A New Apparatus for Combined Measurements of the Viscosity and Density of Fluids for Temperatures from 233 To 523 K at Pressures up to 30 Mpa

A new apparatus for measuring the viscosity and density of fluids is presented. The main element of the instrument is an electronically controlled magnetic suspension coupling. For the density measurement (buoyancy principle according to the single-sinker method), this coupling is used for the contactless transfer of the forces acting on a sinker in the measuring cell to an analytical balance. The coupling also serves as a frictionless bearing for a slender rotating cylindrical body which is slowed down due to the viscous drag of the fluid surrounding the cylinder. The viscosity of the fluid can be directly determined from the decay rate of the rotational frequency. The new combined viscometer-densimeter covers a viscosity range of 5 to 150 Pa·s and a density range from 20 to 2000 kg·m^–3 at temperatures from 233 to 523 K and pressures up to 30 MPa. Test measurements on the viscosities and densities of nitrogen and carbon dioxide at 253, 293, and 523 K at pressures up to 30 MPa show an estimated total uncertainty of ±0.6 to ±1.0% in viscosity and of ±0.02 to ±0.05% in density.     

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.     

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%.     

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.     

Thermophysical Property Measurements of Supercooled and Liquid Rhodium

The density, the isobaric heat capacity, the surface tension, and the viscosity of liquid rhodium were measured over wide temperature ranges, including the supercooled phase, using an electrostatic levitation furnace. Over the 1820 to 2250 K temperature span, the density can be expressed as (T)=10.82×10³–0.76(T–T _m ) (kgm^–3) with T _m =2236 K, yielding a volume expansion coefficient (T)=7.0×10^–5 (K^–1). The isobaric heat capacity can be estimated as C _P (T)=32.2+1.4×10^–3(T–T _m ) (Jmol^–1K^–1) if the hemispherical total emissivity of the liquid remains constant at 0.18 over the 1820 to 2250 K interval. The enthalpy and entropy of fusion have also been measured, respectively, as 23.0 kJmol^–1 and 10.3 Jmol^–1K^–1. In addition, the surface tension can be expressed as (T)=1.94×10³–0.30(T–T _m ) (mNm^–1) and the viscosity as (T)=0.09 exp[6.4×10⁴(RT)] (mPas) over the 1860 to 2380 K temperature range.     

Compressed Liquid and Supercritical Densities of 1,1,1,2,3,3,3-Heptafluoropropane (R227ea)

Densities of 1,1,1,2,3,3,3-heptafluoropropane (R227ea) have been measured with a computer-controlled high-temperature high-pressure vibrating-tube densimeter system (DMA-HDT) in the sub- and supercritical states. The densities were measured at temperatures from 278 to 473 K and pressures up to 30 MPa (overall 257 data points), whereby a density range between 285 and 1588 kgm^–3 was covered. The uncertainty in the density measurement was estimated to be better than ±0.2 kgm^–3. The experimental data of R227ea were correlated with a virial-type equation of state (EoS) and compared with published data. A comparison is also made with a recent wide-range dedicated equation of state for R227ea.     

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.     

The Viscosity of Seven Gases Measured with a Greenspan Viscometer

The viscosity of seven gases (Ar, CH₄, C₃H₈, N₂, SF₆, CF₄, C₂F₆) was determined by interpreting frequency-response data from a Greenspan acoustic viscometer with a detailed model developed by Gillis, Mehl, and Moldover. The model contains a parameter _r that characterizes the viscous dissipation at the ends of the viscometer's duct. It was difficult to determine _r accurately from dimensional measurements; therefore, _r was adjusted to fit the viscosity of helium on the 298 K isotherm (0.6 MPa<p<3.4 MPa). This calibration was tested by additional viscosity measurements using four, well-studied, polyatomic gases (CH₄, C₂H₆, N₂, and SF₆) near 300 K and by measurements using argon in the range 293 K<T<373 K. For these gases, all of the present results agree with reference values to within ±0.5% (±0.4% in the limit of zero density). The viscosities of CF₄ and C₂F₆ were measured between 210 and 375 K and up to 3.3 MPa with average uncertainties of 0.42 and 0.55%, respectively. At the highest density studied for CF₄ (2746 molm^–3), the uncertainty increased to 1.9%; of this 1.9%, 0.63% resulted from the uncertainty of the thermal conductivity of CF₄, which other researchers estimated to be 2% of its value at zero density. As an unexpected bonus, the present Greenspan viscometer yielded values of the speed of sound that agree, within ±0.04%, with reference values.     

