Determination of the thermodiffusion coefficient in three binary organic liquid mixtures by the thermogravitational method (contribution of the Universidad del País Vasco,Bilbao, to the benchmark test)

Within the framework of an international benchmark test, the thermodiffusion coefficients D T of the three binary systems formed with dodecane, isobutylbenzene and 1,2,3,4-tetrahydronaphthalene (with a mass fraction of 0.5 for each component at a temperature of 25C) have been measured. Convective coupling in cylindrical thermogravitational columns has been used to determine D T based on the Furry-Jones-Onsager theory. For each system, several columns with different gaps and heights were employed. Our results for these three coefficients are in good agreement with those obtained by other benchmark tests; the maximum deviation from the proposed benchmark values is 8.5%, which is not too bad owing to the difficulties of measuring a thermodiffusion coefficient.     

Precise determination of the Soret,thermal diffusion and mass diffusion coefficients of binary mixtures of dodecane,isobutylbenzene and 1,2,3,4-tetrahydronaphthalene by a holographic grating technique

Within the framework of an international benchmark test, the Soret coefficient S T , thermal diffusion coefficient D T and mutual mass diffusion coefficient D of the three binary mixtures of dodecane, isobutylbenzene and 1,2,3,4-tetrahydronaphthalene with a concentration of 50 wt% of each component at a temperature of 25C have been measured with a holographic grating technique. For the analysis of the experimental data a new numerical correction algorithm based on linear response theory has been employed. The corrections applied are on the order of 1% for S T and 5% for D . The coefficients S T , D and D T are determined with relative errors of a few per cent.     

Investigation of the Soret effect in binary liquid mixtures by thermal-diffusion-forced Rayleigh scattering (contribution to the benchmark test)

Within the framework of an international benchmark test we have performed measurements of the transport coefficients S T (Soret coefficient), D (mutual diffusion coefficient) and D T (thermal diffusion coefficient) on the three binary organic liquid mixtures 1,2,3,4-tetrahydronaphthalene- n -dodecane, 1,2,3,4-tetra- hydronaphthalene-isobutylbenzene and isobutylbenzene- n -dodecane with the weight fraction c = 0.5 at T = 298.15 K by means of thermal-diffusion-forced Rayleigh scattering (TDFRS) for benchmarking purposes. Our results for the coefficients are in good agreement with those obtained by annular and parallelepipedic thermogravitational columns and by other benchmark tests which also apply TDFRS measurements.     

Transient-state method for coupled evaluation of Soret and Fick coefficients,and related tortuosity factors,using free and porous packed thermodiffusion cells: Application to CuSO4 aqueous solution ( 0.25M)

The measurement of Soret coefficients in liquids is not easy and usually not very precise because the resulting concentration gradient is small and moreover can be perturbed by undesired convection currents. In order to suppress, or to drastically reduce these convection currents, the use of a porous medium is sometimes suggested. The question arises as to whether the Soret coefficient is the same in free fluid and in porous medium. This is the aim of this paper. To this end, for a given liquid mixture, the time evolution of the vertical concentration gradient is experimentally measured in the same thermodiffusion cell filled first with the free liquid and next with a porous medium followed by saturation by the liquid mixture. Both the isothermal diffusion (Fick) coefficient and the Soret coefficient can be deduced, providing that a correct working equation is used. The proposed equation results from integration of the general mass conservation equation with realistic boundary conditions (zero mass flux at the boundaries) and some simplifying assumptions rendering this equation more tractable than the one proposed some decades ago by Bierlein (J.A. Bierlein, J. Chem. Phys. 23, 10 (1955)). The method is applied here to an electrolytic solution (CuSO4, 0.25 M) at a mean temperature of 37^°C. The Soret coefficients in free and porous medium (zircon microspheres in the range of 250- 315 ^. 10^-6m) may be considered to be equal ( S_T = 13.2±0.5 ^. 10^-3 K^-1) and the tortuosity factors for the packed medium are the same relative to thermodiffusion and Fick coefficients ( = 1.51±0.02).     

