Frame-invariant Fick diffusion matrices of multicomponent fluid mixtures.

Extension of a description of mass diffusion in binary fluids based on Fick's law to multicomponent fluids requires introduction of diffusion matrices. A problem is that Fick diffusion matrices commonly adopted for multicomponent fluids depend on the velocity frame of reference. In this paper we show how one can define Fick diffusion matrices for multicomponent fluids that are frame invariant.

Thermal Conductivity of Metastable Ionic Liquid [C2mim][CH3SO3].

Ionic liquids have been suggested as new engineering fluids, namely in the area of heat transfer, as alternatives to current biphenyl and diphenyl oxide, alkylated aromatics and dimethyl polysiloxane oils, which degrade above 200 °C and pose some environmental problems. Recently, we have proposed 1-ethyl-3-methylimidazolium methanesulfonate, [C2mim][CH3SO3], as a new heat transfer fluid, because of its thermophysical and toxicological properties. However, there are some interesting points raised in this work, namely the possibility of the existence of liquid metastability below the melting point (303 K) or second order-disorder transitions (l-type) before reaching the calorimetric freezing point. This paper analyses in more detail this zone of the phase diagram of the pure fluid, by reporting accurate thermal-conductivity measurements between 278 and 355 K with an estimated uncertainty of 2% at a 95% confidence level. A new value of the melting temperature is also reported, Tmelt = 307.8 ± 1 K. Results obtained support liquid metastability behaviour in the solid-phase region and permit the use of this ionic liquid at a heat transfer fluid at temperatures below its melting point. Thermal conductivity models based on Bridgman theory and estimation formulas were also used in this work, failing to predict the experimental data within its uncertainty.

Unusual Transformation of Polymer Coils in a Mixed Solvent Close to the Critical Point.

We have discovered unusual behavior of polymer coils in a binary solvent (nitroethane+isooctane) near the critical temperature of demixing. The exceptionally close refractive indices of the solvent components make the critical opalescence relatively weak, thus enabling us to simultaneously observe the Brownian motion of the polymer coils and the diverging correlation length of the critical fluctuations. The polymer coils exhibit a collapse-reswelling-expansion-reshrinking transition upon approaching the critical temperature. While the first stage (collapse) can be explained by the theory of Brochard and de Gennes, the subsequent expansion-reshrinking transition is a new unexpected phenomenon that has not been observed so far. We believe that this effect is generic and attribute it to microphase separation of the solvent inside the polymer coil.

Random Field Ising Model Criticality in a Complex Binary Liquid System.

While Ising criticality in classical liquids has been firmly established both theoretically and experimentally, much less is known about criticality in liquids in which the growth of the correlation length is frustrated by finite-size effects. A theoretical approach for dealing with this issue is the random-field Ising model (RFIM). While experimental critical-exponent values have been reported for magnetic samples (here, we consider γ, ν and η), little experimental information is available for critical fluctuations in corresponding liquid systems. In this paper, we present a study on a binary liquid consisting of 3-methyl pyridine and heavy water in a very light-weight porous gel. We find that the experimental results are in agreement with the theoretical predictions from the RFIM.

Nonequilibrium velocity fluctuations and energy amplification in planar Couette flow.

In this paper we investigate intrinsic thermally excited nonequilibrium velocity fluctuations in laminar planar Couette flow. For this purpose we have complemented the solution of the stochastic Orr-Sommerfeld equation for the intensity of the fluctuations of the wall-normal velocity, presented in a previous publication, with a solution of the stochastic Squire equation for the intensity of the fluctuations of the wall-normal vorticity. We have obtained exact solutions of these equations without boundary conditions and solutions in a Galerkin approximation when appropriate boundary conditions are included. These results enable us to make a quantitative assessment of the intensity of these nonequilibrium fluctuations, as well as of the related energy amplification, which are always present, even in the absence of any externally imposed noise.

Transverse-velocity fluctuations in a liquid under steady shear.

We present an analysis of the transverse-velocity fluctuations in an isothermal liquid layer with a uniform shear rate between two parallel horizontal boundaries as a function of the wave number and the Reynolds number. The results were obtained by solving a stochastic version of the Orr-Sommerfeld equation subject to no-slip boundary conditions in a second-order Galerkin approximation. We find that the spatial Fourier transform of the transverse-velocity fluctuations exhibits a maximum as a function of the (horizontal) wave number q(parallels). This maximum is associated with a crossover from a q(parallels)(-4) dependence for larger q(parallels) to a q(parallels)(2) dependence for small q(parallels). The q(parallels)(-4) dependence at larger wave numbers is independent of the boundary conditions, but the small- q(parallels) behavior is strongly affected by the boundary conditions. The nonequilibrium enhancement of the intensity of the transverse-velocity fluctuations remains finite for all values of the Reynolds number, but increases approximately with the square of the Reynolds number. The relation between our results and those obtained by previous authors in the absence of boundary conditions is elucidated.

