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.     

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.     

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.     

Precise determination of the Soret,thermodiffusion and isothermal diffusion coefficients of binary mixtures of dodecane,isobutylbenzene and 1,2,3,4-tetrahydronaphthalene (contribution of the University of Mons to the benchmark test)

Within the framework of an international benchmark test, the Soret coefficient S T , the thermodiffusion coefficient D T , and the isothermal mass diffusion coefficient D of the three binary systems formed with dodecane, isobutylbenzene and 1,2,3,4-tetrahydronaphthalene (with a mass fraction of 0.5 in each component at a temperature of 25C) have been measured. Convective coupling in thermogravitational columns has been used to determine D T based on the Furry-Jones-Onsager theory and the so-called open-ended capillary technique for D . The ratio of D T to D , obtained in these two independent experiments, provides the Soret coefficient. In one case, we were able to use laser Doppler velocimetry to measure the modifications of the velocity amplitude due to thermodiffusion, which is also a way to obtain the Soret coefficient. Our results for these three coefficients are in good agreement with those obtained by other benchmark tests.     

Longwave Marangoni instability in a binary mixture under the action of vibration: Influence of the heat transfer on a free surface

We study the influence of low-frequency vibration on a longwave Marangoni convection in a layer of a binary mixture with the Soret effect. Heat loss at a free surface is taken into consideration. Linear stability analysis is performed numerically by means of the Floquet theory. It is shown that with the increase in the Biot number B, the system is stabilized. For heating from below, a crossover is found in a narrow interval of the Soret number: the stability domain decreases stepwise for arbitrary small B.     

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).     

Thermal diffusion in micropores by molecular dynamics computer simulations

This work focuses on the identification of the main microscopic processes that influence thermal diffusion (the Soret effect) in a fluid mixture confined in an uncorrugated slit pore. To achieve this purpose, a boundary driven nonequilibrium molecular dynamics scheme is applied on binary mixtures of super-critical Lennard–Jones (LJ) spheres representing methane and n-decane. Following previous work, we perform a systematic study of the influence of the parameters used to describe a model slit pore on an effective thermal diffusion factor. Among these parameters are: The nature of the reflection of the diffusing particles on the walls (specular or diffusive), the pore width with respect to the particle size and the fluid-wall potential strength. Simulations were run both on equimolar and non-equimolar mixtures. The results indicate that thermal diffusion is effectively lowered only for strong fluid–wall interactions. It is shown that the general trends, which are different under sub- and super-critical conditions, can be explained by a careful analysis of the relative sorption energies of the two compounds.     

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.     

On the theory of electron diffusion under a temperature gradient in degenerate semiconductors having non-parabolic energy bands

The theory of electron diffusion under a temperature gradient (Soret effect) in degenerate semiconductors having non-parabolic energy bands and spherical constant-energy surfaces is worked out for the first time. An expression is given for the Soret coefficient which may be determined from the knowledge of the energy dependence of the relaxation time and can be related to the thermoelectric power.     

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.     

On the establishment of thermal diffusion in binary Lennard-Jones liquids

The establishment of thermal diffusion in an Ar-Kr Lennard-Jones mixture is investigated via dynamical non equilibrium molecular dynamics [G. Ciccotti, G. Jacucci, Phys. Rev. Lett. 35, 789 (1975)]. We observe, in particular, the evolution of the density and temperature fields of the system following the onset of the thermal gradient. In stationary conditions, we also compute the Soret coefficient of the mixture. This study confirms that dynamical non equilibrium molecular dynamics is an effective tool to gather information on transient phenomena, even though the full evolution of the mass and energy fluxes associated to the temperature and density fields requires, in this case, a more substantial numerical effort than the one employed here.     

Freezing and melting of binary mixtures confined in a nanopore

This paper reports on a Grand Canonical Monte Carlo study of the freezing and melting of Lennard–Jones Ar/Kr mixtures confined in a slit pore composed of two strongly attractive structureless walls. For all molar compositions and temperatures, the pore, which has a width of 1.44?nm, accommodates two contact layers and one inner layer. Different wall/fluid interactions are considered, corresponding to pore walls that have a larger affinity for either Ar or Kr. The solid/liquid phase diagram of the confined mixture is determined and results compared with data for the bulk mixture. The structure of the confined mixture is studied using 2D order parameters and both positional g(r) and bond orientational G₆(r) pair correlation functions. It is found that in the confined solid phase, both the contact and inner layers have a hexagonal crystal structure. It is shown that the freezing temperature of the Ar/Kr confined mixture is higher than the bulk freezing point for all molar compositions. Also, it is found that the freezing temperature becomes larger as the ratio α of the wall/fluid to the fluid/fluid interactions increases, in agreement with previous simulation studies on pure substances confined in nanopores. In the case of pore walls having a stronger affinity for Kr atoms (ε _Ar/W<ε _Kr/W), it is observed that both the contact and inner layers of the confined mixture undergo, at the same temperature, a transition from the liquid phase to the crystal phase. The freezing of Ar/Kr mixtures confined between the walls having a stronger affinity for Ar (ε _Ar/W?>?ε _Kr/W) is more complex: for Kr molar concentration lower than 0.35, we observe the presence of an intermediate state between all layers being 2D hexagonal crystals and all the layers being liquid. This intermediate state consists of a crystalline contact layer and a liquid-like inner layer. It is also shown that the qualitative variations of the increase of freezing temperature with the molar composition depend on the affinity of the pore wall for the different components. These results confirm that, in addition to the parameter α the ratio of the wall/fluid interactions for the two species, η=?_Ar/W/?_Kr/W, is a key variable in determining the freezing and melting behaviour of the confined mixture.     

