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.     

Determination of the plastic and viscoelastic properties of a metallic soap by a hot hardness measurement

An analysis of an indentation test in the case of mixed plastic—viscoelastic behaviour, as is met in metallic soaps, is described. The viscoelastic part of the strain is described in terms of a Burgers model whose five rheological parameters are then a yield stress, ₀, two elasticity moduli,G ₀ andG ₁, and two viscosities, ₀ and ₁. This analysis is applied to a hot hardness experiment on a compacted metallic soap, calcium stéarate, between 20 and 130° C. By fitting the model to the experimental curves, values of ₀, ₀, ₁,G ₀ andG ₁ as a function of temperature, have been derived. It is shown that plastic strain is much greater than viscous strain at low temperature, since ₀ is very high. The material is therefore a solid. It is also shown that, as temperature increases, viscous strain increases and plasticity vanishes (above a transition temperature, ₀=0, and only viscoelasticity remains). The curves ₀(T), ₁ (T),G ₀(T) andG ₁ (T) have marked slope changes at about 90° C (which is the crystal—crystal phase transition temperature of calcium stearate), and the viscosities fall at 123° C, which is the first crystal mesomorphic phase-transition temperature. This test seems to be a good simple rheological measurement for bodies exhibiting simultaneous plasticity and viscosity or viscoelasticity.     

The viscosity and some related properties of liquid3He at the melting curve between 1 and 100 mK

The viscosity of liquid ³ He has been measured along the melting curve from 1 to 100 mK by means of a vibrating wire viscometer. In the normal Fermiliquid region we find 1/T² = 1.17–3.10T, where is in P and T in K. At the transition temperature T _A = 2.6 mK a rapid decrease occurs in _n , the viscosity of the normal component. Within 0.3 mK below T _A , _n decreases to about 25% of _A, but then becomes essentially constant. In the B phase _n first decreases to 20% of _A and then seems to increase below 1.4 mK. Data on _n , the density of the normal component, are also presented in the A and B phases. The results show that viscous flow is accompanied by a flow of zero dissipation, thus proving superfluidity in the A and B phases. The viscosity data at magnetic fields up to 0.9T have been related to theoretical calculations of the energy gap of superfluid ³ He near T _A . The splitting of the A transition and the suppression of the B phase in an external field were also measured.     

Viscosity of binary mixtures. I. mono-, di-, and tri-n-butyl and -n-octylamine with cyclohexane

Viscosities for six binary mixtures of n-butylamine, di-n-butylamine, tri-n-butylamine, n-octylamine, di-n-octylamine, and tri-n-octylamine with cyclohexane have been measured at 303.15 K with an Ubbelohde suspendedlevel viscometer. Deviations of viscosities from a rectilinear dependence on mole fraction are attributed to H-bonding and to the size of alkylamine compounds. The application of the Eyring's theory of activation energy is examined. The free volume theory of Prigogine-Flory-Patterson (PFP) and the experimental excess enthalpy have been used to estimate excess viscosity ln = (ln / ₁ ⁰ – x ₂ ln ₂ ⁰ / ₁ ⁰ ) and corresponding free volume, enthalpy, and entropy contributions for five binary mixtures of tri-n-alkylamine: triethyl, tripropyl, tributyl, trihexyl, and trioctylamine with cyclohexane. A comparison of experimental and theoretical excess viscosities indicates a failure of the PFP theory when two components of the mixture differ considerably in size. The size difference contribution to excess viscosity is related to (V ₂ ^*1/2 – V ₁ ^*1/2 ), where V ₁ ^* and V ₂ ^* are hard-core volumes of two components of the mixture.     

Transport properties of nonelectrolyte liquid mixtures. VIII. Viscosity coefficients for toluene and for three mixtures of toluene + hexane from 25 to 100°C at pressures up to 500 MPa

Viscosity coefficients measured using a two-coil self-centering falling-body viscometer are reported for toluene and three binary mixtures of toluene + n-hexane at 25, 50, 75, and 100°C at pressures up to 500 MPa. The data for a given composition at different temperatures and pressures are correlated very satisfactorily by a plot of reduced viscosity ^* versus log V, where V=V·V ₀(T_R)/V₀(T) and V ₀ represents a characteristic volume. The binary mixture data are well represented by the Grunberg and Nissan equation with a mixing parameter which is pressure dependent but composition and temperature independent.     

