Nonequilibrium Casimir pressures in liquids under shear.

In stationary nonequilibrium states coupling between hydrodynamic modes causes thermal fluctuations to become long ranged inducing nonequilibrium Casimir pressures. Here we consider nonequilibrium Casimir pressures induced in liquids by a velocity gradient. Specifically, we have obtained explicit expressions for the magnitude of the shear-induced pressure enhancements in a liquid layer between two horizontal plates that complete and correct results previously presented in the literature. In contrast to nonequilibrium Casimir pressures induced by a temperature or concentration gradient, we find that in shear nonequilibrium contributions from short-range fluctuations are no longer negligible. In addition, it is noted that currently available computer simulations of model fluids in shear observe effects from molecular correlations at nanoscales that have a different physical origin and do not probe shear-induced pressures resulting from coupling of long-wavelength hydrodynamic modes. Even more importantly, we find that in actual experimental conditions, shear-induced pressure enhancements are caused by viscous heating and not by thermal velocity fluctuations. Hence, isothermal computer simulations are irrelevant for the interpretation of experimental shear-induced pressure enhancements.

Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations.

Work fluctuations and work probability distributions are fundamentally different in systems with short-ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with short-ranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet, well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behavior of the work probability distribution and the associated fluctuations is presented.

Contrasting Work Fluctuations and Distributions in Systems with Short-Range and Long-Range Correlations.

It is shown that the work fluctuations and work distribution functions are fundamentally different in systems with short-range versus long-range correlations. The two cases considered with long-range correlations are magnetic work fluctuations in an equilibrium isotropic ferromagnet and work fluctuations in a nonequilibrium fluid with a temperature gradient. The long-range correlations in the former case are due to equilibrium Goldstone modes, while in the latter they are due to generic nonequilibrium effects. The magnetic case is of particular interest, since an external magnetic field can be used to tune the system from one with long-range correlations to one with only short-range correlations. It is shown that in systems with long-range correlations the work distribution is extraordinarily broad compared to systems with only short-range correlations. Surprisingly, these results imply that fluctuation theorems such as the Jarzynski fluctuation theorem are more useful in systems with long-range correlations than in systems with short-range correlations.

Non-local fluctuation phenomena in liquids.

Fluids in non-equilibrium steady states exhibit long-range fluctuations which extend over the entire system. They can be described by non-equilibrium thermodynamics and fluctuating hydrodynamics that assume local equilibrium for the thermophysical properties as a function of space and time. The experimental evidence for the consistency between this assumption of local equilibrium in the equations and the non-local fluctuation phenomena observed is reviewed.

Work, work fluctuations, and the work distribution in a thermal nonequilibrium steady state.

Long-ranged correlations generically exist in nonequilibrium fluid systems. In the case of a nonequilibrium steady state caused by a temperature gradient, the correlations are especially long-ranged and strong. The anomalous light scattering predicted to exist in these systems is well-confirmed by numerous experiments. Recently, the Casimir force or pressure due to these fluctuations or correlations has been discussed in great detail. In this paper, the notion of a Casimir work is introduced, and an alternative way to measure the nonequilibrium Casimir force is suggested. In particular, the nonequilibrium Casimir force is related to nonequilibrium heat, and not, as in equilibrium, to a volume derivative of an average energy. The nonequilibrium work fluctuations are determined and shown to be very anomalous compared to equilibrium work fluctuations. The nonequilibrium work distribution is also computed, and it is contrasted with work distributions in systems with short-range correlations. Again, there is a striking difference in the two cases. Formal theories of work and work distributions in nonequilibrium steady states are not explicit enough to illustrate any of these interesting features.

Nonequilibrium fluctuation-induced Casimir pressures in liquid mixtures.

