The viscosity of simple dense fluids ; a memory-function approach

A gaussian memory function is used to compute the viscosity of dense fluid argon over a large region of states from the Lennard-Jones potential and the radial distribution function. The superposition approximation is used to evaluate the triplet correlation function and estimates of the errors introduced by this approximation are investigated. The agreement with experimental viscosities is quite satisfactory in the liquid region, but less so at lower densities and higher temperatures. The computed stress autocorrelation function exhibits those characteristics which are known from molecular dynamics studies. The stress autocorrelation remains monotonic even close to the triple point, where the same memory function leads to the well-known backscattering behaviour in the velocity autocorrelation function. This, too, is in agreement with the results of molecular dynamics.     

Kinetic theory of dense fluids. III. Density dependence of transport coefficients for dense gases

The viscosity coefficient obtained in a previous paper of this series is calculated as a function of density by developing the N-particle collision operator into a dynamic cluster expansion. The excess transport coefficient Δη is given in an exponential form,

$\text{Δν=ν}{}_0\text{exp}\text{∑}\text{l=1}\text{∞}\text{β}{}_{\mathrm{l}}\text{n}{}^{\mathrm{l}}\text{?1}$

where η₀ is the two-body Chapman-Enskog result for the transport coefficient, n is the density, and β_l is a density-independent quantity consisting of connected cluster contributions of (l + 2) particles. Therefore, the leading term β₁ consists of connected three-body cluster contributions. The excess shear viscosity coefficient is calculated for a monatomic hard-sphere fluid by computing β_l up to the three-body contributions and the result is compared with the molecular dynamics result by Ashurst and Hoover and also with the experimental data on Ar at 75°C. In spite of the crudity of the potential model used and the approximations made the agreement is good. The result can be improved if l-body clusters (l ? 4) are included in the calculation. The thermal conductivity coefficient can be obtained in a similar form by using exactly the same procedure used for the viscosity coefficient.     

Thermodynamic and transport properties of simple fluids using lattice sums: bulk phases and liquid-vapour interface

Molecular dynamics simulations in the canonical ensemble have been performed to obtain the thermodynamic and transport properties of the Lennard-Jones fluid. The dispersion interactions were calculated using lattice sums. This method makes it possible to simulate the full potential avoiding the inclusion of the long range corrections (LRC) during or at the end of simulations. In the calculation of dynamic properties in bulk phases and thermodynamic quantities of inhomogeneous systems where the interface is physically present, in general the LRC cannot easily be included. By using the lattice sums method, the results are independent of the truncation of the potential. In the liquid-vapour interface simulations it is not necessary to make any pre-judgments about the form of the LRC formula to calculate coexisting properties such as the surface tension. The lattice sums method has been applied to evaluate how well the full interaction can be calculated in the liquid phase and in the liquid-vapour interface. In the liquid phase the pressure, configurational energy, diffusion coefficient and shear viscosity were obtained. The results of the thermodynamic properties are compared with those obtained using the spherically truncated and shifted (STS) potential with the LRC added at the end of simulations, and excellent agreement is found. The transport properties are calculated on different system sizes for a state near the triple point. The diffusion coefficient using the lattice sums method increases with the number of molecules, and the results are higher than those of the STS model truncated at 2.5σ (STS2.5). The shear viscosity does not show any system size dependence for systems with more than 256 molecules, and the lattice sums results are essentially the same as those for the STS2.5. In the liquid-vapour equilibria the coexisting densities and vapour pressures for the full potential agree well with those obtained using the Gibbs ensemble and the NPT + test particle methods. The surface tension using lattice sums and truncation of forces at 2.5σ agrees well with STS results using large system sizes and cutoff distances.     

The viscosity and diffusion coefficients of eighteen binary gaseous systems

The paper reports accurate measurements of the viscosity of the eighteen binary gaseous systems: CF₄ with He, Ne, Ar, N₂, CO₂, CH₄; SF₆ with He, Ne, Ar, N₂, CO₂, CH₄, CF₄ and O₂ with He, Ne, CO₂, CF₄, SF₆. The measurements were performed in a high-precision oscillating-disk viscometer at atmospheric pressure and in the temperature range 25–200°C for the systems containing CH₄ or SF₆ and in the temperature range 25–400°C for the remainder. The reported viscosities are believed to be accurate to within ±0.1% at room temperature and to within ±0.2% at 400°C.It is shown that the data conform to the extended law of corresponding states developed by Kestin, Ro and Wakeham despite the complexity of some of the component gases. The standard deviation between the experimental values and those calculated from the law of corresponding states is only 0.3% which is commensurate with the uncertainty in the experimental results.Binary diffusion coefficients derived from the mixture viscosity data are also presented; they have an estimated uncertainty of ±2%.     

