Prediction of transport properties of dense gases and liquids by the Peng-Robinson (PR) equation of state

An attempt is made in this work to combine the Enskog theory of transport properties with the simple cubic Peng-Robinson (PR) equation of state. The PR equation of state provides the density dependence of the equilibrium radial distribution function. A slight empirical modification of the Enskog equation is proposed to improve the accuracy of correlation of thermal conductivity and viscosity coefficient for dense gases and liquids. Extensive comparisons with experimental data of pure fluids are made for a wide range of fluid states with temperatures from 90 to 500 K and pressures from 1 to 740 atm. The total average absolute deviations are 2.67% and 2.02% for viscosity and thermal conductivity predictions, respectively. The proposed procedure for predicting viscosity and thermal conductivity is simple and straightforward. It requires only critical parameters and acentric factors for the fluids.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Transport in fluid helium-3 under pressure

The thermal conductivity of liquid helium-3 has been measured at temperatures between 1.3° K and 4.2° K and at pressures up to 55 atm. The viscosity data for liquid helium-3, reported briefly in Ref. 1 are here presented in full for temperatures 1.20° K, 2.00° K, and 3.02° K and at pressures up to 20 atm. Thermal conductivity and viscosity data at 2.00° K are combined with estimated values ofC _vto giveMK/ C _v(whereM is molecular weight,K is thermal conductivity, is viscosity andC _vis the molar specific heat), a dimensionless parameter that is 5/2 in gases at limiting low pressures. Finally, the thermal conductivity of gaseous helium-3 at 1-cm Hg pressure has been measured between 1.3° K and 4° K and compared with available theoretical estimates.     

Dual Critical Points and Related Phenomena in Simple Fluids from the Perspective of (Approximate) Renormalization Theory

It is known that some single component fluids can have coexisting low-density and high-density liquid phases with two, separate, gas–liquid and liquid–liquid, critical points. Such behavior is found both by experiments and in recent molecular-dynamics simulations performed for certain simple isotropic attractive pair potentials with softened repulsive cores. In the present investigation, a global renormalization group theory that was employed previously to make predictions for simple Lennard–Jones and square-well fluids over wide ranges of density and temperature, including the critical point, in reasonably good agreement with molecular dynamics and Monte Carlo simulations, is applied to simple shoulder potentials and to square-well potentials with softened repulsive cores. Results using this renormalization approach are compared with some previously reported results for a shoulder potential and expectations regarding dual critical points for water.     

Thermal conductivity of carbon tetrachloride in the temperature range 310 to 364 K at pressures up to 0.22 GPa

The paper reports new measurements of the thermal conductivity of carbon tetrachloride in the temperature range 310 to 364 K at pressures up to 0.22 GPa. The experimental data have an estimated uncertainty to ±0.3%. The hard-sphere theory of transport in dense fluids is employed to formulate a correlation scheme for the thermal conductivity as a function of density. A single equation represents the dependence of the thermal conductivity on density for all isotherms, the isotherms being distinguished by a characteristic value of the molar volume. It is shown that earlier measurements of the viscosity and self-diffusion coefficient of carbon tetrachloride may be represented in a similar fashion using consistent values of the characteristic volume.     

Transport properties of helium near the liquid-vapor critical point. IV. The shear viscosity of3He and4He

