Volume 32, Issue 3

This issue of the Journal of Non-Equilibrium Thermodynamics is devoted to papers presented at the Seventh International Meeting on Thermodiffusion (IMT7), held in San Sebastian, Spain, May 29 to June 2, 2006.

We present measurements of aqueous low molecular weight mixtures and aqueous macromolecular solutions. The Soret coefficient S T for ethanol, acetone, and DMSO in water was measured by an optical grating technique, and all systems showed a sign change around a molar fraction of water x water = 0.85 ± 0.05. S T for poly(ethylene oxide), poly(N-isopropylacrylamide), and boehmite rods in ethanol/water mixtures showed also a sign change close to the same concentration. The occurring sign change concentration in the systems will be related to structural reorganizations in the solvent mixture and the Hildebrandt solubility parameter. We will also compare the experimental data within lattice calculations and simulations, which indicate that strong cross-interactions are important for a sign change of the Soret coefficient.

We consider a system that consists of a layer of an incompressible binary liquid with a deformable free surface, and a solid substrate layer heated or cooled from below. The surface tension is assumed to depend linearly on both the temperature and the solute concentration. The Soret effect is taken into account. We investigate the long-wave Marangoni instability in the case of asymptotically small Lewis and Galileo numbers for finite surface tension and Biot numbers. We find both long-wave monotonic and oscillatory modes of instability in various parameter domains of the Biot and the Soret number. The weakly nonlinear analysis is carried out in the case of a specified heat flux at the rigid substrate.

Convective instabilities in side-heated infinite vertical slots containing a single fluid are stationary, shear driven when the Prandtl number Pr 12.5 while they are oscillatory, buoyancy dominated with Pr 12.5 due to the diminished influence of the thermal diffusivity with increasing Pr . Here we examine the influence of the concentration field generated by thermodiffusion in a binary mixture of otherwise uniform concentration on this phenomenon in a thermogravitational column. While positive/negative separation corresponds to enhanced/diminished buoyancy and should promote instability/stability, the induced positive/negative vertical concentration gradient of the light component, i.e., stable/unstable stratification, and the nonmonotonic horizontal species separation demanded by the vanishing vertical mass flux, combine to result in the opposite effect. Thus increasing/decreasing the separation ratio ε is found to stabilize/destabilize both instability branches so that the cut-off Pr where there is a switch from preferred stationary to oscillatory states is a monotonic increasing function of ε.

Thermophoresis (particle motion driven by a temperature gradient) is envisioned here as the ensemble-averaged motion of a Brownian particle in a bathing medium of nonuniform temperature. The theory of Brownian motion pertinent to colloids is reviewed and adapted to the case of a nonuniform temperature field. The thermophoretic velocity of the Brownian particle is not proportional to the force undergone by the particle, but contains a significant additive correction pushing the particle toward regions of lower friction. The correction is independent of the precise nature of the force. The physicochemical nature of the force is briefly discussed.

The effect of nonlinear concentration profiles on the flow patterns of solutal Rayleigh–Bénard–Marangoni convection has been investigated. It has been demonstrated theoretically that similar to the effect of non-Boussinesq fluids in Rayleigh–Bénard convection, the effect of nonlinear concentration profiles in Rayleigh–Bénard–Marangoni convection gives rise to the formation of hexagonal convection.

An accurate thermodiffusion model is of paramount importance to the petroleum industry for the prediction of the compositional variation in hydrocarbon reservoirs. As the most recent theoretical development, Kempers and Firoozabadi models can be used for both binary and multicomponent mixtures. In this paper, we verified these models with three ternary hydrocarbon mixtures. The results reveal that the accuracy of the thermal diffusion coefficients relies on the accuracy of the thermodynamic properties from equations of state, corresponding Fick's diffusion coefficients, and the thermal diffusion modeling.

The scope of this study is to improve the understanding of the thermal diffusion process on a microscopic scale by studying the mass effect on thermal diffusion factors. To achieve such a goal, non-equilibrium molecular dynamics simulations are performed on binary mixtures of simple Lennard–Jones spheres for a large range of thermodynamic states. Mixtures for which only the mass between species differs, up to mass ratios of 50, are analysed (isotope-like mixtures). In equimolar mixtures, it is shown that the link between the thermal diffusion factors and the ratio between the difference in masses and the sum of masses holds approximately for all states studied. In addition, it is found that this link strongly depends on density but weakly on temperature. In nonequimolar mixtures, results indicate that the effect of the mass ratio between species depends on the molar fraction. Using the data computed, a simple density-dependent correlation is proposed to quantify the mass effect in Lennard-Jones binary mixtures. Finally, it is shown that, taking into account only the mass effect, this correlation is able to provide a reasonable estimation of thermodiusion in n -pentane/ n -decane mixtures, which underlines the intrinsic weakness of some of the usual thermodynamic models predicting thermodiffusion.

Three-dimensional time-dependent numerical calculations are performed in a cubic cell filled with a binary mixture of water (90%) and isopropanol (10%). The system is heated from above while the Soret coefficient ( S T ) is negative, i.e., a thermally stable Rayleigh-Benard configuration. Due to the Soret effect, the heavier liquid is accumulated on the top of the lighter one and buoyant convection can be initiated. We report the numerical value of critical solutal Rayleigh number Ra s ≈ 16200 at which motion starts in a cubic cell. The flow has a finger (or columnar) structure where the major mass flux is concentrated near the center line. Later in time, this columnar structure diffuses in the horizontal direction. The development of the motion is shown through the evolution of 3D flow patterns. The upward or downward direction of the flow along the center line depends on the applied temperature difference. We attribute the change in direction of the motion to the finite size of the system and to the features of Rayleigh–Benard convection in a cubic cell.