Viscosity of refrigerants R12, R113, and R114 and mixtures of R12 + R114 at high pressure

New viscosity measurements for the gaseous and supercritical state of the halogenated hydrocarbons R12, R113, and R114 and binary mixtures of R12 + R114 of different compositions are presented. The measurements were carried out at superheated and supercritical temperatures from 30 to 200° C and in the pressure range from 1 to 80 bar. Viscosity was measured with an oscillating-disk viscometer and the data obtained are relative to the viscosity of nitrogen. The estimated accuracy of the measured results is ±0.6%. The results obtained show that, at subcritical temperatures, the pressure effect on viscosity is negative. This anomalous behaviour is investigated in detail in this work. At atmospheric pressure the viscosity of gas mixtures is almost a linear function of their composition. At high pressure, the residual viscosities - ₀ of both the pure components and the mixtures were used to follow a single relationship versus the residual reduced density _r0.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Viscosities of nonelectrolyte liquid mixtures. I. binary mixtures containing p-dioxane

Viscosity measurements are reported for p-dioxans with cyclohexane, n-hexane, benzene, toluene, carbon tetrachloride, tetrachloroethane, chloroform, pentachloroethane, and ethyl acetate at 303.15 K. Excess Gibbs energies of activation G ^*E of viscous flow have been calculated with Eyring's theory of absolute reaction rates. The deviations of the viscosities from a linear dependence on the mole fraction and values of G ^*E for binary mixtures have been explained in terms of molecular interactions between unlike pairs. The Prigogine-Flory-Patterson theory has been used to estimate the excess viscosity, ln , and corresponding enthalpy ln _H, entropy ln _S, and free volume ln _v terms for binary mixtures of p-dioxane with cyclohexane, n-hexane, benzene, toluene, carbon tetrachloride, and chloroform. Estimates of excess viscosities from this theory for p-dioxane with benzene, toluene, and carbon tetrachloride are good, while for the other three mixtures they are poor. The local-composition thermodynamic model of Wei and Rowley estimates the excess viscosity quite well even for p-dioxane mixtures with cyclohexane and n-hexane.     

Effect of heat transfer on the limiting characteristics of magnetofluid seals

A procedure is developed for calculating the maximum temperature in the working gap of a magnetofluid seal and the limiting rate of rotation of hermetically sealed shafts.Notation T_max maximum temperature of heating of the sealing fluid, °C - thickness of the sealing layer, m - v₀ linear velocity of rotation of the surface of the hermetically sealed shaft, m/sec - density, kg/m³ - viscosity, N·sec/m² - c specific heat capacity at constant pressure, J/(kg·deg) - coefficient of thermal conductivity, W/(m·deg) - transfer coefficient, W/(m³·deg) - q heat flux, W/m² Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 58–65, January, 1982.     

High-pressure viscosity and density of n-alkanes

High-pressure viscosities and densities of n-butane, n-pentane, n-hexane, and n-octane have been measured with a specially designed falling cylinder viscometer. Data cover the pressure range from 10 to 70 MPa at temperatures from 310 to 450 K. When the viscosity is plotted as a function of density, the data at all temperatures and pressures are shown to reduce to a single curve for each alkane. An exponential relationship of the form = B ₁ x exp(B ₂x) + B ₃ is used to describe the density dependence of viscosity. The logarithmic viscosity of the alkanes changes linearly with the inverse temperature at all pressures. The density shows a linear dependence on temperature.     

Temperature dependence of the dynamic viscosity of the working liquid of a continuous-medium hydro-integrator

Results are presented of an experimental determination of the dynamic viscosity of solutions of Vinipol in vaseline oil.Notation dynamic viscosity (N· sec/cm² - T thermodynamic temperature of liquids (° K) - A and B coefficients of empirical formula     

An analytical investigation of the longitudinal temperature profile developing during the cooling of a cryogenic pipeline

Analytical expressions are obtained for the longitudinal temperature profiles of the wall and the stream of cryogen during the cooling of a cryogenic pipeline. A comparison of the calculated data with experiment gives their good agreement.Notation T temperature, °K - density, kg/m³ - heat-transfer coefficient between wall and stream, W/m²·°K - perimeter wetted by stream, m - c heat capacity, J/kg·°K - F cross-sectional area, m² - G flow rate of cryogen, kg/sec - t time, sec - x longitudinal coordinate, m - coefficient of thermal conductivity of cryogen, W/m·°K - coefficient of dynamic viscosity, m²/sec - Pr Prandtl number - dimensionless time - dimensionless longitudinal coordinate - dimensionless longitudinal coordinate in the moving coordinate system - width of zone of heat exchange - dimensionless temperature - P pressure of cryogen, N/m² - R gas constant, J/kg·°K - dimensionality of temperature - v₁ dimensionless velocity of movement of steady temperature profile - ¯c_w integral-mean heat capacity of wall, J/kg·°K - a b, m, constant coefficients in the approximating equations. Indices: 0, initial value - w wall - g cryogen - r relative value Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 524–531, September, 1981.     