Determination of the apparent negative Soret coefficient of water-10% alcohol solutions by experimental and numerical methods in packed cells

This study presents two methods for measuring the Soret coefficient of water-alcohol mixtures (with a 10% mass fraction of alcohol: ethanol or propanol-2). These methods performed with porous packing are particularly adapted for apparent negative Soret coefficient determination (i.e. where the transport of the densest compound follows the thermal gradient inside the cell). The first method uses a flat-packed Soret cell operated under a downwards vertical thermal gradient; the second method uses a packed cylindrical thermodiffusion column (operated with an horizontal thermal gradient to yield the so-called coupling between thermodiffusion-convection) and thermogravitation. The porous packing is made of inert balls (ZrO 2 ). The porosity is about 38% and the intrinsic permeability 1.01 210 m10 m 2 or even 1.31 210 m10 m 2 . For each experiment, the time evolution of the alcohol fraction sampled at the top and bottom of the cells is checked against the numerical outputs of a thermodiffusion model: the METSOR code.     

Measuring the Soret coefficient of binary hydrocarbon mixtures in packed thermogravitational columns (contribution of Toulouse University to the benchmark test)

Within the framework of an international benchmark test, our group which researches packed thermogravitational columns has measured the porous medium thermodiffusion coefficient of two hydrocarbon binary mixtures: tetrahydronaphthalene-dodecane and tetrahydronaphthalene-isobutylbenzene. The weight fraction of each component was near 50 wt%.     

Thermodiffusion and Vaporization of Metal from Levitated Droplet V. Determination of Condensation Rate and Thermodiffusion Parameters of Mn, Fe, and Ni Vapours

In the present paper the experimental data of vaporization from levitated droplet for Mn, Co, Ni in the flow of argon obtained from the bibliography were evaluated by means of the new method published in the previous work [Czech. J. Phys. 50 (2000) 737]. The rate constants of condensation, thermodiffusion ratios, thermodiffusion coefficients and the corresponding temperature dependencies were determined together with other physical quantities for Mn vapour at the temperature 2000 K and for Fe, Ni at 2200 K. The rate constant of condensation and the thermodiffusion ratio are higher for Ni than for Fe. The value of thermodiffusion coefficient determined for Mn is rather high and the rate constant of condensation is higher than for Ni. The increase of vaporization resulting from condensation and thermodiffusion for Mn was only 2.7-times and for Fe and Ni (5.5-5.65)-times. The process of vaporization from a levitated droplet includes molecular diffusion and convective diffusion, molecular thermodiffusion with vapour condensation and condensation without thermodiffusion. The proportions of these processes were for Mn in the range (37-29) condensation dominated and its share was over 70 accurate experimental data and this is the reason why the evaluation of the Co vaporization was unsuccessful. The work also presents some proposals of experimental procedures leading to the data accuracy improvement.     

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

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 25C. 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.     

Driving forces and polymer hydrodynamics in the Soret effect

A temperature gradient induces different driving forces on the components of a mixture which translates into their segregation. We show that these driving forces constitute the physical picture behind the thermodiffusion effect, and provide an alternative expression of the Soret coefficient which can be applied to both colloidal suspensions and molecular mixtures. To verify the validity of the formalism, we quantify the related forces in an Eulerian reference frame by non-equilibrium molecular simulations. Furthermore, we present an analytical argument to show that the hydrodynamic interactions need to be accounted for to obtain the proper scaling of the thermophoretic force. This result combined with the presented expression satisfactorily explains the experimentally known size dependence of the thermodiffusion coefficient in dilute polymer solutions.     

Thermodiffusion of charged micelles

We study diffusion of charged nanoparticles in a temperature gradient and derive the corresponding Ludwig-Soret transport coefficient. Charge effects are found to enhance thermodiffusion by up to 2 orders of magnitude. We show that the inverse Soret coefficient 1/S(T) is a linear function of the colloid density n; the proportionality factor, or second virial coefficient, varies algebraically with inverse salinity, n0(-alpha); the precise value of the exponent alpha depends on the ratio of particle size and Debye length. Our findings compare favorably with experimental observations and provide, without adjustable parameters, a good fit to the data on 3-nm sodium dodecylsulfate micelles.     