In this article we derive expressions for Casimir-like pressures induced by nonequilibrium concentration fluctuations in liquid mixtures. The results are then applied to liquid mixtures in which the concentration gradient results from a temperature gradient through the Soret effect. A comparison is made between the pressures induced by nonequilibrium concentration fluctuations in liquid mixtures and those induced by nonequilibrium temperature fluctuations in one-component fluids. Some suggestions for experimental verification procedures are also presented.

Physical origin of nonequilibrium fluctuation-induced forces in fluids.

Long-range thermal fluctuations appear in fluids in nonequilibrium states leading to fluctuation-induced Casimir-like forces. Two distinct mechanisms have been identified for the origin of the long-range nonequilibrium fluctuations in fluids subjected to a temperature or concentration gradient. One is a coupling between the heat or mass-diffusion mode with a viscous mode in fluids subjected to a temperature or concentration gradient. Another one is the spatial inhomogeneity of thermal noise in the presence of a gradient. We show that in fluids fluctuation-induced forces arising from mode coupling are several orders of magnitude larger than those from inhomogeneous noise.

Non-equilibrium concentration fluctuations in binary liquids with realistic boundary conditions.

Because of the spatially long-ranged nature of spontaneous fluctuations in thermal non-equilibrium systems, they are affected by boundary conditions for the fluctuating hydrodynamic variables. In this paper we consider a liquid mixture between two rigid and impervious plates with a stationary concentration gradient resulting from a temperature gradient through the Soret effect. For liquid mixtures with large Lewis and Schmidt numbers, we are able to obtain explicit analytical expressions for the intensity of the non-equilibrium concentration fluctuations as a function of the frequency ω and the wave number q of the fluctuations. In addition we elucidate the spatial dependence of the intensity of the non-equilibrium fluctuations responsible for a non-equilibrium Casimir effect.

Nonequilibrium Casimir-like Forces in Liquid Mixtures.

In this Letter, we consider a liquid mixture confined between two thermally conducting walls subjected to a stationary temperature gradient. While in a one-component liquid nonequilibrium fluctuation forces appear inside the liquid layer, nonequilibrium fluctuations in a mixture induce a Casimir-like force on the walls. The physical reason is that the temperature gradient induces large concentration fluctuations through the Soret effect. Unlike temperature fluctuations, nonequilibrium concentration fluctuations are also present near a perfectly thermally conducting wall. The magnitude of the fluctuation-induced Casimir force is proportional to the square of the Soret coefficient and is related to the concentration dependence of the heat and volume of mixing.

Fluctuation-induced pressures in fluids in thermal nonequilibrium steady states.

Correlations in fluids in nonequilibrium steady states are long range. Hence, finite-size effects have important consequences in the nonequilibrium thermodynamics of fluids. One consequence is that nonequilibrium temperature fluctuations induce nonequilibrium Casimir-like pressures proportional to the square of the temperature gradient. Hence, fluctuations cause a breakdown of the concept of local thermal equilibrium. Furthermore, transport coefficients become dependent on boundary conditions and on gravity. Thus nonequilibrium fluctuations affect some traditional concepts in nonequilibrium thermodynamics.

Communication: minimum in the thermal conductivity of supercooled water: a computer simulation study.

We report the results of a computer simulation study of the thermodynamic properties and the thermal conductivity of supercooled water as a function of pressure and temperature using the TIP4P-2005 water model. The thermodynamic properties can be represented by a two-structure equation of state consistent with the presence of a liquid-liquid critical point in the supercooled region. Our simulations confirm the presence of a minimum in the thermal conductivity, not only at atmospheric pressure, as previously found for the TIP5P water model, but also at elevated pressures. This anomalous behavior of the thermal conductivity of supercooled water appears to be related to the maximum of the isothermal compressibility or the minimum of the speed of sound. However, the magnitudes of the simulated thermal conductivities are sensitive to the water model adopted and appear to be significantly larger than the experimental thermal conductivities of real water at low temperatures.

Giant Casimir effect in fluids in nonequilibrium steady states.