Diffusion of styrene-acrylonitrile copolymers

Tracer diffusion coefficient, D ^*, and the Newtonian zero shear-rate viscosity, ₀, were measured for a high molecular weight random copolymer (SAN) of styrene and acrylonitrile. As predicted by the reptation model, D ^*was in agreement with the molecular-weight scaling of M _w ^–2 (M _w is the weight average molecular weight of the chain being probed) and was independent of matrix molecular weight. ₀ showed a molecular-weight scaling of M _W ^3.4 . While the temperature dependence of these two relaxation processes could be well explained by the free-volume model up to 252 °C, they showed a discrepancy in activation enthalpy, E _a, of about 20%, with a larger value for diffusion.     

Effects of non-steady state nucleation in the kinetics of crystallization of the amorphous alloy Fe80B20

The existence of non-steady state nucleation in the isothermal crystallization of the amorphous alloy Fe₈₀B₂₀ is shown. The incubation time ₀ of isothermal volume crystallization of the alloy is investigated in a wide range as a function of temperature. From these data an equation for the temperature dependence of the viscosity = (T) is derived: = 6.62 exp (2526.97T) × exp [836.52/(T – 530)].[/p]     

Shear viscosity of liquid4He and3He-4He mixtures,especially near the superfluid transition

High-resolution measurements of are reported for liquid⁴He and³He-⁴He mixtures at saturated vapor pressures between 1.2 and 4.2 K with particular emphasis on the superfluid transition. Here is the mass density, the shear viscosity, and in the superfluid phase both and are the contributions from the normal component of the fluid ( _n and _n ). The experiments were performed with a torsional oscillator operating at 151 Hz. The mole fraction X of³He in the mixtures ranged from 0.03 to 0.65. New data for the total density and data for _n by various authors led to the calculation of . For⁴He, the results for are compared with published ones, both in the normal and superfluid phases, and also with predictions in the normal phase both over a broad range and close to T. The behavior of and of in mixtures if presented. The sloped/dT near T and its change at the superfluid transition are found to decrease with increasing³He concentration. Measurements at one temperature of versus pressure indicate a decreasing dependence of on molar volume asX(³He) increases. Comparison of at T, the minimum of _n in the superfluid phase and the temperature of this minimum is made with previous measurements. Thermal conductivity measurements in the mixtures, carried out simultaneously with those of , revealed no difference in the recorded superfluid transition, contrary to earlier work. In the appendices, we present data from new measurements of the total density for the same mixtures used in viscosity experiments. Furthermore, we discuss the data for _n determined for⁴He and for³He-⁴He mixtures, and which are used in the analysis of the data.     

Viscosity of aqueous solutions of 1,2-ethanediol and 1,2-propanediol under high pressures

New experimental data on the viscosity of aqueous solutions of 1,2-ethanediol (ethylene glycol) and 1,2-propanediol (propylene glycol) are presented at 298 and 323 K under pressures up to 120 MPa. The measurements were performed by a falling-cylinder viscometer on a relative basis with an uncertainty of less than ±2%. The viscosity of these aqueous solutions at a constant temperature and pressure increases monotonously with increasing concentrations of diols (glycols) and is slightly lower than the mole fraction average value at each composition. The viscosity also increases almost linearly with pressure at a constant temperature and composition. The pressure coefficient of the viscosity, (/P)_T,x, increases with decreasing temperature and increasing concentrations of diols. The experimental results are correlated with pressure, density, and composition by several empirical equations.     

Correlation of high-pressure thermal conductivity,viscosity, and diffusion coefficients for n-alkanes

Thermal conductivity, viscosity, and self-diffusion coefficient data for liquid n-alkanes are satisfactorily correlated simultaneously by a method based on the hard-sphere theory of transport properties. Universal curves are developed for the reduced transport properties ^*, ^*, and D ^* as a function of the reduced volume. A consistent set of equations is derived for the characteristic volume and for the parameters R , R , and R _D, introduced to account for the nonsphericity and roughness of the molecules. The temperature range of the above scheme extends from 110 to 370 K, and the pressure range up to 650 MPa.     

