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It has been established experimentally that the thermodynamic properties of fluids satisfy scaling laws with universal critical exponents asymptotically close to a single critical point of the vapor–liquid phase transition. In contrast to the conjecture of Woodcock, there is no reliable experimental evidence to doubt the existence of such a single critical point in the thermodynamic limit and of the validity of the scaling theory for critical thermodynamic behavior.

The thermal conductivity and viscosity of fluids are known to exhibit an enhancement due to critical fluctuations. Procedures proposed in the literature for estimating the correlation length determining the magnitude of these enhancements have been reviewed, and a recommendation to reduce complexity and computation time is presented.

This paper reviews the available information for the thermal-conductivity enhancement. This enhancement can be represented by a simplified solution of the mode-coupling theory of critical dynamics with two critical amplitudes and one cutoff wave number as fluid-specific parameters. Using corresponding states, these fluid-specific parameters are correlated in terms of their dependence on the acentric factor. A universal representation of the critical enhancement of the thermal conductivity for a large number of molecular fluids is presented.

There exists a formulation for the critical locus of aqueous solution of NaCl recommended by the International Association for the Properties of Water and Steam. In this article, we present slightly modified equations for the critical parameters of H2O + NaCl that incorporate a non-analytic concentration dependence predicted by theory.

In a recent publication, it has been shown how a non-analytic scaling theory of critical phenomena can describe the available experimental information for the thermodynamic properties of supercooled water, when it is assumed to exhibit a liquid–liquid critical point. In this article, we present a mean-field equation of state which also represents the experimental data for supercooled water. Compared to the scaling theory, the mean-field equation has the advantage of simplicity for practical calculations of the properties of supercooled water. The insensitivity to a particular form of a critical equation of state is due to a lack of experimental data asymptotically close to the liquid–liquid critical point. Hence, while the assumed existence of a liquid–liquid critical point in water can account for the observed thermodynamic behavior of supercooled water, the actual location of such a liquid–liquid critical point cannot be determined accurately from the available experimental thermodynamic property data.

The asymptotic critical behavior of the thermal diffusivity of H2O, deduced from dynamic light-scattering measurements, is shown to be in good agreement with the mode-coupling theory for critical dynamics in fluids. Consistency of the thermal-diffusivity measurements with the critical enhancement of the viscosity of H2O is also demonstrated.

It has been well established that thermodynamic and transport properties of fluids exhibit singular behavior near the critical point. In this article, the theoretical predictions for the enhancement of the viscosity near the critical point are reviewed. It is then shown how these predictions can be used to obtain a representative equation for the viscosity of H2O in the critical region.

Experimental data are presented for the thermal conductivity of mixtures of carbon dioxide and ethane. The thermal conductivity has been measured with a parallel-plate instrument, as a function of temperature along isochores, so as to obtain detailed information on the behavior of the thermal conductivity of a mixture near the locus of vapor–liquid critical points. The experimental results are in agreement with theoretical predictions from the mode-coupling theory for critical dynamics in binary mixtures.

This note presents an update of an evaluation of the critical parameters of mixtures of carbon dioxide and ethane, previously reported by Abbaci et al. (Int. J. Thermophys. 13, 1043 (1993)).

The period and damping of the free motion of a body oscillating in a fluid depend on the fluid's viscosity and density. Commonly, a working equation which expresses the damping as a function of the viscosity and density is solved for the viscosity, the damping being measured and the density being treated as an independently supplied parameter. Another working equation exists for the period, and, in general, the period depends on a combination of the viscosity and the density which is linearly independent of the combination that appears in the damping equation. It is, therefore, in principle, possible to determine both the viscosity and the density by a simultaneous solution of the two coupled working equations, since the period also is measured. In this paper, the working equations that describe the oscillating-disk viscometer are reviewed and their simultaneous solution is considered. The effect of fixed plates symmetrically located above and below the oscillating disk is of specific interest. The paper's main result is that fixed plates can dramatically increase the independence of the damping and period working equations, so that it becomes indeed feasible to determine the viscosity and the density of a fluid simultaneously from the damping and period of oscillating motion. A price is paid, however, because the instrument's working equations when plates are present have multiple solutions. Under special conditions, these multiple solutions can coalesce, and then one can only deduce the viscosity from the damping equation if the density is known a priori.

