Frequency-dependent viscosity of xenon near the critical point

Reference Correlation for the Viscosity of Xenon from the Triple Point to 750 K and up to 86 MPa

A new wide-ranging correlation for the viscosity of xenon, based on the most recent theoretical calculations and critically evaluated experimental data, is presented. The correlation is designed to be used with an existing equation of state, and it is valid from the triple point to 750 K, at pressures up to 86 MPa. The estimated expanded uncertainty (at a coverage factor of k = 2) varies depending on the temperature and pressure, from 0.2 % to 3.6 %. A term accounting for the critical enhancement is also included. The correlation behaves in a physically reasonable manner when extrapolated to 200 MPa, however care should be taken when using the correlations outside of the validated range.

Detecting protein folding by thermal fluctuations of microcantilevers

The accurate characterization of proteins in both their native and denatured states is essential to effectively understand protein function, folding and stability. As a proof of concept, a micro rheological method is applied, based on the characterization of thermal fluctuations of a micro cantilever immersed in a bovine serum albumin solution, to assess changes in the viscosity associated with modifications in the protein’s structure under the denaturant effect of urea. Through modeling the power spectrum density of the cantilever’s fluctuations over a broad frequency band, it is possible to implement a fitting procedure to accurately determine the viscosity of the fluid, even at low volumes. Increases in viscosity during the denaturant process are identified using the assumption that the protein is a hard sphere, with a hydrodynamic radius that increases during unfolding. This is modeled accordingly through the Einstein-Batchelor formula. The Einstein-Batchelor formula estimates are verified through dynamic light scattering, which measures the hydrodynamic radius of proteins. Thus, this methodology is proven to be suitable for the study of protein folding in samples of small size at vanishing shear stresses.

The Effect of Alkali Halides on the Critical Exponents of the 2,6-Dimethylpyridine-Water System

The diffusion coefficients and shear viscosities of 2,6-dimethylpyridine-water mixtures of critical composition have been measured without and with small amounts of alkali halides added. The data have been analyzed in terms of power law behavior. Deviations from power law behavior indicate a coupling between the critical fluctuations in the local concentrations and the formation of mesoscopic molecular aggregates. The critical exponent of the fluctuation correlation length, the shear viscosity exponent, and the critical exponent of the relaxation rate of fluctuations have been evaluated to show noticeable influences from the salts. The correlation length exponent indicates a suppression of the critical fluctuations, whereas the viscosity exponent rather points at the activation of some extra fluctuations. No clear evidence has been obtained that the added salts affect the critical behavior, and thus cause the opposed effects in the exponents, directly by the long-range ionic fields. Alternatively, the ions may have an influence on the aggregate formation which in turn could modify the critical fluctuations either by reducing the region of true critical exponents or by affecting the critical behavior due to the presence as well as the formation and disintegration kinetics of the multimolecular structures.

Direct imaging of long-range concentration fluctuations in a ternary mixture

We used a direct imaging technique to investigate concentration fluctuations enhanced by thermal fluctuations in a ternary mixture of methanol (Me), cyclohexane (C), and partially deuterated cyclohexane (C*) within 1mK above its consolute critical point. The experimental setup used a low-coherence white-light source and a red filter to visualize fluctuation images. The red-filtered images were analyzed off-line using a differential dynamic microscopy algorithm that allowed us to determine the correlation time, τ, of concentration fluctuations. From τ, we determined the mutual mass diffusion coefficient, D, very near and above the critical point of Me-CC* mixtures. We also numerically estimated both the background and critical contributions to D and compared the results against our experimental values determined from τ. We found that the experimental value of D is close to the prediction based on Stokes-Einstein diffusion law with Kawasaki's correction.