Calculation of transport coefficients for a moderately dense gas

Russian Physics Journal -     

Collision-induced absorption in dense mixtures of simple fluids

Summary Collision-induced absorption (CIA) spectroscopy is a probe of the dynamical properties of dense systems. Two simple cases of CIA spectra are here discussed: the translational band observed in solutions of a noble gas in liquid Ar and the rotational lines of H₂ observed in solutions of H₂ in Ar. In the first case, the analysis of the translational band allows one to derive the characteristic frequency ω₀, associated with the rattling component of the motion of the impurity in the Ar medium. In the second case, the analysis of the rotational lines allows one to derive the parameter δ, that characterizes the density narrowing effect. In the high-density region, the parameter δ is directly related to the diffusive motion of the Ar atoms around the impurity. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

Random time-scale invariant diffusion and transport coefficients

Single particle tracking of mRNA molecules and lipid granules in living cells shows that the time averaged mean squared displacement delta2[over ] of individual particles remains a random variable while indicating that the particle motion is subdiffusive. We investigate this type of ergodicity breaking within the continuous time random walk model and show that delta2[over ] differs from the corresponding ensemble average. In particular we derive the distribution for the fluctuations of the random variable delta2[over ]. Similarly we quantify the response to a constant external field, revealing a generalization of the Einstein relation. Consequences for the interpretation of single molecule tracking data are discussed.     

Estimation of transport coefficients of dense hadronic and quark matter

In this study, we calculated transport coefficients including the shear viscosity and electrical conductivity relative to the density of dense hadronic and quark matter. By considering the simple massless limit for the quark matter and two different effective models for the hadronic matter, we estimated the transport coefficients of the two phases separately. Accordingly, density profiles of the transport coefficients were depicted in two parts: the phase-space part and the relaxation time part. From calculating the shear viscosity to density ratio, we also explored the nearly perfect fluid domain of the quark and hadronic matter.     

The viscosity and diffusion coefficients of the binary mixtures of xenon with the other noble gases

This paper presents new experimental data for the viscosity of binary mixtures of xenon with the remaining monatomic gases, helium, neon, argon, and krypton. The measurements have been performed in a high precision oscillating-disk viscometer at atmospheric pressure and within the temperature range 25–500°C. The data have an estimated uncertainty of ±0.1% at 25°C increasing to ±0.3% at 500°C. The collision integrals for the interactions of xenon with the other monatomic species conform to the extended law of corresponding states formulated by Kestin, Ro and Wakeham. For each binary interaction the scaling parameters σ_ij and ∈_ij have been obtained. The ensemble of experimental results can be correlated by means of the appropriate kinetic theory expressions reinforced by the extended law of corresponding states. The deviations do not exceed 0.5%. The binary diffusion coefficients were calculated from the measured mixture viscosity and compared with the available experimental results. The standard deviation was estimated as ±2% which is within the mutual uncertainty of the two sets.     

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用高密度等离子体模型可以计算出一整套输运参数,并且在很宽的等离子体温度和密度范围内有合理的精度,可广泛应用于Z箍缩等离子体、激光聚变和磁约束聚变等领域,并将这个模型计算出的各种输运参数拟合成了实用的公式。     

Application of a new perturbation theory to evaluate the shear and bulk viscosity coefficients

Three liquids, CH₃F, CH₃Cl and CHF₃, have been submitted to systematic investigation in the microwave and far infra-red frequency domains.

The studies have been extended over a gradual variation of temperature and density scanning the whole liquid range beneath the critical region. Accordingly, the relative location in time of absorption processes were observed to evolve towards each other as the liquids expand when approaching their critical region.

We discuss the dielectric relaxation processes and their characteristic times, together with some very important features from the very intense absorption in the far infra-red. The correlative dispersion is fitted by a distribution of resonances model. The occurrence of specific alignment effects are shown to be responsible for local enhancement of the dipole moments, resulting in excess of integrated intensities.

Throughout this report a direct presentation of the experimental features displays already a number of characteristics of molecular dynamics. Their analysis will be completed and refined through the correlation functions formalism developed in a following paper.     