New problems of particle transfer in ferrocolloids: Magnetic Soret effect and thermoosmosis

The paper deals with critical reviewing of the experiments on thermodiffusion in ferrocolloids. The observed magnetic Soret effect is much stronger than that predicted theoretically. It is shown that the main reason of that is the influence of the magnetic field on mass diffusion. Besides, some measurements are affected by uncontrolled thermal and solutal magnetic convection. In porous media, when macroscopic convection is suppressed, thermodiffusion is accompanied by thermoosmosis as well as by a microconvective mass transfer induced by particle magnetophoresis on filter grains.     

Molecular dynamics study of thermal diffusion in a binary mixture of alkanes trapped in a slit pore

We have used direct non-equilibrium molecular dynamics computer simulations to study the influence of an aluminosilicate slit pore on thermal diffusion in equimolar methane- n -decane. We have computed the Soret coefficient S T as a function of the pore width. The S T values deviate from those in a pore-free situation only for pores narrower than 35 Å. We have then investigated the possible causes for this deviation. We have noticed that the solid behaves as a thermal short circuit for the liquid but this has no consequence on the thermal and solutal profiles in the mixture. The main influence of the confinement of the liquid lies in the 'freezing' of the layer of molecules in contact with the pore walls. Outside this layer, the thermal diffusive behaviour of the mixture does not depart from that in the bulk fluid. This finding has enabled us to compute a 'corrected' Soret coefficient where the influence of the porous medium is eliminated.     

Effect of Soret diffusion on lean hydrogen/air flames at normal and elevated pressure and temperature

The influence of Soret diffusion on lean premixed flames propagating in hydrogen/air mixtures is numerically investigated with a detailed chemical and transport models at normal and elevated pressure and temperature. The Soret diffusion influence on the one-dimensional (1D) flame mass burning rate and two-dimensional (2D) flame propagating characteristics is analysed, revealing a strong dependency on flame stretch rate, pressure and temperature. For 1D flames, at normal pressure and temperature, with an increase of Karlovitz number from 0 to 0.4, the mass burning rate is first reduced and then enhanced by Soret diffusion of H₂ while it is reduced by Soret diffusion of H. The influence of Soret diffusion of H₂ is enhanced by pressure and reduced by temperature. On the contrary, the influence of Soret diffusion of H is reduced by pressure and enhanced by temperature. For 2D flames, at normal pressure and temperature, during the early phase of flame evolution, flames with Soret diffusion display more curved flame cells. Pressure enhances this effect, while temperature reduces it. The influence of Soret diffusion of H₂ on the global consumption speed is enhanced at elevated pressure. The influence of Soret diffusion of H on the global consumption speed is enhanced at elevated temperature. The flame evolution is more affected by Soret diffusion in the early phase of propagation than in the long run due to the local enrichment of H₂ caused by flame curvature effects. The present study provides new insights into the Soret diffusion effect on the characteristics of lean hydrogen/air flames at conditions that are relevant to practical applications, e.g. gas engines and turbines.     

Diffusion and thermal diffusion of semidilute to concentrated solutions of polystyrene in toluene in the vicinity of the glass transition

The approaching glass transition in polystyrene/toluene solutions leads to a sharp decay of both the collective diffusion coefficient D and the thermal diffusion coefficient D(T) at concentrations above 0.2 g/cm(3). The Soret coefficient S(T) = D(T)/D follows power-law scaling from semidilute to concentrated and is not influenced by the slowing down of the dynamics associated with the glass transition. Both D and D(T) are governed by the same friction coefficient. The scaling behavior of S(T) with concentration on approach of the glass transition is compared to the divergence of S(T) near a consolute critical point.     

Measurement of the Soret,diffusion, and thermal diffusion coefficients of three binary organic benchmark mixtures and of ethanol–water mixtures using a beam deflection technique

We have measured the Soret (S _T ), diffusion (D), and thermal diffusion (D _T ) coefficients of three binary mixtures of dodecane (DD), isobutylbenzene (IB) and 1,2,3,4-tetrahydronaphthalene (TH) for a concentration of 50 wt% at a temperature of 25°C by means of an optical beam deflection cell. This relevant experimental technique was still missing from a recent benchmark campaign for the measurement of the Soret effect. The measured coefficients agree to within a few percent (10% for S _T , D of TH/IB) with the proposed benchmark values. A detailed analysis of the measurement process of the beam deflection cell, which allows for an elegant extension to include temperature gradients within the windows, is given, and improved benchmark values are suggested. In addition, ethanol–water mixtures have been investigated very carefully over a broad concentration and temperature range. Comparison with data of Kolodner and Wiegand gives a generally good agreement with some systematic deviations. Contrary to theoretical predictions, we have not been able to identify a second sign change of S _T at high ethanol concentrations.     