Monomer Exchange Kinetics, Dynamics of Concentration Fluctuations, and Chain Isomerization of Nonionic Surfactant/Water Systems. Evidence from Broadband Ultrasonic Spectra

Ultrasonic absorption spectra, measured between 0.1 and 2000 MHz, are discussed for a variety of poly(ethylene glycol) monoalkyl ether/water (CiEj=H2O) mixtures. Depending on the temperature, the surfactant concentration, and on the length of the hydrophobic (Ci) as well as the hydrophilic part (Ej) of the surfactant molecules, the spectra reveal a multitude of shapes. The set of spectra, however, can be consistently described considering (i) a relaxation term representing the monomer exchange of the micellar solutions, (ii) another one that reflects the local fluctuations in the surfactant concentration, and, with several systems, (iii) additional terms due to CiEj associations or conformational isomerizations. The parameters of these terms are discussed in the light of relevant models. Evidence is presented for a more general view of a fluctuation controlled monomer exchange mechanism that combines aspects of both theoretical models, the micelle formation/decay kinetics and dynamics of local concentration fluctuations.

Critical dynamics of an isothermal compressible nonideal fluid

A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible nonideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.

Viscoelasticity of 2D liquids quantified in a dusty plasma experiment

The viscoelasticity of two-dimensional liquids is quantified in an experiment using a dusty plasma. An experimental method is demonstrated for measuring the wave-number-dependent viscosity η(k), which is a quantitative indicator of viscoelasticity. Using an expression generalized here to include friction, η(k) is computed from the transverse current autocorrelation function, which is found by tracking random particle motion. The transverse current autocorrelation function exhibits an oscillation that is a signature of elastic contributions to viscoelasticity. Simulations of a Yukawa liquid are consistent with the experiment.

Shear thinning near the critical point of xenon

We measured shear thinning, a viscosity decrease ordinarily associated with complex liquids, near the critical point of xenon. The data span a wide range of reduced shear rate: 10(-3)<gamma tau<700 , where gamma tau is the shear rate scaled by the relaxation time tau of critical fluctuations. The measurements had a temperature resolution of 0.01 mK and were conducted in microgravity aboard the Space Shuttle Columbia to avoid the density stratification caused by Earth's gravity. The viscometer measured the drag on a delicate nickel screen as it oscillated in the xenon at amplitudes 3 microm<x 0<430 microm and frequencies 1 Hz<omega/2pi<5 Hz . To separate shear thinning from other nonlinearities, we computed the ratio of the viscous force on the screen at gamma tau to the force at gamma tau approximately 0: C gamma triple bond F(x 0,omega tau,gamma tau)/F(x 0,omega tau,0) . At low frequencies, (omega tau)2<gamma tau , C gamma depends only on gamma tau , as predicted by dynamic critical scaling. At high frequencies, (omega tau)2>gamma tau , C gamma depends also on both x 0 and omega . The data were compared with numerical calculations based on the Carreau-Yasuda relation for complex fluids: eta(gamma)/eta(0)=[1+A gamma|gamma tau|]-x eta/(3+x eta) , where x eta=0.069 is the critical exponent for viscosity and mode-coupling theory predicts A gamma=0.121 . For xenon we find A gamma=0.137+/-0.029 , in agreement with the mode coupling value. Remarkably, the xenon data close to the critical temperature Tc were independent of the cooling rate (both above and below Tc ) and these data were symmetric about Tc to within a temperature scale factor. The scale factors for the magnitude of the oscillator's response differed from those for the oscillator's phase; this suggests that the surface tension of the two-phase domains affected the drag on the screen below Tc .

Dynamic Scaling and Slowing Down in Chemical Reactions of the Critical Triethylamine−Water System

Between 100 kHz and 1 MHz, special ultrasonic attenuation measurements of the triethylamine-water mixture of critical composition have been performed for the determination of the Bhattacharjee-Ferrell scaling function. The experimental data are evaluated considering two noncritical Debye-type relaxation terms as revealed by broadband ultrasonic spectra. Shear viscosity and dynamic light scattering data from the literature are re-evaluated to yield the relaxation rate of order parameter fluctuations of the critical system as a function of temperature. The power law behavior found for the relaxtion rate fits to the scaling function in the ultrasonic spectra. The relaxation times of the noncritical Debye terms display a non-Arrhenius temperature dependence, pointing at effects of slowing in the chemical reactions associated with the relaxations.