Shear viscosity measurements with a precision of 0.05% are reported for³He and⁴He along near-critical isochores 0.85 c <1.12, where _c is the critical density. The temperature range was –10^–4<<1, where =(T – T _c)/T _c is the reduced temperature. The experiments were carried out with a torsional oscillator operating at 158 Hz, driven at resonance in a phase-locked loop. The absolute value of the viscosity was obtained by calibration at the superfluid transition of⁴He, based on published values and from direct calculations using the free decay time constant of the oscillations. The data are analyzed in terms of a model using the recent mode-coupling (MC) expressions by Olchowy and Sengers, and where account is taken of the earth's gravity effects. The theory could be fitted very well to the experiment with a single free parameter, the cutoff wave numberq _D, which was found to be 3.0×10⁶ and 7.0×10⁶ cm^–1 for³He and⁴He, respectively. We have used for the critical exponent the MC predicted value of z=0.054, which permits a fit superior to that using z=0.064 predicted by dynamic renormalization group (DRG) theories. Detailed comparisons are made between the model calculations and data for various isochores and isotherms and good agreement is obtained. The effects of gravity are described in some detail. The predicted frequency effect in viscosity measurements is calculated for³He and is shown to be obscured by gravity effects. Using the Olchowy-Sengers formulas, we have also fitted the MC theory to the critical thermal conductivity data of³He, again withq _D as the only free parameter. This fit gaveq _D=6 × 10⁷ cm^–1, which in the ideal situation should have been the same asq _D from viscosity. We also discuss a representation of the³He viscosity data along the critical isochore by a power law and first correction-to-scaling erm. Using the viscosity and the critical conductivity data for³He, we have calculated the dynamic amplitude ratio and obtained =1.05±0.10, in agreement with predictions from MC and DRG theories. Also, agrees with data of classical fluids. Finally, a comparison is made of recent shear viscosity data for CO₂ by Bruschi and Torzo with those on He. The CO₂ data are also analyzed in terms of the MC theory, and the discrepancies are discussed. In the Appendices, we present the results of new compressibility measurements on³He along the critical isochore, as used in the MC analysis. We also present a brief analysis of the fluid hydrodynamics in the torsional oscillator leading to relations for the viscosity as a function of the measured quantities. Finally, we give a short outline of the vertical density profile calculations from the earth's gravity field for the calculations of the viscosity nearT _c.     

Correlation and prediction of dense fluid transport coefficients. I. n-alkanes

Recent accurate measurements of the self-diffusion coefficient for n-hexadecane and n-octane and of the viscosity coefficient for n-heptane, n-nonane, and n-undecane over wide pressure ranges have been used to provide a critical test of a previously described method, based on consideration of hard-sphere theory, for the correlation of transport coefficient data. It is found that changes are required to the universal curve for the reduced viscosity coefficient as a function of reduced volume and, also, to the parameters R _D, R , and R which were introduced to account for effects of nonspherical molecular shape. The scheme now accounts most satisfactorily for the self-diffusion, viscosity, and thermal conductivity coefficient data for all n-alkanes from methane to hexadecane at densities greater than the critical density.     

Transport properties of (La,Pr)Sn3 alloys at low temperatures

We report on measurements concerning the transport properties of polycrystalline (La_1–x Pr _x )Sn₃samples with impurity concentrations 0.07 x 0.2 in the temperature range 0.3 T 12 K. The experimental results of the electrical resistivity, the thermopower, and the thermal conductivity show pronounced anomalies which are referred to crystal-field effects and a Kondo effect of excited levels. A quantitative comparison with existing theories confirms the importance of the aspherical Coulomb scattering in addition to the isotropic spin-exchange scattering of the conduction electrons by the magnetic ions. Taking into account the Kondo effect in a phenomenological ansatz, we are able to fit the magnetic part of the resistivity. Furthermore, we present the first experimental proof of the theoretically predicted influence of crystal-field split impurities on the thermal conductivity in dilute magnetic alloys. The thermopower is qualitatively discussed by a model including both the effect from inelastic scattering on the crystal-field levels and the Kondo effect. Finally the temperature dependence of the Lorenz number is compared with a calculation in the framework of crystal-field theory.Work supported by the Deutsche Forschungsgemeinschaft.     

Relations Between Transport Coefficients in Lennard–Jones Fluids and in Liquid Metals

Several simple approximate hard-sphere relations for transport coefficients are compared with the results of molecular dynamics (MD) simulations performed on Lennard–Jones (LJ) fluids. Typically the individual transport coefficients: self-diffusion coefficients, D, shear viscosity, _s, bulk viscosity, _B, and thermal conductivity, , agree within a factor of two of the exact results over the fluid and liquid parts of the phase diagram, which seems reasonable in view of the approximations involved in the models. We have also considered the ratio, /_s, and the product, D_s, for which simple analytic expressions exist in the hardsphere models. These two quantities also agree within a factor of two of the simulation values and hard sphere analytic expressions. Using time correlation functions, Tankeshwar has recently related the ratio /D to thermodynamic quantities, in particular, to the differences in specific heats, C _p – C _V, and to the isothermal compressibility, T. Using D and thermodynamic values taken solely from LJ MD simulations, his relation was tested and found to give typically better than ~20% agreement at liquid densities, deteriorating somewhat as density decreases into the gas phase. Finally liquid metals are considered. In this case, is dominated by its electronic contribution, which is related approximately to the electrical conductivity by the Wiedemann–Franz Law. Some theoretical results for the electrical conductivity of Na are referenced, which allow a semiquantitative understanding of the measured thermal conductivity of the liquid metal. Shear viscosity is also discussed and, following the work of Tosi, is found to be dominated by ionic contributions; Nevertheless, at the melting temperature of Na, a relation emerges between thermal conductivity, electrical resistivity and shear viscosity.     