In this Letter, we consider the fluctuation-induced force exerted between two plates separated by a distance L in a fluid with a temperature gradient. We predict that for a range of distances L, this nonequilibrium force is anomalously large compared to other Casimir forces. The physical reason is that correlations in a nonequilibrium fluid are generally of longer range than other correlations, even than those near an equilibrium critical point. This giant Casimir force is related to a divergent Burnett coefficient that characterizes an Onsager cross effect between the pressure and the temperature gradient. The predicted Casimir force should be detectable with currently available experimental techniques.

Thermodynamics of supercooled water.

We review the available experimental information on the thermodynamic properties of supercooled water and demonstrate the possibility of modeling these thermodynamic properties on a theoretical basis. We show that by assuming the existence of a liquid-liquid critical point in supercooled water, the theory of critical phenomena can give an accurate account of the experimental thermodynamic-property data up to a pressure of 150 MPa. In addition, we show that a phenomenological extension of the theoretical model can account for all currently available experimental data in the supercooled region, up to 400 MPa. The stability limit of the liquid state and possible coupling between crystallization and liquid-liquid separation are also discussed. It is concluded that critical-point thermodynamics describes the available thermodynamic data for supercooled water within experimental accuracy, thus establishing a benchmark for further developments in this area.

Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case.

In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gradient, while still being far away from any chemical instability. This study extends the analysis in our first paper on the subject [J. M. Ortiz de Zárate, J. V. Sengers, D. Bedeaux, and S. Kjelstrup, J. Chem. Phys. 127, 034501 (2007)], where we considered fluctuations in a non-isothermal reaction-diffusion system but still close to equilibrium. The present extension is based on mesoscopic non-equilibrium thermodynamics that we recently developed [D. Bedeaux, I. Pagonabarraga, J. M. Ortiz de Zárate, J. V. Sengers, and S. Kjelstrup, Phys. Chem. Chem. Phys. 12, 12780 (2010)] to derive the law of mass action and fluctuation-dissipation theorems for the random contributions to the dissipative fluxes in the nonlinear macroscopic description. Just as for non-equilibrium fluctuations close to equilibrium, we again find an enhancement of the intensity of the concentration fluctuations in the presence of a temperature gradient. The non-equilibrium concentration fluctuations are in both cases spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a ∝q(-4) to a ∝q(-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 experimentally. The important conclusion overall is that non-equilibrium fluctuations in non-isothermal reaction-diffusion systems are always long ranged.

Critical behavior of the dielectric constant in asymmetric fluids.

By applying a thermodynamic theory that incorporates the concept of complete scaling, we derive the asymptotic temperature dependence of the critical behavior of the dielectric constant above the critical temperature along the critical isochore and below the critical temperature along the coexistence curve. The amplitudes of the singular terms in the temperature expansions are related to the changes of the critical temperature and the critical chemical potential upon the introduction of an electric field. The results of the thermodynamic theory are then compared with the critical behavior implied by the classical Clausius-Mossotti approximation. The Clausius-Mossotti approximation fails to account for any singular temperature dependence of the dielectric constant above the critical temperature. Below the critical temperature it produces an apparent asymmetric critical behavior with singular terms similar to those implied by the thermodynamic theory, but with significantly different coefficients. We conclude that the Clausius-Mossotti approximation only can account for the observed asymptotic critical behavior of the dielectric constant when the dependence of the critical temperature on the electric field is negligibly small.

Mesoscopic non-equilibrium thermodynamics of non-isothermal reaction-diffusion.

We show how the law of mass action can be derived from a thermodynamic basis, in the presence of temperature gradients, chemical potential gradients and hydrodynamic flow. The solution gives the law of mass action for the forward and the reverse contributions to the net chemical reaction. In addition we derive the fluctuation-dissipation theorem for the fluctuating contributions to the reaction rate, heat flux and mass fluxes. All these results arise without any other assumptions than those which are common in mesoscopic non-equilibrium thermodynamics; namely quasi-stationary transport across a high activation energy barrier, and local equilibrium along the reaction coordinate. Arrhenius-type behaviour of the kinetic coefficients is recovered. The thermal conductivity, Soret coefficient and diffusivity are significantly influenced by the presence of a chemical reaction. We thus demonstrate how chemical reactions can be fully reconciled with non-equilibrium thermodynamics.

