Abstract The Soret effect describes diffusive motion that originates from a temperature gradient. It is observed in mixtures of gases, liquids and even solids. Although there is a formal phenomenological description based on linear nonequilibrium thermodynamics, the Soret effect is a multicause phenomenon and there is no univocal microscopic picture. After a brief historical overview and an outline of the fundamental thermodynamic concepts, this review focuses on thermodiffusion in binary and ternary liquid mixtures. The most important experimental techniques used nowadays are introduced. Then, a modern development in studying thermal diffusion, the discovery of both integral and specific additivity laws, is discussed. The former relate to the general behavior of the substances in a temperature field according to their thermophobicities, which prove to be pure component properties. The thermophobicities allow for a convenient classification of the phenomenon, a simple interpretation and a proper estimation and prediction of the thermodiffusion parameters. The specific laws relate to the additivity of the particular contributions. Among the latter, we discuss the isotopic Soret effect and the so-called chemical contribution. From the theoretical side, there are kinetic and thermodynamic theories, and the nature of the driving forces of thermodiffusion can be either of volume or surface type. Besides analytical models, computer simulations become increasingly important. Polymer solutions are special as they represent highly asymmetric molecular systems with a molar mass-independent thermophoretic mobility. Its origin is still under debate, and draining and non-draining models are presently discussed. Finally, some discussion is devoted to ternary mixtures, which only recently have been investigated in more detail.

The Soret Effect in Liquid Mixtures – A Review

With the aim of providing reliable benchmark values, we have measured the Soret, diffusion and thermal diffusion coefficients of the three binary mixtures of dodecane, isobutylbenzene and 1,2,3,4 tetrahydronaphthalene for a concentration of 50 wt% at a temperature of 25°C. The experimental techniques applied by the five participating laboratories are transient holographic gratings, annular and parallelepipedic thermogravitational columns, and vertical parallelepipedic columns with velocity amplitude determination by laser doppler velocimetry. The systems have also been studied in a annular thermogravitational column filled with a porous medium in the gap. There is a good agreement between the different experiments with deviations of the order of a few per cent in most cases (8.5% at most). The numerical values are tabulated in the paper.

Benchmark values for the Soret, thermal diffusion and diffusion coefficients of three binary organic liquid mixtures

Soret coefficients of the ternary system of poly(ethylene oxide) in mixed water/ethanol solvent were measured over a wide solvent composition range by means of thermal diffusion forced Rayleigh scattering. The Soret coefficient S(T) of the polymer was found to change sign as the water content of the solvent increases with the sign change taking place at a water mass fraction of 0.83 at a temperature of 22 degrees C. For high water concentrations, the value of S(T) of poly(ethylene oxide) is positive, i.e., the polymer migrates to the cooler regions of the fluid, as is typical for polymers in good solvents. For low water content, on the other hand, the Soret coefficient of the polymer is negative, i.e., the polymer migrates to the warmer regions of the fluid. Measurements for two different polymer concentrations showed a larger magnitude of the Soret coefficient for the smaller polymer concentration. The temperature dependence of the Soret coefficient was investigated for water-rich polymer solutions and revealed a sign change from negative to positive as the temperature is increased. Thermodiffusion experiments were also performed on the binary mixture water/ethanol. For the binary mixtures, the Soret coefficient of water was observed to change sign at a water mass fraction of 0.71. This is in agreement with experimental results from the literature. Our results show that specific interactions (hydrogen bonds) between solvent molecules and between polymer and solvent molecules play an important role in thermodiffusion for this system.

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Sign change of the Soret coefficient of poly(ethylene oxide) in water/ethanol mixtures observed by thermal diffusion forced Rayleigh scattering

A formalism based on powerful concepts of the thermodynamics of irreversible processes is derived for calculating multicomponent diffusion flux both at the critical point and away from the critical point. The derivations are based on the entropy balance expression combined with the phenomenological equations and Onsager reciprocal relations. The formalism results in a clear expression of the thermal contribution in the diffusion flux for nonideal multicomponent mixtures. The diffusion flux analysis at the critical point showed that, unlike isothermal and isobaric conditions where molecular diffusion flux is zero, molecular diffusion flux is finite and nonzero at the critical point. The thermal contribution in the diffusion flux is also finite at the critical point in multicomponent mixtures. At nonisothermal conditions, as well as nonisothermal and nonisobaric conditions, the composition gradient reaches infinity at the critical point; therefore, the mol fraction plot vs. spatial coordinates has an inflection point.

Molecular, pressure, and thermal diffusion in nonideal multicomponent mixtures

Thermal diffusion coefficients in three ternary mixtures are measured in a thermogravitational column One of the mixtures consists of one normal alkane and two aromatics (dodecane-isobutylbenzene-tetrahydronaphthalene), and the other two consist of two normal alkanes and one aromatic (octane-decane-1-methylnaphthalene) This is the first report of measured thermal diffusion coefficients (for all species) of a ternary nonelectrolyte mixture in literature The results in ternary mixtures of octane-decane-1-methylnaphthalene show a sign change of the thermal diffusion coefficient for decane as the composition changes, despite the fact that the two normal alkanes are similar In addition to thermal diffusion coefficients, molecular diffusion coefficients are also measured for three binaries and one of the ternary mixtures The open-end capillary-tube method was used in the measurement of molecular diffusion coefficients The molecular and thermal diffusion coefficients allow the estimation of thermal diffusion factors in binary and ternary mixtures However, in the ternaries one also has to calculate phenomenological coefficients from the molecular diffusion coefficients A comparison of the binary and ternary thermal diffusion factors for the mixtures comprised of octane-decane-1-methylnaphthalene reveals a remarkable difference in the thermal diffusion behavior in binary and ternary mixtures

Measurements of molecular and thermal diffusion coefficients in ternary mixtures

Soret effects in ternary systems heated from below

On s'interesse a la transition repos-convection d'une couche horizontale d'un melange polynaire chauffee par le bas (configuration de Rayleigh-Benard). Une etude theorique de stabilite lineaire de l'etat de repos, pour des conditions aux limites de parois libres, permeables et conductrices nous donne l'ecart de temperature critique (ΔT crit ) et la periode critique (π crit ) au debut de la transition repos-convection. D'un autre cote on a realise des experiences, sur un melange ternaire, a l'aide d'un interferometre differentiel, qui ont aussi fourni ces nombres critiques. On compare ces deux resultats et on suggere differentes sources d'erreur

J. P. Larre

Papers

Soret effects in ternary systems heated from below

Convection thermique en milieu fluide dans un mélange polynaire