Corresponding states correlation for the thermal conductivity of molten alkali halides

The principle of corresponding states has been applied to the thermal-conductivity data for molten alkali halides which have been obtained by recent forced Rayleigh scattering measurements. The theory, which was developed by Harada et al. for the transport properties of uni-univalent molten salts, is based on the fluctuation-dissipation theorem with the pair interaction between ions composed of core repulsive and Coulombic potentials. Four characteristic parameters specific to each salt have been used to reduce the thermal conductivity and temperature. It has been found that the thermal conductivity of molten alkali halides is adequately correlated by the corresponding-states correlation ( ^* 1/T ^*) within experimental accuracy. By employing the correlation, the thermal conductivity of molten alkali fluorides, which could not be measured by the forced Rayleigh scattering method, is predicted.Paper dedicated to Professor Joseph Kestin.     

Thermal conductivity of difluoromonochloromethane in the critical region

The thermal conductivity of difluoromonochloromethane (refrigerant R22) has been measured along six near-critical isotherms at reduced temperatures varying from =1.005 to =1.112 and at pressures ranging from 2.0 to 9.5 MPa. An anomalous enhancement of the thermal conductivity has been observed in the critical region. This anomalous behavior is consistent with theoretical predictions and equations for the thermal conductivity as a function of density and temperature are presented.     

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.     

Knudsen molecular flow in a channel with a small temperature difference at its ends

The thermomolecular pressure difference (TPD) of helium, argon, and krypton is measured in a packet of glass capillaries for temperatures 273 and 293 K at their ends in a 10–100 range of Knudsen numbers.Notation exponent of the thermomolecular pressure difference effect - Kn Knudsen number - rarefaction parameter - Q_T reduced thermal creep flux - Q_P reduced Poiseuille flux - C(_t) Cercignani-Lampis scattering kernel - R specular scattering kernel - (1 – ) fraction of specular reflection - _t accommodation coefficient of the tangential momentum - P_c, P_h gas pressure in the cold and hot volumes, respectively - coefficient of dynamic viscosity - m mass of gas molecules - k Boltzmann constant - D, L the capillary diameter and length, respectively Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 719–724, May, 1988.     

Evaluation of the infrared absorption in nm-thick heavily boron-doped Si1-xGex layers on silicon

Infrared absorption due to free carriers was measured in the spectral range of 1.5–25 m at 77 and 300 K on a large variety of heavily p-doped, p⁺⁺=(2-7)×10²⁰cm^-3 strained Si_1-xGe_x quantum wells on Si grown by molecular beam epitaxy (MBE). The validity of the commonly applied theoretical approaches to describe the spectra has been thoroughly analyzed. The well-known dependence yielded by the Drude theory is not observed. Moreover, it is shown that the Boltzmann kinetic equation is invalid under our experimental conditions. The necessity of a new theory, where the interaction energy of carriers with scattering centers would be included into the energy spectrum of the system, is shown.     

Low temperature thermal conductivity of twinned and untwinned indium-thallium alloys

The low-temperature lattice thermal conductivity of twinned and untwinned, martensitic and non-martensitic, indium-thallium alloys has been measured to probe the effect of twin boundaries on phonon thermal transport. The phonon scattering by electrons, sample surfaces, dislocations, and thallium impurities is accounted for adequately by existing theoretical models. The reduced lattice thermal conductivity seen in twinned samples is attributed to additional phonon scattering by twin boundaries and, for the polycrystalline samples, by grain boundaries. Phonon scattering by twin boundaries is much weaker than that generally reported for grain boundaries, and is well represented by an acoustic-mismatch model.     