Bulk viscosity, thermoacoustic boundary layers, and adsorption near the critical point of xenon

We present an improved model for the dissipation and dispersion in an acoustic resonator filled with xenon near its critical temperature Tc. We test the model with acoustic measurements in stirred xenon that have a temperature resolution of (T - Tc)/Tc approximately 7 x 10(-6). The model includes the frequency-dependent bulk viscosity calculated numerically from renormalization-group theory and it includes critical-point adsorption. Because the density of adsorbed xenon exceeds the critical density, the bulk viscosity's effect on surface dissipation is reduced, thereby improving the agreement between theory and experiment.

Static and dynamic critical behavior of a symmetrical binary fluid: A computer simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near a liquid-liquid critical temperature T(c). Choosing equal chemical potentials for the two species, the SGMC switches identities (A-->B-->A) to generate well-equilibrated configurations of the system on the coexistence curve for T<T(c) and at the critical concentration, x(c)=12, for T>T(c). A finite-size scaling analysis of the concentration susceptibility above T(c) and of the order parameter below T(c) is performed, varying the number of particles from N=400 to 12 800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.

Dynamic scaling of the critical binary mixture methanol-hexane

Acoustical attenuation spectrometry, dynamic light scattering, shear viscosity, density, and heat capacity measurements of the methanol/n-hexane mixture of critical composition have been performed. The critical part in the sonic attenuation coefficients nicely fits to the empirical scaling function of the Bhattacharjee-Ferrell [Phys. Rev. A 24, 1643 (1981)] dynamic scaling model if the theoretically predicted scaled half-attenuation frequency Omega(12) (BF)=2.1 is used. The relaxation rates of order parameter fluctuations, as resulting from the acoustical spectra, within the limits of experimental error agree with those from a combined evaluation of the light scattering and shear viscosity measurements. Both series of data display power law with amplitude Gamma(0)=44x10(9) s(-1). The amplitude of the fluctuation correlation length follows as xi(0)=0.33 nm from the light scattering data and as xi(0)=0.32 nm from the amplitude of the singular part of the heat capacity if the two-scale factor universality relation is used. The adiabatic coupling constant g=0.11 results from the amplitude of the critical contribution to the acoustical spectrum near the critical point, in conformity with g=0.12 as following from the variation of the critical temperature with pressure along the critical line and the thermal expansion coefficient.

Nonequilibrium statistical physics with fictitious time

Problems in nonequilibrium statistical physics are characterized by the absence of a fluctuation dissipation theorem. The usual analytic route for treating these vast class of problems is to use response fields in addition to the real fields that are pertinent to a given problem. This line of argument was introduced by Martin, Siggia, and Rose. We show that instead of using the response field, one can, following the stochastic quantization of Parisi and Wu, introduce a fictitious time. In this extra dimension a fluctuation dissipation theorem is built in and provides a different outlook to problems in nonequilibrium statistical physics.

Critical Dynamics of the Binary System Nitroethane/3-Methylpentane: Relaxation Rate and Scaling Function

Shear viscosity and dynamic light scattering measurements as well as ultrasonic spectrometry studies of the nitroethane/3-methylpentane mixture of critical composition have been performed at various temperatures near the critical temperature, T(c). A combined evaluation of the shear viscosity and mutual diffusion coefficient data yielded the amplitude, xi(0), of the fluctuation correlation length, xi, assumed to follow power law, and the relaxation rate, Gamma, or order parameter fluctuations. The latter was found to follow power law with the theoretical universal exponent. The amplitudes xi(0) = 0.23 +/- 0.02 nm and Gamma(0) = (125 +/- 5) x 10(9) s(-1) nicely agree with literature values. Using the relaxation rates resulting from the viscosity and diffusion coefficient data, the scaling function has been calculated assuming the ultrasonic spectra to be composed of a critical part and a noncritical background contribution. The experimental scaling function fits well to the predictions of the Bhattacharjee-Ferrell dynamic scaling model with scaled half-attenuation frequency, Omega(BF)1/2= 2.1. The amplitude of the sonic spectra yields the amount |g| = 0.26 of the adiabatic coupling constant, g, in fair agreement with -0.29 from another thermodynamic relation.

