylcyclohexane + cis-Decalin Versus Temperature and Pressure

Viscosity and density measurements have been carried out for binary mixtures composed of methylcyclohexane + cis-decalin in the temperature range 293.15 to 353.15 K and at pressures up to 100 MPa. The viscosity was measured with a falling-body viscometer, except at atmospheric pressure where an Ubbelohde viscometer was used. The experimental uncertainty for the measured viscosities is 2%. The density was measured up to 60 MPa and extrapolated by a Tait-type relationship to 100 MPa. For the reported densities the uncertainty is less than 1 kgm^–3. An evaluation of the simple mixing laws of Grunberg and Nissan and of Katti and Chaudhri, which require only the density and viscosity of the pure compounds, showed that they can represent the viscosity of the binary mixtures with an average absolute deviation of 2%, corresponding to the experimental uncertainty.     

Reference Correlation for the Viscosity of Liquid Toluene from 213 to 373 K at Pressures to 250 MPa

A correlation in terms of temperature and molar volume is recommended for the viscosity of liquid toluene as a reference for high-pressure viscosity measurements. The temperature range covered is from 213 to 373 K, and the pressure range from atmospheric up to 250 MPa. The standard deviation of the proposed correlation is 1.36%, and, within a 95% confidence limit, the error is 2.7%. It is estimated that for densities up to 920 kg·m^–3the uncertainty of the viscosity values generated by this correlation is about ±2%.     

Viscosity Measurements of Liquid Toluene at Low Temperatures Using a Dual Vibrating-Wire Technique

A recently developed dual vibrating-wire technique has been used to perform viscosity measurements of liquid toluene in the temperature range 213 KT298 K, and at pressures up to approximately 20 MPa. The results were obtained by operating the vibrating-wire sensor in both forced and free decay modes. The estimated precision of the viscosity measurements, in either mode of operation, is ±0.5%, for temperatures above or equal to 273 K, increasing with decreasing temperature up to ±1% at 213 K. The corresponding overall uncertainty is estimated to be within ±1% and ±1.5%, respectively.     

Thermal conductivity of hydrogen for temperatures between 78 and 310 K with pressures to 70 MPa

The paper presents new experimental measurements of the thermal conductivity of hydrogen. The ortho-para compositions covered are normal, near normal, para, and para-rich. The measurements were made with a transient hot wire apparatus. The temperatures covered the range from 78 to 310 K with pressures to 70 MPa and densities from 0 to a maximum of 40 mol · L^–1. For compositions normal and near normal, the isotherms cover the entire range of pressure, and the temperatures are 78, 100, 125, 150, 175, 200, 225, 250, 275, 294, 300, and 310K. The para measurements include eight isotherms at temperatures from 100 to 275 K with intervals of 25 K, pressures to 12 MPa, and densities from 0 to 12 mol · L^–1. Three additional isotherms at 150, 250, and 275 K cover para-rich compositions with para percentages varying from 85 to 72%. For these three isotherms the pressures reach 70 MPa and the density a maximum of 30 mol · L^–1. The data for all compositions are represented by a single thermal conductivity surface. The data are compared with the experimental measurements of others through the new correlation. The precision (2) of the hydrogen measurements is between 0.5 and 0.8% for wire temperature transients of 4 to 5 K, while the accuracy is estimated to be 1.5%.     

Density and Viscosity of Mixtures of n-Hexane and 1-Hexanol from 303 to 423 K up to 50 MPa

Experimental results for the density and viscosity of n-hexane+1-hexanol mixtures are reported at temperatures from 303 to 423 K and pressures up to 50 MPa. The binary mixture was studied at three compositions, and measurements on pure 1-hexanol are also reported. The two properties were measured simultaneously using a single vibrating-wire sensor. The present results for density have a precision of ±0.07% and an estimated uncertainty of ±0.3%. The viscosity measurements have a precision of ±1% and an estimated uncertainty of ±4%. Representations of the density and viscosity of the mixture as a function of temperature and pressure are proposed using correlation schemes.     

The Thermal Conductivity, Thermal Diffusivity and Isobaric Heat Capacity of Toluene and Argon

This paper presents absolute measurements for the thermal conductivity and thermal diffusivity of toluene obtained with a transient hot-wire instrument employing coated wires over the density interval of 735 to 870 kgm^–3. A new expression for the influence of the wire coating is presented, and an examination of the importance of a nonuniform wire radius is verified with measurements on argon from 296 to 323 K at pressures to 61 MPa. Four isotherms were measured in toluene between 296 and 423 K at pressures to 35 MPa. The measurements have an uncertainty of less than ±0.5% for thermal conductivity and ±2% for thermal diffusivity. Isobaric heat capacity results, derived from the measured values of thermal conductivity and thermal diffusivity, using a density determined from an equation of state, have an uncertainty of ±3% after taking into account the uncertainty of the applied equation of state. The measurements demonstrate that isobaric specific heat determinations can be obtained successfully with the transient hot wire technique over a wide range of fluid states provided density values are available.     