Experimental data reported in the literature indicate a strong dependence of the critical temperature of aqueous solutions of sodium chloride on salt concentration, especially in the limit of pure water. Critical pressures and densities also show strong dependences on salt concentration. We propose a new set of equations for the critical locus and compare the results with evaluations reported previously by a number of investigators. The new equations yield a better description of the experimental data from the limit of pure water to the highest salt concentration for which data are available (0.3 mass fraction of sodium chloride).

A description is presented of the construction and operating procedure of an improved guarded parallel-plate instrument for measuring the thermal conductivity of fluids in the critical region. With the improved arrangement, it has been possible to reduce the temperature differences across the fluid layer between the two horizontal plates to values as low as 0.3 mK, thus allowing the thermal conductivity of fluids to be measured at temperatures as close as 20 mK to the critical temperature. The instrument has been used to measure the thermal conductivity of methane and of a mixture of methane and ethane in the close vicinity of the critical point.

A compact photon-correlation spectrometer for basic and applied research in physics, chemistry, biology, medicine, engineering, and environmental technology as well as for educational laboratory courses in these subjects has been developed. The instrumental setup enables one to make absolute measurements of the sizes of particles suspended in liquids in the range from 0.001 to 5 μm. The measurements are fast, lasting usually from seconds to several minutes. Real-time size monitoring, such as of kinetic aggregation processes, is also possible. The optical arrangement of the spectrometer even makes it possible to measure light scattering in opaque systems which are characterized by strong light absorption. The quantity of the sample to be studied can be quite small, starting from 0.01 cm3. The system includes specially designed software for performing data interpretation and for implementing fitting procedures, for exchange of data with other programs, and for automation of measurements of long duration or of sequences of measurements. Measurements verifying the accuracy of the system are presented for latex suspensions, for aniline dye dissolved in water, and for dilute solutions of polystyrene in toluene.

This paper is concerned with theological properties of a phase-separating mixture in the presence of macroscopic shear flow. Specifically, we have investigated the shear viscosity of a nonionic micellar solution in shear-induced quasi-stationary states, where a dynamical balance between the growing concentration domains and the suppression by shear is established. During the phase separation, when concentration domains of the two phases with viscosity difference are formed, the measured viscosity of all mixtures as a function of temperature is found to satisfy to a good approximation a novel theological equation proposed by Onuki. In addition, we have determined that the observed characteristic temperature related to the crossover from the shear-affected regime to the shear-unaffected regime depends on the shear rate asS p , withp=1:vz≃0.51, wherev andz are universal critical exponents associated with the range and decay rate of the critical fluctuations. This power law depdendence onS. expected for a mixture at the critical composition, appears to be valid also for all off-critical mixtures.

We present an equation of state for the thermodynamic properties of mixtures of methane and ethane in the critical region that incorporates the crossover from singular thermodynamic behavior near the locus of vapor-liquid critical points to regular thermodynamic behavior outside the critical region. The equation of state yields a satisfactory representation of the thermodynamic-property data for the mixtures in a large range of temperatures and densities.

Based on reliable. carefully selected data sets. equations for the thermal conductivity and the viscosity of the refrigerant R 112a are presented. They are valid at temperatures from 240 to 440 K, pressures up to 20 MPa. and densities up to 1050 kg · m−3. including the critical region.

We have investigated the dynamic behavior of a nonionic micellar solution of tetra-ethylene glycoln-decylether (C10 E4) in water near its critical point in the presence of shear. The non-Newtonian behavior of the viscosityν can be represented byν ν* = [ 1 +a(Sτ4)=]ω2, whereν* is the viscosity in the absence of shear,S is the shear rate. τ4 is the lifetime of the critical Iluctuations,a is a system-dependent constant, and ω = 0.02 In addition, we have found that, before attaining a steady state, the sheared mixture undergoing phase separation shows significant shear-dependent rheological effects due to the presence of concentration domains.

We have developed an experimental arrangement for measuring Rayleigh scattering in liquids and liquid mixtures that are either in thermal equilibrium or in thermal nonequilibrium states. As an illustrative example we report experimental values for the thermal dilfusivity, the mass diffusion coefficient, the Rayleigh-factor ratio, and the Suret coefficient of an equimolar mixture of liquid toluene andn-hexane.