Nonlinear and nonlocal transport effects in simple fluids

Correlation function formulae for transport coefficients of 2nd order in arbitrarily dense fluids are derived, using a modified Chapman-Enskog solution of the Liouville equation. Some static correlations are neglected. Approximate evaluation for dilute gases gives essentially the same results as the solution of Boltzmann's equation. As an application higher order transport effects in the critical region are estimated. It is conjectured that they are apparent in sound absorption and the line width of Rayleigh scattering if (T?T_c)/T _c?10^?3.     

Reciprocal relations of transport coefficients in simple materials

The cross effects of viscosity and heat conduction in anisotropic simple materials (solids or liquids) are given in the linear regime, using our dissipation function theory introduced recently. Depending on whether the temperature gradient or the heat flux is used in the dissipation function, we show that two different but unambiguous reciprocal relations between the transport coefficients follow. These are compared and contrasted with the confusing predictions from the Onsager theory, and to the results of rational thermodynamics. The uncertain experimental situation in regard to these reciprocal relations is discussed. Experimental tests are strongly urged.     

A memory function model for the velocity autocorrelation function and the self-diffusion coefficient in simple dense fluids

A memory-function model is used to compute the velocity autocorrelation function and the self-diffusion coefficient of a dense Lennard-Jones fluid from the zero-time correlation functions of the molecular velocity and its first two time derivatives. It is shown that these zero-time correlation functions can be evaluated in terms of the radial distribution function and the pair potential only, i.e. without considering higher order correlation functions. Since molecular dynamics results are available for the radial distribution function as well as the velocity autocorrelation function and the self-diffusion coefficient, a rigorous test of the chosen memory function is possible. The agreement is reasonable, although generally not within the error bands of the molecular dynamics results.     

Relativistic transport theory for simple fluids to first order in the gradients

In this paper we show how using a relativistic kinetic equation the ensuing expression for the heat flux can be cast in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so called “first order in the gradients” theories propose. Since the specific expressions for the transport coefficients are irrelevant for our purposes, the BGK form of the kinetic equation is used. Moreover, from the resulting hydrodynamic equations it is readily seen that the equilibrium state is stable in the presence of the spontaneous fluctuations in the transverse hydrodynamic velocity mode of the simple relativistic fluid. The implications of this result are thoroughly discussed.     

Integral-equation theories and Mayer-sampling Monte Carlo: a tandem approach for computing virial coefficients of simple fluids

Mayer-sampling Monte Carlo (MSMC) has enabled computation of higher-order virial coefficients than previously possible for a variety of potential models, but it is not required for computation of the entire virial coefficient for models that are spherically symmetric: approximations that result from the hypernetted-chain (HNC) or Percus–Yevick (PY) integral-equation theories in conjunction with the compressibility equation (c) or virial equation (v) can be computed quickly by fast Fourier transforms. For the fourth and fifth virial coefficients of the Lennard–Jones potential (with parameters σ and ε), we demonstrate that the corrections to each of the four approximations (HNC(c), HNC(v), PY(c), and PY(v)) are faster to compute to a desired precision by MSMC than the full coefficient itself, with the exception of the PY(v) correction at fifth order, and that the optimal decomposition with regard to precision can be identified using a fraction of the steps required to obtain precise virial coefficients. At reduced temperatures kT/ε greater than 4, the PY(c) correction is fastest to compute by MSMC at both fourth and fifth orders. For lower temperatures, the HNC(v) decomposition is most efficient at fourth order, while the HNC(c) decomposition is most efficient at fifth order. These results are specific to the Lennard–Jones potential, but the method for determining the optimal decomposition is applicable to any spherically symmetric potential.     

Transport coefficients of dense fluids of molecules interacting according to a square well potential

A simplified kinetic theory is described for spherical molecules interacting according to a square well potential. The statistical premises of this theory correspond closely to those of Longuet-Higgins' and Pople's theory of dense fluids of rigid spheres. The thermal conductivity λ, shear viscosity η and bulk viscosity κ are predicted to be in the ratio where k is Boltzmann's constant and m the mass of a molecule. To calculate any of these coefficients absolutely requires independent information about the equilibrium pair distribution. This may be obtained from the self-diffusion constant D, whose value is also given by the theory. For argon the measured value of D leads to a theoretical value for η which is in good agreement with experiment; for this liquid however the observed ratio κ:η is very much smaller than predicted.