Universality versus nonuniversality of critical transport properties in liquid mixtures

The critical behavior near consolute points and plait points in mixtures and along lines connecting such points in the phase diagram belongs to the universality class of gas-liquid transitions in pure liquids. We give a survey of the results for the temperature dependence of transport coefficients, thermal conductivity, mass diffusion, and thermal-diffusion ratio, in mixtures within a non-asymptotic renormalization-group theory of critical dynamics. The observable critical behavior in some cases is nonuniversal and may be strongly concentration dependent. This is explained by different crossover temperatures in the singular Onsager coefficient of the order parameter and in the hydrodynamic transport coefficients. At the plait point the value of (ie1363-01) determines the crossover to the asymptotic behavior in the transport coefficients, and its smallness explains the situation in³He-⁴He mixtures. We also consider ionic solutions, where long-range forces may be present. The dynamical universality class in this case is different from that of mixtures with short-range interaction. As well as the classical static behavior for sufficient long-range interaction potentials, the dynamical critical behavior depends on the exponent of the power law for the spatial decrease in this interaction. This offers an additional possibility to determine this exponent by measuring the temperature dependence of the hydrodynamic transport coefficients.     

Nonasymptotic Transport Properties in Fluids and Mixtures Near a Critical Point

We review the critical dynamics of fluids and mixtures. Special attention in the comparison with experiment is paid to nonasymptotic effects. Our theoretical results are based on the complete model H of Siggia, Halperin, and Hohenberg including the sound mode variables. Using the dynamic renormalization group theory, we calculate the temperature dependence of the transport coefficients as well as the frequency-dependent sound velocity and sound attenuation. In mixtures a time ratio between the Onsager coefficients related to the diffusive modes, which is directly related to the critical enhancement of the thermal conductivity near a consolute point, has to be taken into account. The sound mode contains, besides the dynamic parameters, a static coupling related to the logarithmic derivative of the weakly diverging specific heat. The deviation from the asymptotic value of this coupling at finite frequencies and temperature distance from T _c leads to additional nonasymptotic effects. Our theory, which derives the phenomenological ansatz of Ferrell and Bhattacharjee for pure fluids and mixtures near a consolute point, is also applicable near a plait point.     

Crossover behavior of the transport coefficients of critical binary mixtures

The behavior of the transport coefficients related to diffusion, heat conduction, and their cross-processes in fluid mixtures near the consolute point and the liquid-vapor critical line is investigated. Simple crossover equations for the critical enhancement of those coefficients are developed by incorporating a finite cutoff and time-dependent correlation functions of the order parameter and of the entropy into decoupled-mode theory integrals. It is shown that the thermal conductivity of a binary mixture is nondivergent and the crossover from the critical background in the critical point to the regular background far from the critical point is elucidated. The crossover to the behavior of the thermal conductivity in the one-component limit is also discussed.     

Transport properties of fluid mixtures in the critical region

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.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Ternary liquid diffusion coefficients near plait points

Mutual diffusion coefficients were measured as a function of temperature above the 30°C plait point of the water + 2-propanol + cyclohexane system using a Gouy interferometer and a new temperature-jump procedure. The four independent diffusion coefficients were found to decrease rapidly along the constant plait-point line as the temperature approached the consolute or plait temperature. Effective critical exponents were found to be 0.55 for the individual diffusion coefficients and 1.31 for the determinant of the diffusion coefficient matrix. The measured diffusion coefficients satisfy all stability requirements, although cross diffusion coefficients were found to be as large as main diffusion coefficients and a negative value was obtained for the water main diffusion coefficient in the component representation utilized in this work.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Diffusion Modes of an Equimolar Methane–Ethane Mixture from Dynamic Light Scattering

The hydrodynamic diffusion modes of an equimolar methane–ethane mixture have been investigated by dynamic light scattering. Measurements were performed over a wide temperature range between the plait critical point at 263.55 K and 310 K along the critical isochore. Two relaxation modes have been observed which are commonly associated with pure mass diffusion and pure thermal diffusion, but in near-critical binary fluid mixtures—according to recent theory—may alternatively be interpreted as two effective diffusivities resulting from a coupling between mass and thermal diffusion. Diffusivity values for the slow mode were obtained with typical standard deviations of 1% over the whole temperature range, whereas the low amplitude of the fast mode only allowed values of this component with a large measurement uncertainty. The results are discussed in connection with literature data available for the thermophysical properties of this binary fluid mixture and regarding the various possibilities of theoretical interpretation.     