Numerical study of flow in a constricted curved annulus: An application to flow in a catheterised artery

The flow of an incompressible Newtonian fluid in a curved annulus with a local constriction at the outer wall is investigated numerically. The three-dimensional nonlinear elliptic partial differential equations governing the flow are simplified by use of small curvature and mild constriction approximations. The simplified equations of motion, which are locally two-dimensional elliptic in nature at each cross-section, are solved numerically by means of the finite-difference method described by Collins and Dennis [Quart. Jour. Mech. Appl. Math. 28 (1975) 133–156]. Although the results are restricted to small curvature and mild constriction, these are valid for all Dean numbers D in the entire laminar flow regime. The numerical results show that, for higher values of radii ratio k, the pressure gradient, pressure drop, and frictional resistance increase considerably and they vary markedly across the constricted length. These results are used to estimate the increase in frictional resistance in an artery when a catheter is inserted into it. In the absence of constriction (₁=0) and depending on the value of k ranging from 01 to 07, the frictional resistance increases by a factor ranging from 132 to 2391 for D=500 and 120 to 1656 for D=2000. But, in the presence of constriction (₁ = 01) with the same range for k, the increase in frictional resistance is by a factor ranging from 134 to 4232 for D=500 and 118 to 295 for D=2000. In a straight annulus, the increased factor ranges from 174 to 3261 for ₁=0 and 178 to 5827 for ₁ = 01 (for all Dean numbers D).     

Deviation from Wiedemann–Franz Law for the Thermal Conductivity of Liquid Tin and Lead at Elevated Temperature

The thermal conductivities of tin and lead in solid and liquid states have been determined using a nonstationary hot wire method. Measurements on tin and lead were carried out over temperature ranges of 293 to 1473 K and 293 to 1373 K, respectively. The thermal conductivity of solid tin is 63.9±1.3 Wm^–1K^–1 at 293 K and decreases with an increase in temperature, with a value of 56.6±0.9 Wm^–1K^–1 at 473 K. For solid lead, the thermal conductivity is 36.1±0.6 Wm^–1K^–1 at 293 K, decreases with an increase in temperature, and has a value of 29.1±1.1 Wm^–1K^–1 at 573 K. The temperature dependences for solid tin and lead are in good agreement with those estimated from the Wiedemann–Franz law using electrical conductivity values. The thermal conductivities of liquid tin displayed a value of 25.7±1.0 Wm^–1K^–1 at 573 K, and then increased, showing a maximum value of about 30.1 Wm^–1K^–1 at 673 K. Subsequently, the thermal conductivities gradually decreased with increasing temperature and the thermal conductivity was 10.1±1.0 Wm^–1K^–1 at 1473 K. In the case of liquid lead, the same tendency, as was the case of tin, was observed. The thermal conductivities of liquid lead displayed a value of 15.4±1.2 Wm^–1K^–1 at 673 K, with a maximum value of about 15.6 Wm^–1K^–1 at 773 K and a minimum value of about 11.4±0.6 Wm^–1K^–1 at 1373 K. The temperature dependence of thermal conductivity values in both liquids is discussed from the viewpoint of the Wiedemann–Franz law. The thermal conductivities for Group 14 elements at each temperature were compared.     

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%.     

Density Determination of Liquid Copper, Nickel, and Their Alloys

A method for the determination of the density of electromagnetically levitated metallic liquids has been developed. This method employs an enlarged beam of parallel laser light to produce a shadow image of the sample. The shadow is recorded by a digital CCD-camera, and the images are analyzed using an edge detection algorithm. The circumference is fitted by Legendre polynomials that can be used for calculations of the volume of the sample. The method has been tested successfully on various alloys of copper-nickel (Ni _x Cu _y ), as well as on the pure elements, Cu and Ni. Densities were measured for each sample at different temperatures below and above the melting point, and a linear behavior was observed. At the melting point the densities for copper and nickel were 7.9 and 7.93gcm^–3, respectively. For T=1270°C liquid copper has a density of 7.75gcm^–3 which strongly increases up to roughly 8.1gcm^–3 if a small amount (10–40 at.%) of nickel is added to the system. For nickel concentrations larger than 50at.% the density remains nearly constant.     

Surface Tension of 1,1,1-Trifluoroethane (HFC-143a), 1,1,1,2,3,3,3-Heptafluoropropane (HFC-227ea), and Their Binary Mixture HFC-143a/227ea

The surface tension of 1,1,1-trifluoroethane (HFC-143a), 1,1,1,2,3,3,3-hepta-fluoropropane (HFC-227ea), and their binary mixture HFC-143a/227ea at 3 nominal mass fractions of 27.91%/72.09%, 49.44%/50.56%, and 74.11%/25.89% were measured in the temperature range from 253 to 333K using the differential capillary rise method (DCRM) under vapor-liquid equilibrium conditions. The temperature and surface tension uncertainties were estimated to be within ±10 mK and ±0.15 mNm^–1, respectively. The present data were used to develop a van der Waals-type surface tension correlation for pure HFC-143a and HFC-227ea. Correlations for pure HFC-143a and HFC-227ea were used to develop a surface tension correlation for the experimental data of the HFC-143a/227ea mixtures as a function of the mass fraction.     

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.     