Universal dynamic exponent at the liquid-gas transition from molecular dynamics

The liquid-gas system is expected to exhibit distinct dynamic behavior in the fluid's critical region (model H). We present molecular dynamics simulations of a Lennard-Jones fluid model starting from specially designed, near-equilibrium, initial conditions. By following the fluid's relaxation towards equilibrium, we calculate the requisite transport coefficients in the critical region. The results yield the scaling behavior of the thermal diffusion coefficient D(T) approximately xi(-1.023+/-0.018) (xi is the correlation length) and a nonconventional divergent heat conductivity, all of which are in accord with mode-coupling and renormalization group predictions, as well as some experimental data.

Bulk viscosity of stirred xenon near the critical point

We deduce the thermophysical properties of near-critical xenon from measurements of the frequencies and half-widths of the acoustic resonances of xenon maintained at its critical density in centimeter-sized cavities. In the reduced temperature range 1 x 10-3<(T-Tc)/Tc<7 x 10 (-6), we measured the resonance frequency and quality factor (Q) for each of six modes spanning a factor of 27 in frequency. As Tc was approached, the frequencies decreased by a factor of 2.2 and the Q's decreased by as much as a factor of 140. Remarkably, these results are predicted (within +/-2% of the frequency and within a factor of 1.4 of Q) by a model for the resonator and a model for the frequency-dependent bulk viscosity zeta(omega) that uses no empirically determined parameters. The resonator model is based on a theory of acoustics in near-critical fluids developed by Gillis, Shinder, and Moldover [Phys. Rev. E 70, 021201 (2004)]. In addition to describing the present low-frequency data (from 120 Hz to 7.5 kHz), the model for zeta(omega) is consistent with ultrasonic (0.4--7 MHz) velocity and attenuation data from the literature. However, the model predicts a peak in the temperature dependence of the dissipation in the boundary layer that we did not detect. This suggests that the model overestimates the effect of the bulk viscosity on the thermal boundary layer. In this work, the acoustic cavities were heated from below to stir the xenon, thereby reducing the density stratification resulting from Earth's gravity. The stirring reduced the apparent equilibration time from several hours to a few minutes, and it reduced the effective temperature resolution from 60 mK to approximately 2 mK, which corresponds to (T-Tc)/Tc approximately =7 x 10(-6).

Power-law exponents for the shear viscosity of non-Newtonian simple fluids

Nonequilibrium molecular-dynamics simulations are performed to compute the shear viscosities of a simple Lennard-Jones fluid across a wide range of densities and temperatures that span the liquid phase. It is found that the standard mode-coupling value of beta = 0.05 for the exponent of the strain rate power-law dependence (eta = eta0-eta1gammabeta) is only applicable in a very narrow region of the thermodynamic state-space. More generally, the exponent is a remarkably simple linear function of temperature and density, analogous to the linear relationship that exists for the scaling exponents of the pressure and energy found previously by Ge et al. [Phys. Rev. E 67, 061201 (2003)], and ranges between approximately 0.2 and 1.6. It is also found that the parameters eta0 and eta1 are steep functions of increasing density for any particular temperature and can be represented by a stretched exponential of the density.

Dynamics of fluids near the consolute critical point: A molecular-dynamics study of the Widom–Rowlinson mixture

Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.

Two typical time scales of the piston effect

The existence of a fourth mode of heat transfer near the critical point, named the piston effect, has been known for more than a decade. The typical time scale of temperature relaxation due to this effect was first predicted by Onuki [Phys. Rev A 41, 2256 (1990)], and this author's formula has been extensively used since then to predict the thermal behavior of near-critical fluids. Recent studies, however, pointed out that the critical divergence of the bulk viscosity could have a strong influence on piston-effect-related processes. In this paper, we conduct a theoretical analysis of near-critical temperature relaxation showing that the piston effect is not governed by one (as was until now believed) but by two typical time scales. These two time scales exhibit antagonistic asymptotic behaviors as the critical point is approached: while the classical piston-effect time scale (as predicted by Onuki ) goes to zero at the critical point (critical speeding up), the second time scale (related to bulk viscosity) goes to infinity (critical slowing down). Based on this property, an alternative method for measuring near-critical bulk viscosity is proposed.