Density and Viscosity of the 1-Methylnaphthalene+2,2,4,4,6,8,8-Heptamethylnonane System from 293.15 to 353.15 K at Pressures up to 100 MPa

The dynamic viscosity of the binary mixture 1-methylnaphthalene+2,2,4,4,6,8,8-heptamethylnonane was measured in the temperature range 293.15 to 353.15K (in progressive 10K steps) at pressures of 0.1, 20, 40, 60, 80, and 100MPa. The composition of the system is described by nine molar fractions (0 to 1 in 0.125 progressive steps). The density was measured at pressures from 0.1 to 60MPa in progressive 5 MPa steps. The measurements of are used to determine the excess viscosity ^E and the excess activation energy of flow G ^E as a function of pressure, temperature, and composition. Some models have been used to represent the viscosity of this binary mixture.     

Transport properties of nonelectrolyte liquid mixtures—IV. Viscosity coefficients for benzene,perdeuterobenzene, hexafluorobenzene,and an equimolar mixture of benzene + hexafluorobenzene from 25 to 100°c at pressures up to the freezing pressure

Viscosity coefficient measurements made with an estimated accuracy of ±2% using a self-centering falling body viscometer are reported for benzene, perdeuterobenzene, hexafluorobenzene and an equimolar mixture of benzene + hexafluorobenzene at 25, 50, 75 and 100°C at pressures up to the freezing pressure. The data for each liquid at different temperatures and pressures are correlated very satisfactorily by a graphical method based on plots of 9.118×10⁷ V ^2/3/(MRT)^1/2 versus logV, and are reproduced to within the experimental uncertainty by a free-volume form of equation. Application of the empirical Grunberg and Nissan equation to the mixture viscosity coefficient data shows that the characteristic constant G is practically temperature- and pressure-independent for this system.     

Prediction of friction and heat transfer for viscoelastic fluids in turbulent pipe flow

Experimental measurements of the friction factor and the dimensionless heat-transfer j-factor were carried out for the turbulent pipe flow of viscoelastic aqueous solutions of polyacrylamide. The studies covered a wide range of variables including polymer concentration, polymer and solvent chemistry, pipe diameter, and flow rate. Degradation effects were also studied. It is concluded that the friction factor and the dimensionless heat transfer are functions only of the Reynolds number, the Weissenberg number, and the dimensionless distance, provided that the rheology of the flowing fluid is used.Nomenclature cp Specific heat of fluid, J · kg^–1 · K^–1 - d Diameter of tube, m - f Fanning friction factor, _w/(V²/2) - h Convective heat-transfer coefficient, q _w(T _w{T _b), W · m^–2 · K^–1 - k Thermal conductivity of fluid, W · m^–1 · K^–1 - j _H Heat-transfer j-factor, StPr _a ^2/3 - L _e Entrance length, m - Nu Nusselt number, hd/k - Pr _a Prandtl number based on apparent viscosity at the wall, c _p/k - q _w Heat flux at the wall, W · m^–2 - Re _a Reynolds number based on apparent viscosity at the wall, Vd/ - St Stanton number, Nu/(Re _a Pr _a) - T Temperature, K - T _b Bulk temperature of fluid, K - T _w Inside-wall temperature, K - V Average velocity, m · s^–1 - Ws Weissenberg number, V/d - x Axial coordinate, m Greek symbols g Shear rate, s^–1 - Apparent viscosity evaluated at the wall, P⁵ - ₀ Zero shear-rate viscosity, P⁵ - Apparent viscosity at infinite shear rate, P⁵ - Characteristic time of fluid, s - Density of fluid, kg · m^–3 - _w Wall shear stress, N · m^–2 Invited paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Creep and glass transition behaviour of fractionated petroleum pitches: the influence of molecular weight and its distribution

The dependence of viscoelastic properties on the molecular weight of fractionated and and blended petroleum pitches was examined in relation to the creep and glass transition behaviour. The steady-state viscosity,, as a measure of energy dissipation, and the steady-state creep compliance,J _e ⁰ , as a measure of elastic stored energy, were empirically related to the glass transition point,T _g. The values of showed a steep dependence on the number average molecular weight,¯M _n (f ¯M _n ⁴² ). It was proved that the molecular weight dependence of andJ _e ⁰ manifest through the dependence ofT _g on¯M _n (T _gf 1/¯M _n). Discussion of the blending laws to elucidate the effect of molecular weight distribution has revealed that In,J _e ⁰ , andT _g are expressed additively by using the mole fraction of each pitch component with different molecular weights.