Forced Rayleigh scattering (FRS) is a powerful technique for investigating heat and mass transfers in colloids. In the present work, we determine the Soret coefficient S T and the thermal diffusion coefficient D T of magnetic colloids (ferrofluids). It has been theoretically predicted that the thermal diffusion coefficient D T of colloids depends both on the particle–solvent interfacial interaction and on the interactions between the colloidal particles. In order to understand the microscopic behavior of the Soret effect in these ionic magnetic colloids, experiments are performed on aqueous samples of various volume fractions Φ and ionic strengths. The dominant effect on the Soret coefficient comes from the particle–solvent interaction and determines its sign. Interparticle interactions have an influence on S T in the moderate concentration range where virial-like expansions are possible. In this range (Φ ≤ 0.10) and within the experimental error bars, the thermal diffusion does not depend on the ionic strength of the dispersion, and the Φ-dependence of the friction coefficient is comparable to that of hard spheres. At larger concentrations, the thermal diffusion drastically decreases as the colloid approaches its dynamical glass transition.

Over the last six years, we have published a series of papers developing a hydrodynamic model of thermodiffusion in liquids and liquid mixtures. Initial work focused on the movement of polymers dissolved in nonpolar solvents arising from the pressure gradient induced by asymmetry in polymer–solvent interactions as a result of the temperature-induced concentration gradient in the solvent. As that model was refined, we examined secondary effects of a macroscopic pressure gradient in the solvent, and finally extended our hydrodynamic approach to cross-diffusion and thermodiffusion in solvent mixtures. Application of the model is currently limited to non-ionic liquids, where molecular interaction energies can be estimated by Hamaker constants or similar parameters. In this paper we present the body of work as a whole, in order to ensure a consistent nomenclature and unify the model for application to liquid mixtures in general. To test the model, values of Soret coefficients for mixtures of toluene and n -hexane have been calculated using parameters in the literature.

Many studies have been made on species separation in thermogravitational columns. All the analytical modelling resolutions developed so far for parallelepipedic columns take only into account the thickness e and the height h of the cavity when the experimental work concerns obviously three-dimensional cavities. We propose a study of the fluid behaviour and the resulting species separation taking into account the width b . The system of three-dimensional modelling equations is integrated using the usual geometric conditions of thermal diffusion columns ( h ≫ e ). The width influence on velocity profiles is validated by comparison with experimental measurements made with the PIV (particle image velocimetry) technique. The analytical solution proposed gives temperature and velocity profiles and the whole concentration distribution within the cavity. It appears that the use of small width cavities generates higher species separation than those predicted with classical two-dimensional approaches. A simple correlation between this deviation and the transversal aspect ratio e/b is proposed.

By measuring the mass fraction difference between the top and the bottom of a thermogravitational column as a function of time, we show that this transient evolution of the separation toward its steady value gives the isothermal mass diffusion coefficient, at least in the validity limit of the Furry–Jones–Onsager theory, whereas the final steady separation produces the thermodiffusion coefficient. The following mixtures have been considered: water–ethanol (39.12 wt% ethanol), toluene–hexane (51.7 wt% toluene), and the three systems of the so-called “benchmark of Fontainebleau”, which are the three binaries composed of isobutylbenzene and/or dodecane and/or 1,2,3,4 tetrahydronaphthalene (50 wt% in each component for each case). The obtained results indicate that reliable values of the isothermal diffusion coefficient can be determined by using the thermogravitational method.

In this work, the thermogravitational technique has been used to determine the thermodiffusion coefficient of 18 binary mixtures of normal alkanes formed with the n -octadecane as the densest component and mixed with normal alkanes from n -pentane to n -tridecane in two series of experimental tests (nine binary mixtures with mass fraction c = 0.5 and nine binary mixtures with molar fraction x = 0.5 in each component for each mixture). The measurement of the steady separation of these mixtures in the thermogravitational column, as well as their corresponding thermophysical properties, has been determined at the average temperature of 25°C. The main result shows a linear dependency of the thermodiffusion coefficient on the relative density difference, and this in both series of experimental tests (mass and molar fraction equal to 0.5).

Thermal fluctuations in fluids and fluid mixtures in stationary non-equilibrium states are spatially long ranged. This long-ranged nature of the non-equilibrium fluctuations is caused by a coupling between hydrodynamic modes through the non-equilibrium fluxes or gradients. The phenomena are discussed with some illustrative examples in fluids and fluid mixtures.

In the present work, attention is paid to some significant effects (phenomena) in forced Rayleigh scattering (FRS) experiments with an applied magnetic field, ∇ T ∥ H , which have not been analyzed before. The work deals with the idea that the experimentally observed effects are caused by microconvection. The dimensionless numbers Cm and Rm , which are responsible for the onset of microconvection, are calculated from experiments as well as from the linear stability analysis in a Hele-Shaw approximation. The problem of definition of the true values of diffusion and Soret coefficients from experiments and their field dependence, which are not affected by the assumed microconvection, is solved by original data processing.

We study a reacting mixture (2F ↔ F2) in a temperature gradient. We had previously used boundary-driven non-equilibrium molecular dynamics (NEMD) simulations to study this system, and found that the reaction was close to local chemical equilibrium in temperature gradients up to 10 12 K/m. Using the condition of local chemical equilibrium, we show that the heat of transfer of the reacting mixture is equal to minus the enthalpy of the reaction. The fact that the sign of the heat of transfer is determined by the type of reaction adds insight to the discussion of the origin of the sign.