Viscosity anomaly near the critical point in nitrobenzene + alkane binary systems

The viscosity near the critical point in nitrobenzene+hexane and nitrobenzene+heptane binary systems was studied by examining the viscosity values for critical mixtures at a variable temperature as obtained with a falling-ball viscometer. The regular part of the viscosity of the critical mixtures was calculated by interpolating measurements made at noncritical concentrations. Because viscosity anomaly studies must be conducted at zero shear, a method allowing the estimation of the effective shear for this type of viscometer was developed with a view to introducing the corrections required. This methodology was used to determine the critical exponent for the viscosity anomaly in nitrobenzene+hexane and nitrobenzene+heptane systems, which were found to be 0.0422+/-0.0004 and 0.0432+/-0.0013 , respectively, very consistent with the accepted value: 0.043.

Shear thinning of a critical viscoelastic fluid

The frequency and shear dependent critical viscosity at a correlation length xi= kappa(-1) has the form eta= eta(0) kappa(- x(eta) ) G ( z(1) , z(2) ) , where z(1) and z(2) are the independent dimensionless numbers in the problem defined as z(1) =-iomega/2 Gamma(0) kappa(3) and z(2) =-iomega/2 Gamma(0) kappa(3)(c) . The decay rate of critical fluctuations of correlation length kappa(-1) is Gamma(0) kappa(3) and k(c) is the effective wave number for which Gamma(0) k(3)(c) =S , the shear rate. The function G ( z(1) , z(2) ) is calculated in a one-loop self-consistent theory.

Critical viscosity exponent for classical fluids

A self-consistent mode-coupling calculation of the critical viscosity exponent z(eta) for classical fluids is performed by including the memory effect and the vertex corrections. The incorporation of the memory effect is through a self-consistency procedure that evaluates the order parameter and shear momentum relaxation rates at nonzero frequencies, thereby taking their frequency dependence into account. This approach offers considerable simplification and efficiency in the calculation. The vertex corrections are also demonstrated to have significant effects on the numerical value for the critical viscosity exponent, in contrast to some previous theoretical work which indicated that the vertex corrections tend to cancel out from the final result. By carrying out all of the integrations analytically, we have succeeded in tracing the origin of this discrepancy to an error in earlier work. We provide a thorough treatment of the two-term epsilon expansion, as well as a complete three-dimensional analysis of the fluctuating order-parameter and transverse hydrodynamic modes. The study of the interactions of these modes is carried out to high order so as to arrive at z(eta) = 0.0679+/-0.0007 for comparison with the experimentally observed value, 0.0690+/-0.0006 .

Thermoacoustic boundary layers near the liquid-vapor critical point

We measure and calculate the sound attenuation within thermoacoustic boundary layers between solid surfaces and xenon at its critical density rhoc as the reduced temperature tau identical with (T- Tc)/Tc approaches zero. (Tc is the critical temperature.) Using the known thermophysical properties of xenon, we predict that the attenuation at the boundary first increases approximately as tau(-0.6) and then saturates when the effusivity of the xenon exceeds that of the solid. [The effusivity is epsilon identical with (rhoCPlambdaT)(1/2), where CP is the isobaric specific heat and lambdaT is the thermal conductivity.] The model correctly predicts (+/-1.0%) the quality factors Q of resonances measured in a stainless steel resonator (epsilon(ss) =6400 kg K(-1) s(-5/2)); it also predicts the observed increase of the Q, by up to a factor of 8, when the resonator is coated with a polymer (epsilon(pr) =370 kg K(-1) s(-5/2)). The test data span the frequency range 0.1<f<7.5 kHz and the reduced temperature range 10(-3) <tau< 10(-1). We also predict that the thickness deltaT of the thermal boundary layer in the xenon decreases approximately as tau(0.4) until 2pifgammazeta/(rhoc2) approximately 0.5. (zeta is the bulk viscosity, gamma is the heat capacity ratio, and c is the speed of sound.) Still closer to Tc, deltaT becomes complex and its magnitude increases. These predictions concerning deltaT have not yet been tested. We deduce accurate values for the heat capacity CV and thermal conductivity lambdaT for xenon in the range 10(-3) <tau< 10(-1).