Principle of isomorphism and complete scaling for binary-fluid criticality.

The extension of the principle of critical-point universality to binary fluid mixtures, known as isomorphism of critical phenomena, has been reformulated in terms of complete scaling, a concept that properly matches asymmetric fluid-phase behavior with the symmetric Ising model. The controversial issue of the proper definition of the order parameter in binary fluid mixtures is clarified. We show that asymmetry of liquid-liquid coexistence in terms of mole fractions originates from two different sources: one is associated with a correlation between concentration and entropy fluctuations, whereas the other source is the correlation between concentration and density fluctuations. By analyzing the coexistence curves of liquid solutions of nitrobenzene in a series of hydrocarbons (from n -pentane to n -hexadecane), we have separated these two sources of asymmetry and found that the leading nonanalytical contribution to the asymmetry correlates linearly with the solute-solvent molecular-volume ratio. Other thermodynamic consequences of complete scaling for binary mixtures, such as an analog of the Yang-Yang anomaly in the behavior of the heat capacity and a curvature correction to the interfacial tension, are also discussed.

Mesoscopic Diffusion of Poly(ethylene oxide) in Pure and Mixed Solvents.

We present results from an experimental dynamic light-scattering study of poly(ethylene oxide) (PEO) in both a pure solvent (water) and a mixed solvent (tert-butanol + water). The concentration dependence of the diffusive relaxation of the PEO molecules is found to be typical of polymers in a good solvent. However, the mesoscopic diffusive behavior of PEO in the mixed solvent is very different, indicating an initial collapse and subsequent reswelling of PEO caused by co-nonsolvency. Furthermore, in the solutions of PEO with very large molecular weights, we found additional hydrodynamic modes indicating the presence of PEO clusters and aggregates similar to those found by some other investigators.

Comment on "Shear-induced quench of long-range correlations in a liquid mixture".

Recently, Wada [Phys. Rev. E 69, 031202 (2004)] presented an analysis of the long-range nature of concentration fluctuations in a binary liquid mixture subjected to a concentration gradient in a uniform shear flow as a function of the wave number k of the fluctuations. Specifically, he argued that the presence of a uniform shear causes the intensity of the concentration fluctuations to crossover from the well-known k(-4) dependence at large wave numbers to a k(-4/3) dependence for small wave numbers. The purpose of this comment is to point out that the wave-number dependence of the concentration fluctuations to be expected in realistic experimental conditions will be affected by gravity and finite-size effects.

Long-wavelength nonequilibrium concentration fluctuations induced by the Soret effect.

In this paper we evaluate the enhancement of nonequilibrium concentration fluctuations induced by the Soret effect when a binary fluid layer is subjected to a stationary temperature gradient. Starting from the fluctuating Boussinesq equations for a binary fluid in the large-Lewis-number approximation, we show how one can obtain an exact expression for the nonequilibrium structure factor in the long-wavelength limit for a fluid layer with realistic impermeable and no-slip boundary conditions. A numerical calculation of the wave-number dependence of the nonequilibrium enhancement and of the corresponding decay rate of the concentration fluctuations is also presented. Some physical consequences of our results are briefly discussed.

Boundary effects on the nonequilibrium structure factor of fluids below the Rayleigh-Bénard instability.

We consider a horizontal fluid layer between two rigid boundaries, maintained in a stationary thermal nonequilibrium state below the convective Rayleigh-Bénard instability. We derive an explicit expression for the nonequilibrium structure factor in a first-order Galerkin approximation valid for negative and positive Rayleigh numbers R up to the critical Rayleigh number R(c) associated with the appearance of convection. The results obtained for rigid boundaries by the Galerkin-approximation method are compared with exact results previously derived for the case of free boundaries. The nonequilibrium structure factor exhibits a maximum as a function of the wave number q of the fluctuations. This maximum is associated with a crossover from a q(-4) dependence for larger q to a q(2) dependence for small q. This maximum is present at both negative and positive R, becomes pronounced at positive R and diverges as R approaches the critical value R(c).

Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection.