Thermal diffusion in ionic micellar solutions

Thermal diffusion studies of complex fluids may have a deep impact on determining the microscopic origins of the Soret effect, allowing in particular for a clear distinction between single-particle and collective effects. We show for instance that electrostatic interactions have a dramatic influence on the thermal diffusion of charged surfactant micelles. In the dilute regime, the Soret coefficient strongly decreases with increasing solution ionic strength and scales as the square of the Debye-Hückel screening length. Yet, collective effects yield a reversed scenario even at fairly low surfactant concentrations. We find that the single-particle behaviour can be explained using an interfacial tension-driven mechanism originally proposed by Ruckenstein. Interparticle interactions drastically change the Soret coefficient mainly owing to their effects on the solution's osmotic compressibility. The proposed mechanism can be extended to other kinds of solvent-particle interaction and may open up the way to a general picture of thermal diffusion in disperse systems.     

Thermal diffusion in disperse systems

This paper discusses a theory for a new effect, the migration of solid dispersed particles initiated by a nonuniform temperature field. The reason for the motion is the inhomogeneity of the properties of a thin protective layer around a particle. The example of ionic dispersion shows that the sign of the coefficient of thermodiffusion depends on the magnitude of the electrostatic potential at the particle surface and the thickness of the Debye layer and that the coefficientis larger than the values known for molecular systems by a factor of 100 to 10000. In contrast to molecular systems, in disperse systems thermodiffusion should play a much more important role. Zh. éksp. Teor. Fiz. 115, 1721–1726 (May 1999)     

Role of the velocity frame of reference in thermodiffusion in liquid mixtures

The role and significance of the velocity frame of reference in the interpretation, modeling and formulation of thermodiffusion in multicomponent liquid mixtures were investigated, focused on the nonequilibrium thermodynamics modeling approach. The effect of the velocity frame of reference on the phenomenological equations and thermodiffusion coefficients and expressions is explored. Theoretically and also by the aid of representative calculations, it is shown that while in binary mixtures transformation from one frame to another does not affect the sign and magnitude of the thermodiffusion coefficients, in multicomponent mixtures (ternary and higher), even the sign of the thermodiffusion coefficients may change when an alternative frame is used. This implies that in multicomponent mixtures for either experimental data or model estimations, the employed velocity frame for the thermodiffusion coefficients plays an important role in calculations. The Soret coefficients and the thermodiffusion factors are independent of the frame of reference.     

Investigation of the sign of the Soret coefficient in different ionic and surfacted magnetic colloids using forced Rayleigh scattering and single-beam Z -scan techniques

The sign of the Soret coefficient S T of a large set of ionic magnetic colloids (ionic ferrofluids (IFFs)) and surfacted magnetic colloids (surfacted ferrofluids (SFFs)) is determined using forced Rayleigh scattering and the single-beam Z -scan techniques. Different samples were investigated: acid and alkaline colloids with different values of pH; colloids with different concentrations of magnetic grains; colloids with grains of different typical diameters; colloids with magnetic grains with different coating natures; colloids with different non-polar and polar liquid carriers. Our results indicate that the sign of S T depends on the sign of the surface charge of grains in IFFs. In the case of water-based SFFs, the thermodiffusive behaviour is opposite to that of IFFs; that is, grains coated with a cationic surfactant behave like negatively charged IFF (alkaline) grains and grains coated with an anionic surfactant behave like positively charged IFF (acid) grains. SFFs with grains coated with non-ionic surfactants dispersed in non-polar fluid carriers behave like SFFs with grains coated with a cationic surfactant. The nature of the liquid carrier itself is not the only determinant factor, except apparently in the case of non-polar fluids, where only S T > 0 is found. These results cannot be explained with the available theories and it is highly probable that different mechanisms are present in the thermodiffusive behaviour of these complex fluids.