Transport properties of fluid mixtures exhibit anomalous behavior near the vapor-liquid critical line. These anomalies are a result of long-range fluctuations in the system in the vicinity of a critical point. We use mode-coupling theory to describe the critical enhancements of the thermal conductivity, the viscosity, the mutual diffusivity, and the thermal-diffusion coefficients of binary mixtures. The resulting expressions not only are valid in the asymptotic critical region but also describe the crossover to regular behavior far away from a critical point. The crossover functions depend on the thermodynamic properties of the mixtures, background values of all transport coefficients, and two concentration-dependent cutoff wave numbers. We compare the proposed crossover model with experimental thermal-conductivity data for mixtures of carbon dioxide and ethane in the critical region and find good agreement between theory and experiment.

In this paper we present a method which modifies a classical equation of state by incorporating the nonclassical critical behavior. As an example we have applied our procedure to the Carnahan-Starling-DeSantis (CSD) equation of state. The resulting equation reproduces the universal scaling behavior near the critical point and reduces to the universal ideal-gas behavior at low densities. We show that the renormalized CSD equation yields an improved and consistent representation of both mechanical and caloric thermodynamic properties. In addition, the suppression of the critical temperature due to the critical fluctuations is clearly demonstrated.

A new representation of the viscosity of ethane is presented. The representative equations are based upon a body of experimental data that have been critically assessed for internal consistency and for agreement with theory in the zero-density limit, vapor phase, and critical region. The representation extends over the temperature range from 100 K to the critical temperature in the liquid phase and from 200 K to the critical temperature in the vapor phase. In the supercritical region, the temperature range extends to 1000 K for pressures up to 2 MPa and to 500 K for pressures up to 60 MPa. The ascribed accuracy of the representation varies according to the thermodynamic state from ±0.5 % for the viscosity of the dilute gas near room temperature to ±3.0% for the viscosity at high pressures and temperatures. Tables of the viscosity, generated by the relevant equations, at selected temperatures and pressures and along the saturation line, are also provided.

A new representation of the thermal conductivity of ethane is presented. The representative equations are based upon a body of experimental data that have been critically assessed for internal consistency and for agreement with theory in the zero-density limit and in the critical region. The representation extends over the temperature range from 100 K to the critical temperature in the liquid phase and from 225 K to the critical temperature in the vapor phase. In the supercritical region the temperature range extends to 1000 K for pressures up to 1 MPa and to 625 K for pressures up to 70 MPa. The ascribed accuracy of the representation varies according to the thermodynamic state from ±2% for the thermal conductivity of the dilute gas near room temperature to ±5% for the thermal conductivity at high pressures and temperatures. Tables of the thermal conductivity, generated by the relevant equations, at selected temperatures and pressures and along the saturation line are also provided.

New equations for the thermal conductivity and the viscosity of R134a that are valid in a wide range of pressures and temperatures are presented. They were obtained through a theoretically based, critical evaluation of the available experimental data, which showed considerable inconsistencies between data sets, in particular in the vapor phase. In the critical region the observed enhancement in the thermal conductivity is well represented by a crossover model for the transport properties of fluids. Since thermodynamic properties enter into the calculation of the critical enhancement of the transport properties, a new fundamental equation for the critical region was developed also.

An improved parametric equation for the thermodynamic properties of fluids is presented that incorporates the crossover from singular thermodynamic behavior in the immediate vicinity of the critical point to regular thermodynamic behavior far away from the critical point. Based on a comparison with experimental data for ethane and methane, it is demonstrated that the crossover model is capable of representing the thermodynamic properties of fluids in a large range of temperatures and densities around the critical point.

A scaled fundamental equation is presented for the thermodynamic properties of methane in the critical region. The equation supplements the international formulation for the thermodynamic properties of methane issued by IUPAC.

New experimental results are reported for the surface tension of normal pentane, hexane, heptane, and octane. The data were obtained with a differential capillary-rise method and cover the entire liquid range from the triple-point temperature to the critical temperature. Equations for calculating the surface tension of these n-alkanes as a function of temperature are presented.

It is demonstrated that the Taylor dispersion method can be used to measure the mutual diffusivity of liquid mixtures near a critical mixing point. For this purpose we have measured the mutual diffusivity of a liquid mixture of n-hexane and nitrobenzene at the critical composition at temperatures from 16 K down to 1 K above the critical temperature. The results are in agreement with the theoretically predicted behavior of the diffusivity near a critical point of mixing.