Asymmetric criticality in weakly compressible liquid mixtures.

The thermodynamics of asymmetric liquid-liquid criticality is updated by incorporating pressure effects into the complete-scaling formulation earlier developed for incompressible liquid mixtures [C. A. Cerdeirina et al., Chem. Phys. Lett. 424, 414 (2006); J. T. Wang et al., Phys. Rev. E 77, 031127 (2008)]. Specifically, we show that pressure mixing enters into weakly compressible liquid mixtures as a consequence of the pressure dependence of the critical parameters. The theory is used to analyze experimental coexistence-curve data in the mole fraction-temperature, density-temperature, and partial density-temperature planes for a large number of binary liquid mixtures. It is shown how the asymmetry coefficients in the scaling fields are related to the difference in molecular volumes of the two liquid components. The work resolves the question of the so-called "best order parameter" discussed in the literature during the past decades.

Phenomenological description of phase inversion.

We propose an extended Ginzburg-Landau model for a description of the ambivalence region associated with the phenomenon of phase inversion observed in dispersed water-oil flow through a pipe. In analogy to the classical mean-field theory of phase transitions, it is shown that a good quantitative representation of the ambivalence region is obtained by using the injected phase volume fraction and a friction factor as the appropriate physical parameters.

Dynamics of critical fluctuations in polymer solutions.

Using dynamic light scattering we have investigated the time dependence of fluctuations near the critical point of phase separation in solutions of polystyrene in cyclohexane with polymer molecular weights ranging from 196,000 to 11.4 x 10(6) g mol(-1). At the lowest polymer molecular weight the dynamic correlation function follows a single-exponential decay with a decay rate that can be represented by the mode-coupling theory of critical dynamics but with a mesoscopic viscosity that characterizes the hydrodynamic environment of the polymers in the solution. At all higher polymer molecular weights two distinct dynamic modes are observed, a slow and a fast mode, that originate from a coupling of the critical concentration fluctuations with viscoelastic relaxation of the polymer chain in solutions. This coupling causes an additional slowing down of the fluctuations on top of the well-known critical slowing down expected in the absence of a coupling between the two modes. From an analysis of the time dependence of the experimental dynamic correlation functions in terms of a theory of coupling of dynamic modes we are able to determine the viscoelastic properties of the polymers in the solution. These viscoelastic properties diverge in the theta-point limit of infinite polymer molecular weight.

Competition of mesoscales and crossover to theta-point tricriticality in near-critical polymer solutions.

The approach to asymptotic critical behavior in polymer solutions is governed by a competition between the correlation length of critical fluctuations diverging at the critical point of phase separation and an additional mesoscopic length scale, the radius of gyration. In this paper we present a theory for crossover between two universal regimes: a regime with Ising (fluctuation-induced) asymptotic critical behavior, where the correlation length prevails, and a mean-field tricritical regime with theta-point behavior controlled by the mesoscopic polymer chain. The theory yields a universal scaled description of existing experimental phase-equilibria data and is in excellent agreement with our light-scattering experiments on polystyrene solutions in cyclohexane with polymer molecular weights ranging from 2 x 10(5) up to 11.4 x 10(6). The experiments demonstrate unambiguously that crossover to theta-point tricriticality is controlled by a competition of the two mesoscales. The critical amplitudes deduced from our experiments depend on the polymer molecular weight as predicted by de Gennes [Phys. Lett. 26A, 313 (1968)]. Experimental evidence for the presence of logarithmic corrections to mean-field tricritical theta-point behavior in the molecular-weight dependence of the critical parameters is also presented.