c-Axis Transport in a Normal-State Bilayer Cuprate and Relation to Pseudogap

We study the effect of interband transitions on the normal-state optical conductivity, dc resistivity, and thermal conductivity along the c-axis, for a plane-chain bilayer cuprate coupled by a perpendicular hopping matrix element (t). When t is small, the c-axis dc resistivity shows a characteristic upturn as the temperature is lowered, and the c-axis optical conductivity develops a pseudogap at low frequencies. As t is increased, intraband transitions start to dominate and a more conventional response is obtained. Similar pseudogap behavior is predicted in the thermal conductivity for which strong depression at low temperature is found. Analytical results for a simple plane-plane bilayer are also given, including the frequency sum rule of the optical conductivity.     

Volt-ampere characteristics of an ac arc in a transverse gas flow

An analytical dependence of the volt-ampere characteristic of an arc on the velocity of the incoming transverse gas flow is obtained. The stability threshold of arc combustion is determined.Notation h enthalpy - density - t time - v velocity - , thermal conductivity and electrical conductivity - E electric field strength - U potential at the arc - Q radiant flux - T period of oscillation of the current - r radius - l length of electric arc - d, L diameter and length of electrode - temperature - kinematic viscosity - Pr Prandtl number - current function Indices 0 gas parameters far from arc - 1 parameters at arc boundary - x projection on the axis 0x - y projection on the axis 0y - E effective value - e characteristic value Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 133–138, July, 1984.     

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.     

Local heating effect in point-contact spectroscopy for magnetic metals of Ni and α-Mn

The current-voltage characteristics at a homojunction point-contact of ferromagnetic Ni single crystal and antiferromagnetic -phase Mn polycrystalline metal have been measured at 4.2 K. Several singularities in the first and second derivative of I–V curves are observed at specific bias voltages for both metals. Taking into account the observed temperature dependence of the bulk electrical resistivity and thermal conductivity (and thus mean free path of electrons), we have performed computer simulations of these nonlinear I–V characteristics based on a modified local heating model and compared with the results by a traditional spherical spreading-out (SSO) model. When a constant additive correction to the bulk resistivity near a contact interface is incorporated, our calculated curves are in good agreement with the experimental results.     

Thermal conductivity of liquid n-alkanes

The thermal conductivity of liquids has been shown in the past to be difficult to predict with a reasonable accuracy, due to the lack of accurate experimental data and reliable prediction schemes. However, data of a high accuracy, and covering wide density ranges, obtained recently in laboratories in Boulder, Lisbon, and London with the transient hot-wire technique, can be used to revise an existing correlation scheme and to develop a new universal predictive technique for the thermal conductivity of liquid normal alkanes. The proposed correlation scheme is constructed on a theoretically based treatment of the van der Waals model of a liquid, which permits the prediction of the density dependence and the thermal conductivity of liquid n-alkanes, methane to tridecane, for temperatures between 110 and 370 K and pressures up to 0.6 MPa, i.e., for 0.3T/T _c0.7 and 2.4P/P _c3.7, with an accuracy of ±1%, given a known value of the thermal conductivity of the fluid at the desired temperature. A generalization of the hard-core volumes obtained, as a function of the number of carbon atoms, showed that it was possible to predict the thermal conductivity of pentane to tetradecane±2%, without the necessity of available experimental measurements.     

Two singular points finite elements in the analysis of kinked cracks

A formulation for incorporating two singular points (TSP) of variable orders in a single finite element is presented. Though the element does not satisfy any of the convergence criterion, its performance is found to be good, which has been demonstrated by considering number of examples on kinked cracks. In each case only one such element is incorporated in the whole discretization. These examples illustrate the usefulness of the element to analyse kinked cracks of various sizes and shapes and subjected to different loading and boundary conditions. Computed J-integrals are compared with analytical solutions, wherever possible, and the accuracy appears quite good. Effect of size of the element on, and the path independence of, J are also examined.List of symbols , conventional natural coordinate system - ₁, ₂ another elemental natural coordinate system - L _ij equation of side ij of an element - A _ij , B _ij constants - N _i shape function associated node i - ₁, ₂ constants associated with the order of singularities - , an elemental natural coordinate system - u _i , v _i displacement components in the Cartesian directions