The results of an experimental study of surface-tension effects in kinematic capillary viscometers of the suspended-level type are presented. These results are deduced from a comparison with measurements obtained with a special Ostwald viscometer in which surface-tension effects are negligibly small. It is shown that surface-tension effects in suspended-level viscometers are sensitive to the shape of the capillary exit. Recommendations how to minimize these effects are discussed.

A theoretically based simplified crossover model, which is capable of representing the thermodynamic properties of fluids in a large range of temperatures and densities around the critical point, is presented. The model is used to predict the thermodynamic properties of R134a in the critical region from a limited amount of available experimental information. Values for various thermodynamic properties of R134a at densities from 2 to 8 mol·L−1 and at temperatures from 365 to 450 K are presented.

The following is a correction to the paper titled “Thermal Diffusivity of H2O near the Critical Point” by J. V. Sengers, R. A. Perkins, M. L. Huber, and B. Le Neindre that appeared in Int. J. Thermophys. 30: 1453 (2009). The information for RD in Table 1 yielding RD = 1.05 ± 0.05 was obtained by using the IAPWS Formulation 1985 for the Thermal Conductivity [49] for estimating the background thermal conductivity of H2O and not the estimate proposed by Le Neindre et al. [58] as was stated in the paper. If we do use the estimate proposed by Le Neindre et al. [58] for the background thermal conductivity, we find RD = 1.01± 0.05.

The paper reviews the theoretical and experimental results for the asymptotic behavior of the dynamics of critical fluctuations in fluids and fluid mixtures near a critical point. The implications of these results for the development of accurate representative equations for the viscosity and thermal conductivity of gases in the critical region are discussed.

New accurate experimental data are presented for the viscosity of liquid toluene. The viscosity was measured relative to the viscosity of liquid water with the aid of an Ubbelohde capillary viscometer. The data cover a temperature range from approximately 25 to 75°C and are represented with high precision by an Arrhenius equation

New measurements are reported for the density and viscosity of tetralin and trans-decalin. The density was determined from room temperature to 60°C for tetralin and to 95°C for trans-decalin. The kinematic viscosity was measured up to temperatures slightly above 100°C. Our results improve upon the values recommended by the American Petroleum Institute for these liquids.

The shear viscosity of fluids exhibits an anomalous enhancement in the close vicinity of the critical point. A detailed experimental study of the viscosity of steam in the critical region has been reported by Rivkin and collaborators. A reanalysis of the experimental data indicates that the behavior of the viscosity of steam near the critical point is similar to that observed for other fluids near the critical point. An interpolating equation for the viscosity of water and steam is presented that incorporates the critical viscosity enhancement.

We have developed a “crossover” formalism that reconciles the singular asymptotic critical behavior of the thermodynamic properties of fluids with the classical behavior of these properties well away from the critical point. The proposed formalism is based on theoretical predictions for the crossover behavior suggested by the renormalization-group theory of critical phenomena. We demonstrate the formalism for a fluid whose classical behavior away from the critical point is represented by the equation of state of van der Waals.

A practical representation for the critical thermal conductivity enhancement is developed by incorporating a finite cutoff into the asymptotic mode-coupling integrals for the diffusivity associated with the critical fluctuations. This procedure yields a simplified approximation to a more complete nonasymptotic solution of the mode-coupling integrals obtained by us earlier. A comparison is made with thermal conductivity data for carbon dioxide, ethane, and methane.

To characterize the behavior of the thermodynamic properties of systems near a critical point, systems are grouped into universality classes. Systems within a universality class have the same universal critical exponents and scaling functions. Specifically, fluids are expected to belong to the universality class of three-dimensional Ising-like systems for which the universal quantities have been calculated with considerable accuracy. A scaled fundamental equation is presented which incorporates these theoretical predictions. Results obtained for various technologically important fluids, namely ordinary steam, heavy steam, ethylene, and isobutane, are discussed.

Gravity induces an inhomogeneous density distribution in fluids near the gas-liquid critical point. In first approximation the local properties of the fluid at a given height can be identified with those of a homogeneous system with the same temperature and density. Very close to the critical point the density gradients become so steep that gravity affects the local properties of the fluid directly. A survey is presented of the nature and magnitude of these intrinsic gravity effects.