A crossover description for the thermodynamic properties of fluids in the critical region

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.     

Transport properties of refrigerants R32, R125, R134a, and R125+R32 mixtures in and beyond the critical regionPropriétés de transport des frigorigènes R32, R125, R134a et des mélanges de R125+R32 dans et au-delà la région critique

A practical representation for the transport coefficients of pure refrigerants R32, R125, R134a, and R125+R32 mixtures is presented which is valid in the vapor–liquid critical region. The crossover expressions for the transport coefficients incorporate scaling laws near the critical point and are transformed to regular background values far away from the critical point. The regular background parts of the transport coefficients of pure refrigerants are obtained from independently fitting pure fluid data. For the calculation of the background contributions of the transport coefficients in binary mixtures, corresponding-states correlations are used. The transport property model is compared with thermal conductivity and thermal diffusivity data for pure refrigerants, and with thermal conductivity data for R125+R32 mixtures. The average relative deviations between the calculated values of the thermal conductivity and experimental data are less than 4–5% at densities ρ0.1ρ_c and temperatures up to T=2T_c.     

Transport properties of fluids near critical points

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.Invited lecture presented at the 10th International Conference on the Properties of Steam, Moscow, USSR, September 2–7, 1984.     

Thermodynamic and transport properties of fluids and fluid mixtures in the extended critical region

A practical representation of the thermodynamic properties and the transport coefficients related to diffusion, heat conduction, and their cross-processes in pure fluids and binary mixtures near the liquid-vapor critical line is developed. Crossover equations for the critical enhancement of those coefficients incorporate the scaling laws near the critical point and are transformed to the regular background far away from the critical point. The crossover behavior of the thermal conductivity and the thermal diffusion ratio in binary mixtures is also discussed. A comparison is made with thermal-conductivity data for pure carbon dioxide, pure ethane, and carbon dioxide add ethane mixtures.     

Specific heat of a liquid mixture near the consolute point in the bulk phase and in a porous medium

The critical behavior of the specific heat of the mixture 2.6-lutidine+water near the consolute point was investigated in the bulk phase and in a porous medium. The measurements of the bulk specific heat yield a critical exponent =0.111±0.018 and a universal amplitude ratio A ^–/A⁺=1.77, in good agreement with theoretical predictions. Using previous experimental data for nitroethane+isooctane, we also determined the two-scale-factor ratio X ⁺=0.271 between the critical amplitude of the specific heat and of the correlation length in agreement with the results reported for other fluid systems. The specific heat in the porous medium with a pore size of about 100 nm was measured. The behavior of the specific heat differs from that of the bulk specific heat. This may be the result of finite size effects, of a wetting layer in the pores, and of a distortion of the coexistence curve.     

Critical Light Scattering in Pure Liquids

Light-scattering experiments near the critical point (T _c, _c) in fluid systems and, in particular, the central Rayleigh peak in the frequency spectrum are reviewed. Within a nonasymptotic renormalization-group theory, the crossover function is calculated between several regions: (i) from the background to the asymptotic region, (ii) from the hydrodynamic region (wave lengthcorrelation length) to the critical region (wave lengthcorrelation length), and (iii) from critical densities to noncritical densities. Contrary to the mode-coupling expression, the appropriate scaling function is well defined in all limits of its arguments. At T _c the crossover in the wave-vector dependence of the linewidth is also considered. Theoretical results are compared with experiments for pure liquids. Nonuniversal parameters are chosen consistent with the transport coefficients (i.e., the shear viscosity) for the same substance which can be evaluated within the same formalism.     