Non-Contact Measurements of the Thermophysical Properties of Hafnium-3 Mass% Zirconium at High Temperature

Several thermophysical properties of hafnium-3 mass % zirconium, namely the density, the thermal expansion coefficient, the constant pressure heat capacity, the hemispherical total emissivity, the surface tension and the viscosity are reported. These properties were measured over wide temperature ranges, including overheated and undercooled states, using an electrostatic levitation furnace developed by the National Space Development Agency of Japan. Over the 2220 to 2875 K temperature span, the density of the liquid can be expressed as _L (T)=1.20×10⁴–0.44(T–T _m ) (kgm^–3) with T _m =2504 K, yielding a volume expansion coefficient _L (T)=3.7×10^–5 (K^–1). Similarly, over the 1950 to 2500 K span, the density of the high temperature and undercooled solid -phase can be fitted as _S (T)=1.22×10⁴–0.41(T–T _m ), giving a volume expansion coefficient _S (T)=3.4×10^–5. The constant pressure heat capacity of the liquid phase can be estimated as C _PL (T)=33.47+7.92×10^–4(T–T _m ) (Jmol^–1K^–1) if the hemispherical total emissivity of the liquid phase remains constant at 0.25 over the 2250 K to 2650 K temperature interval. Over the 1850 to 2500 K temperature span, the hemispherical total emissivity of the solid -phase can be represented as _TS (T)=0.32+4.79×10^–5(T–T _m ). The latent heat of fusion has also been measured as 15.1 kJmol^–1. In addition, the surface tension can be expressed as (T)=1.614×10³–0.100(T–T _m ) (mNm^–1) and the viscosity as h(T)=0.495 exp [48.65×10³/(RT)] (mPas) over the 2220 to 2675 K temperature range.     

Viscosity and density of binary mixtures of cyclohexane with n-octane,n-dodecane,and n-hexadecane under high pressures

The viscosity and density of three binary mixtures of cyclohexane with n-octane, n-dodecane, and n-hexadecane have been measured at 298, 323, and 348 K at pressures up to 150 MPa or freezing pressures. The measurements of the viscosity were performed by a torsionally vibrating crystal viscometer on a relative basis using benzene and cyclohexane as reference materials. The density was measured using a high-pressure burette apparatus. The uncertainties of the measurements are estimated to be less than 2% for viscosity and 0.1% for density, respectively. The effects of temperature, pressure, density, and composition on the viscosity are discussed. Applicabilities of several empirical correlating equations to the viscosity data were examined.     

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.     

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.     

Thermophysical Properties of 1,1,1,3,3-Pentafluorobutane (R365mfc)

This paper presents an experimental study on various thermophysical properties of a new fluoroalkane, 1,1,1,3,3-pentafluorobutane (R365mfc). The thermal conductivity of R365mfc was measured in the liquid phase near saturation conditions at temperatures between 263 and 333 K using a parallel plate instrument with an uncertainty of less than ±5%. For the measurement of the saturated liquid density between 273 and 353 K, a vibrating tube instrument was used. The uncertainty of the density measurements is less than ±0.1%. In addition, experimental data have been obtained for R365mfc under saturation conditions over a wide temperature range from about 253 to 460 K using light scattering techniques. Light scattering from the bulk fluid has been applied for measuring both the thermal diffusivity and the sound speed in the liquid and vapor phases. Light scattering by surface waves on a horizontal liquid–vapor interface has been used for the simultaneous determination of the surface tension and kinematic viscosity of the liquid phase. With the light scattering techniques, uncertainties of less than ±1.0, ±0.5, ±1.0, and ±1.2% have been achieved for the thermal diffusivity, the sound speed, the kinematic viscosity, and the surface tension, respectively.     

Enthalpy and Temperature of the Titanium Alpha-Beta Phase Transformation

The specific enthalpy and the temperature of the titanium - phase transformation were measured by a pulse-heating system operating in the millisecond time regime. The measurement technique is based on self-heating of a tube-shaped specimen from room temperature to the beta phase of titanium. A comparison between the measured phase transition temperature during heating and cooling of the specimen shows a difference of approximately 20 K. The temperature measured during the heating period is higher than the value obtained from the cooling cycle of the specimen. For the evaluation of the specific enthalpy of the alpha-beta transformation, the specific enthalpy versus temperature function of the beta phase of the heating period was extrapolated to the transition temperature obtained from the cooling cycle (1152 K). A total of 12 measurements on 3 tube-shaped specimens was made, an average value of 89.9 kJkg^–1 was obtained for the specific enthalpy of the transformation. The reproducibility of the measured specific enthalpy at the beginning and at the end of the transformation was 0.5%. The reproducibility of the phase transformation enthalpy as difference between the beginning and the end was 3%. The extended measurement uncertainty (at a confidence level of 95%) is estimated to be ±6% for the specific enthalpy of the transformation and ±6 K for the transformation temperature.