Viscosity Measurements on Gaseous Argon, Krypton, and Propane1

A new vibrating-wire viscometer was designed to perform quasi-absolute measurements of very high precision on gases. It was applied to determine the viscosity of argon at temperatures of 298.15, 348.15, and 423.15 K and pressures up to 20 MPa, and the viscosity of krypton at 298.15 and 348.15 ,K and pressures up to 16 MPa. Furthermore, several isothermal series of viscosity measurements on gaseous propane were carried out. The subcritical isotherms at 298.15, 323.15, 348.15, and 366.15 K were restricted to 95% of the saturated vapor pressure, the supercritical isotherms at 373.15, 398.15, and 423.15 K to 20 MPa. In general, the measurements are characterized by a reproducibility of ±0.05% and an accuracy of ±0.2%. However, close to the critical point an accuracy of ±3% has to be accepted, mainly due to the uncertainty of the density. In this context the influence of the equation of state used for propane is discussed.     

The Viscosity of Organic Liquid Mixtures

The paper reports measurements of the viscosity and density of two heavy hydrocarbon mixtures, Dutrex and Arab Light Flashed Distillate (ALFD), and of their mixtures with hydrogen. The measurements have been carried out with a vibrating-wire device over a range of temperatures from 399 to 547 K and at pressures up to 20 MPa. Measurements have also been carried out on systems in which hydrogen at different concentrations has been dissolved in the liquids. The measurements have an estimated uncertainty of ±5% for viscosity and ±2% for density and represent the first results on these prototypical heavy hydrocarbons. The results reveal that the addition of hydrogen reduces both the density and viscosity of the original hydrocarbon mixture at a particular temperature and pressure.Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui, P. R. China.     

Densities of Sulfur Hexafluoride and Dinitrogen Monoxide over a Wide Temperature and Pressure Range in the Sub- and Supercritical States

Densities of sulfur hexafluoride (SF₆) and dinitrogen monoxide (N₂O) have been measured with a fully computer-controlled high-temperature high-pressure vibrating tube densimeter system in the sub- and supercritical states. The uncertainty in density measurement was estimated to be between ±0.2 and ±0.3kg·m^–3 depending on the temperature. With respect to accuracy, reliability, suitability, and time consumption, this system has significant advantages for measuring PT properties in the compressed liquid and supercritical states. The densities were measured for temperatures from 273 to 623K and at pressures up to 30MPa for SF₆ (442 data points) and from 273 to 473K and up to 40MPa for N₂O (251 data points), which encompassed density ranges between 142.9 and 1778.5kg·m^–3 for SF₆ and between 124.4 and 1051.1kg·m^–3 for N₂O. Furthermore, the liquid densities of SF₆ and N₂O were correlated with a new three-dimensional density correlation system (TRIDEN) and the complete set of PT data in the sub- and supercritical states were correlated with a virial-type equation of state. For checking the accuracy and suitability of the vibrating tube densimeter system, the experimental densities of SF₆ were compared with published data and with the results of a reference equation of state.     

The viscosity of liquid carbon dioxide

The paper reports new masurements of the viscosity of liquid carbon dioxide along three isotherms at 260, 280, and 300 K for pressures up to 100 MPa. The measurements have been carried out in a vibrating-wire viscometer and have an estimated accuracy of ±0.5%. The results are employed to distinguish between conflicting data sets that already exist in the literature and that have inhibited accurate representations of the viscosity of this important fluid. It is shown that the experimental results can be represented with a high precision by means of procedures founded on the hard-sphere theory of liquids, although the observed density dependence of the viscosity is different from that characteristic of hydrocarbons.     

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%.     

Thermodynamic Properties of Air from 60 to 2000 K at Pressures up to 2000 MPa

A thermodynamic property formulation for standard dry air based upon experimental P––T, heat capacity, and speed of sound data and predicted values, which extends the range of prior formulations to higher pressures and temperatures, is presented. This formulation is valid for temperatures from the solidification temperature at the bubble point curve (59.75 K) to 2000 K at pressures up to 2000 MPa. In the absence of experimental air data above 873 K and 70 MPa, air properties were predicted from nitrogen data. These values were included in the fit to extend the range of the fundamental equation. Experimental shock tube measurements ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 28 GPa. In the range from the solidification point to 873 K at pressures to 70 MPa, the estimated uncertainty of density values calculated with the fundamental equation for the vapor is ±0.1%. The uncertainty in calculated liquid densities is ±0.2%. The estimated uncertainty of calculated heat capacities is ±1% and that for calculated speed of sound values is ±0.2%. At temperatures above 873 K and 70 MPa, the estimated uncertainty of calculated density values is ±0.5%, increasing to ±1% at 2000 K and 2000 MPa.