Novel Phase-Transition Behavior in an Aqueous Electrolyte Solution

We have investigated the near-critical behavior of the susceptibility of a ternary liquid mixture of 3-methylpyridine, water, and sodium bromide as a function of the salt concentration. The susceptibility was determined from light-scattering measurements performed at a scattering angle of 90° in the one-phase region near the locus of lower consolute points. A sharp crossover from asymptotic Ising behavior to mean-field behavior has been observed at concentrations ranging from 8 to 16.5 mass% NaBr. The range of asymptotic Ising behavior shrinks with increasing salt concentration and vanishes at a NaBr concentration of about 17 mass%, where complete mean-field-like behavior of the susceptibility is observed. A simultaneous pronounced increase in the background scattering at concentrations above 15 mass%, as well as a dip in the critical locus at 17 mass% NaBr, suggests that this phenomenon can be interpreted as mean-field tricritical behavior associated with the formation of a microheterogeneous phase due to clustering of the molecules and ions. An analogy with tricritical behavior observed in polymer solutions as well as the possibility of a charge-density-wave phase is also discussed. In addition, we, have observed a third soap-like phase on the liquid–liquid interface in several binary and ternary liquid mixtures.     

Prediction of the viscosity and thermal conductivity coefficients of mixtures

A corresponding states procedure to predict the viscosity and thermal conductivity coefficients of a pure fluid or mixture is discussed. We show the transport properties of a fluid or mixture can be calculated to within experimental error given only corresponding values for a reference fluid and equation of state data. With methane, as the reference fluid, we consider nitrogen, ethane, propane, butane, carbon dioxide, and mixtures of these fluids. LNG is also included. It is shown that the conventional corresponding states approach is not sufficient to predict correctly the transport properties. The effect of internal degrees of freedom on the thermal conductivity coefficient and the enhancement in the critical region for this coefficient is discussed briefly.     

Mutual Diffusion Coefficient and Dynamic Viscosity Near the Critical Consolute Point Probed by Dynamic Light Scattering

The possibility of applying dynamic light scattering to simultaneous determination of the mutual diffusion coefficient and the viscosity of binary liquid systems was studied near the critical consolute point. When seed particles are added to the system, the particle diffusion coefficient is measured, and the viscosity is obtained using the Stokes–Einstein relation. Since the amplitude of light scattered from concentration fluctuations is low in a mixture with a small difference between the refractive indices of the pure components, this approach allowed the determination of the viscosity of a critical mixture of nitroethane and isooctane, without a signal component from mutual diffusivity superimposed. In contrast, particle aggregation prevented the determination of the viscosity of a critical mixture of triethylamine and water. Despite this difficulty, and an unidentified contribution in the signals obtained, the mutual diffusion coefficient and the critical exponent v could be determined in this system without a noticeable influence from the addition of seed particles.     

Crossover SAFT Equation of State and Thermodynamic Properties of Propan-1-ol

In this work we have developed a new equation of state (EOS) for propan-1-ol on the basis of the crossover modification (CR) of the statistical-associating-fluid-theory (SAFT) EOS recently developed and applied to n-alkanes. The CR SAFT EOS reproduces the nonanalytical scaling laws in the asymptotic critical region and reduces to the analytical-classical SAFT EOS far away from the critical point. Unlike the previous crossover EOS, the new CR SAFT EOS is based on the parametric sine model for the universal crossover function and is able to represent analytically connected van der Waals loops in the metastable fluid region. The CR SAFT EOS contains 10 system-dependent parameters and allows an accurate representation of the thermodynamic properties of propan-1-ol over a wide range thermodynamic states including the asymptotic singular behavior in the nearest vicinity of the critical point. The EOS was tested against experimental isochoric and isobaric specific heats, speed of sound, PVT, and VLE data in and beyond the critical region. In the one-phase region, the CR SAFT equation represents the experimental values of pressure with an average absolute deviation (AAD) of less than 1% in the critical and supercritical regions and the liquid densities with an AAD of about 1%. A corresponding states principle is used for the extension of the new CR SAFT EOS for propan-1-ol to higher n-alkanols.     

Viscosity of H<Subscript>2</Subscript>O in the Critical Region

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. Contribution of the National Institute of Standards and Technology, not subject to U.S. copyright.