We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with the mean temperature of the layer corresponding to the critical isochore of sulfur hexafluoride above but near the critical point where fluctuations are exceptionally strong. They cover a wide range of temperature gradients below the onset of Rayleigh-Bénard convection, and span wave numbers on both sides of the critical value for this onset. The decay rates were determined from experimental shadowgraph images of the fluctuations at several camera exposure times. We present a theoretical expression for an exposure-time-dependent structure factor which is needed for the data analysis. As the onset of convection is approached, the data reveal the critical slowing down associated with the bifurcation. Theoretical predictions for the decay rates as a function of the wave number and temperature gradient are presented and compared with the experimental data. Quantitative agreement is obtained if allowance is made for some uncertainty in the small spacing between the plates, and when an empirical estimate is employed for the influence of symmetric deviations from the Oberbeck-Boussinesq approximation which are to be expected in a fluid with its density at the mean temperature located on the critical isochore.

Generation of narrowly distributed ultra-high-molecular-weight polyethylene particles by surface texturing techniques.

Ultra-high-molecular-weight polyethylene (UHMWPE) wear particles have been recognized as the cause of aseptic loosening in total joint replacement. Macrophage phagocytosis of wear particles induces human biological/physiological responses which eventually lead to bone resorption and osteolysis. However, the dependence of these reactions on the size and shape of the particles has not been elucidated and is not understood. This article describes a procedure to generate narrowly distributed UHMWPE particles of controlled size and shape through surface texturing by microfabrication. The textured surface is then used to rub against the polymer pins to produce wear particles in water. The surface texture produces elongated particles or equiaxed particles by design. The distribution of the particles, due to the surface-texture control, is quite narrow as compared with randomly produced surfaces. With this technique, we are able to generate UHMWPE wear particles of different size and shape within phagocytosable and nonphagocytosable populations for biological response studies.

Thermal conductivity of supercooled water.

The heat capacity of supercooled water, measured down to -37°C, shows an anomalous increase as temperature decreases. The thermal diffusivity, i.e., the ratio of the thermal conductivity and the heat capacity per unit volume, shows a decrease. These anomalies may be associated with a hypothesized liquid-liquid critical point in supercooled water below the line of homogeneous nucleation. However, while the thermal conductivity is known to diverge at the vapor-liquid critical point due to critical density fluctuations, the thermal conductivity of supercooled water, calculated as the product of thermal diffusivity and heat capacity, does not show any sign of such an anomaly. We have used mode-coupling theory to investigate the possible effect of critical fluctuations on the thermal conductivity of supercooled water and found that indeed any critical thermal-conductivity enhancement would be too small to be measurable at experimentally accessible temperatures. Moreover, the behavior of thermal conductivity can be explained by the observed anomalies of the thermodynamic properties. In particular, we show that thermal conductivity should go through a minimum when temperature is decreased, as Kumar and Stanley observed in the TIP5P model of water. We discuss physical reasons for the striking difference between the behavior of thermal conductivity in water near the vapor-liquid and liquid-liquid critical points.

Simulating critical dynamics in liquid mixtures: short-range and long-range contributions.

Recently, Das et al. [J. Chem. Phys. 125, 024506 (2006)] established that computer simulations of critical dynamics in a binary Lennard-Jones mixture are consistent with the predicted Stokes-Einstein behavior of the asymptotic decay rate of the order-parameter fluctuations near criticality. Here, we show that the noncritical or "background" contributions to the computed diffusion coefficient are also in agreement with both theory and experiment, thus further validating the feasibility of molecular dynamics simulations for studying dynamic critical behavior.

Concentration fluctuations in nonisothermal reaction-diffusion systems.

In this paper a simple reaction-diffusion system, namely a binary fluid mixture with an association-dissociation reaction between the two components, is considered. Fluctuations at hydrodynamic spatiotemporal scales when a temperature gradient is present in this chemically reacting system are studied. First, fluctuating hydrodynamics when the system is in global equilibrium (isothermal) is reviewed. Comparing the two cases, an enhancement of the intensity of concentration fluctuations in the presence of a temperature gradient is predicted. The nonequilibrium concentration fluctuations are spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a proportional, variantq(-4) to a proportional, variantq(-2) behavior depending on whether the corresponding wavelength is smaller or larger than the penetration depth of the reacting mixture. This opens a possibility to distinguish between diffusion- or activation-controlled regimes of the reaction by measuring these fluctuations. In addition, the possible observation of these fluctuations in nonequilibrium molecular dynamics simulations is considered.

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 TT(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.

Critical dynamics in a binary fluid: simulations and finite-size scaling.

We report comprehensive simulations of the critical dynamics of a symmetric binary Lennard-Jones mixture near its consolute point. The self-diffusion coefficient exhibits no detectable anomaly. The data for the shear viscosity and the mutual-diffusion coefficient are fully consistent with the asymptotic power laws and amplitudes predicted by renormalization-group and mode-coupling theories provided finite-size effects and the background contribution to the relevant Onsager coefficient are suitably accounted for. This resolves a controversy raised by recent molecular simulations.