Molecular dynamics simulations of a fluid near its critical point

We present computer simulations for the static and dynamic behavior of a fluid near its consolute critical point. We study the Widom-Rowlinson mixture, which is a two component fluid where like species do not interact and unlike species interact via a hard core repulsion. At high enough densities this fluid exhibits a second order demixing transition that is in the Ising universality class. We find that the mutual diffusion coefficient DAB vanishes as DAB approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from renormalization-group and mode coupling theory predictions for model H, which are DAB approximately xi(-1.065) and DAB approximately xi(-1), respectively.

Critical fluctuations near the consolute point of n-pentanol-nitromethane. An ultrasonic spectrometry, dynamic light scattering, and shear viscosity study

Ultrasonic attenuation spectra, the shear viscosity, and the mutual diffusion coefficient of the n-pentanol-nitromethane mixture of critical composition have been measured at different temperatures near the critical temperature. The noncritical background contribution, proportional to frequency, to the acoustical attenuation-per-wavelength spectra has been determined and subtracted from the total attenuation to yield the critical contribution. When plotted versus the reduced frequency, with the relaxation rate of order-parameter fluctuations from the shear viscosity and diffusion coefficient measurements, the critical part in the sonic attenuation coefficient displays a scaling function which nicely fits to the data for the critical system 3-methylpentane-nitromethane and also to the empirical scaling function of the Bhattacharjee-Ferrell dynamic scaling theory. The scaled half-attenuation frequency follows from the experimental data as Omega(1/2)emp= 1.8+/-0.1. The relaxation rate of order-parameter fluctuation shows power-law behavior with the theoretically predicted universal exponent and the extraordinary high amplitude Gammao= (187+/-2) x 10(9) s(-1). The amount of the adiabatic coupling constant /g/= 0.03, as estimated from the amplitude of the critical contribution to the acoustical spectra, is unusually small.

Critical viscosity exponent for fluids: effect of the higher loops

We arrange the loopwise perturbation theory for the critical viscosity exponent x(eta), which happens to be very small, as a power series in x(eta) itself, and argue that the effect of loops beyond two is negligible. We claim that the critical viscosity exponent should be very closely approximated by x(eta)=(8/15pi(2))(1+8/3pi(2)) approximately 0.0685.

Zero-frequency critical bulk viscosity: is the amplitude ratio truly universal?

It was shown by Onuki that the zero-frequency bulk viscosity is associated with a universal amplitude ratio that was calculated to be around 0.10. We show that the sound attenuation data can be used to extract a value for this universal number and we find this number to be around 0.18, reasonably close to Onuki's estimate. However, we argue that a reconsideration of this amplitude ratio shows that this ratio is not truly universal. It has a logarithmic correction instead.

Frequency-dependent viscosity near the critical point: the scale to two-loop order

The recent accurate measurements of Berg, Moldover, and Zimmerli [Phys. Rev. Lett. 82, 920 (1999); Phys. Rev. E 60, 4079 (1999)] of the viscoelastic effect near the critical point of xenon has shown that the scale factor involved in the frequency scaling is about twice the scale factor obtained theoretically. We show that this discrepancy is a consequence of using first order perturbation theory. Including two-loop contribution goes a long way towards removing the discrepancy.

Critical light scattering in liquids

We compare theoretical results for the characteristic frequency of the Rayleigh peak calculated in one-loop order within the field theoretical method of the renormalization group theory with experiments and other theoretical results. Our expressions describe the nonasymptotic crossover in temperature, density, and wave vector. In addition we discuss the frequency dependent shear viscosity evaluated within the same model and compare our theoretical results with recent experiments in microgravity.