Analytical and numerical exploration of oscillatory convection in porous media

This study is part of the research about the influence of the thermal gradient on the composition and the stability of fluids in geological environments. This paper presents modelling results of oscillatory convection in a porous medium using the METSOR code. The model solves the heat and mass transport equations in a porous medium and takes into account the Soret effect (mass transport under thermal gradient). Oscillatory convection may occur in pure fluids and in binary mixtures (as a consequence of the Soret effect). Experimental data confirm the existence of this phenomenon in porous media. Here, the outputs of the METSOR code are verified against existing analytical solutions. A first modelling attempt of oscillatory convection in mixtures is presented (salt aquifer).     

The synthesis of the chiral non-mesogenic d-seco estrone derivatives and their influence on the phase transitions of cholesteric liquid crystals

The synthesis of new chiral seco-estrone derivatives is presented, as well as their influence on the phase transition of binary mixtures of cholesteryc liquid crystals. The new chiral derivatives do not posses any liquid crystalline phases and were synthesized in several synthetic steps, starting from estrone. We have studied the mixtures of cholesteryl non-anoate (40%) with cholesteryl myristate (40%) and addition of new chiral derivatives 3 4, or 5 (20%). It was concluded that the addition of chiral derivative 3 to the binary mixture stabilizes smectic A and cholesteric phase and shifts the phase transition temperature with respect to pure binary mixture for about 5°C towards lower temperatures. The extension of the temperature range of the cholesteric phase from 5°C to 15°C was established in the case when the derivatives 3 and 4 are added to the binary mixture of cholesteryl nonanoate with cholesteryl myristate. The phase diagrams of investigated compounds are formed on the basis of data obtained by the optical microscopy. Using X-ray diffraction on the crystalline powder of unoriented samples we have determined the molecular parameters: the thickness of smectic and cholesteric layers and average distance between the long axes of neighboring molecules.     

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.     

Transport properties of a binary mixture of CO2ben N2 from the pair potential energy functions based on a semi-empirical inversion method

The potential energy surface of a CO₂-N₂ mixture is determined by using an inversion method, together with a new collision integral correlation [J. Phys. Chem. Ref. Data 19 1179 (1990)]. With the new invert potential, the transport properties of CO₂-N₂ mixture are presented in a temperature range from 273.15 K to 3273.15 K at low density by employing the Chapman-Enskog scheme and the Wang Chang-Uhlenbeck-de Boer theory, consisting of a viscosity coefficient, a thermal conductivity coefficient, a binary diffusion coefficient, and a thermal diffusion factor. The accuracy of the predicted results is estimated to be 2% for viscosity, 5% for thermal conductivity, and 10% for binary diffusion coefficient.     

Dufour effect in superionic copper selenide

The Dufour effect has been observed in the superionic conductor copper selenide, Cu_2−x Se. This effect is the opposite of the Soret thermal diffusion effect which was previously only observed in gaseous and liquid systems. Fiz. Tverd. Tela (St. Petersburg) 40, 242–244 (February 1998)     

Effect of confinement in nano-porous materials on the solubility of a supercritical gas

By combining Gibbs Ensemble Monte Carlo simulations and density functional theory, we investigate the influence of confinement in a slit-shaped carbon pore on the solubility of a supercritical solute gas in a liquid solvent. In the cases studied here, competing adsorption of the solvent and solute determines whether the solubility is enhanced or suppressed for larger pores. We find that the solubility in the confined system is strongly dependent on pore width, and that molecular packing effects are important for small pore widths. In addition, the solubility decreases on increase in the temperature, as for the bulk mixture, but the rate of decrease is greater in the pore due to a decrease in the partial molar enthalpy of the solute in the pore; this effect becomes greater as pore width is decreased. The solubility is increased on increasing the bulk pressure of the gas in equilibrium with the pore, and obeys Henry's law at lower pressures. However, the Henry constant differs significantly from that for the bulk mixture, and the range of pressure over which Henry's law applies is reduced relative to that for the bulk mixture. The latter observation indicates that solute–solute interactions become more important in the pore than for the bulk at a given bulk pressure. Finally, we note that different authors use different definitions of the solubility in pores, leading to some confusion over the reported phenomenon of ‘oversolubility’. We recommend that solubility be defined as the overall mole fraction of solute in the pores, since it takes into account the increase in density of the solvent in the pores, and avoids ambiguity in the definition of the pore volume.     

分离比对混合流体Rayleigh-Bénard对流解的影响

混合流体Rayleigh-Bénard对流是研究非平衡对流的非线性动力学特性的典型模型之一.基于流体力学方程组的数值模拟,首先探讨了矩形腔体中具有强Soret效应(分离比Ψ=-0.60)的混合流体行波对流的分叉特性及斑图演化,沿着分叉曲线的上部分支,随着相对瑞利数的增加,此系统依次出现了局部行波对流、具有缺陷的行波对流、行波对流、摆动行波对流及定常对流5种行波对流解.然后,研究了分离比Ψ对对流解的影响,与弱Soret效应(Ψ=-0.11)时的对流解相比较,强Soret效应(Ψ=-0.60)时出现的对流解更丰富.由于有强Soret效应的对流的复杂性,Ψ=-0.60时的对流解与Ψ=-0.20,-0.4时的对流解不同.     

Molecular-dynamics simulation of evaporation of a liquid

The molecular-dynamics method is used to investigate high-temperature evaporation of a simple liquid. The interaction of the atoms is described by a Lenard-Jones 6–12 potential. The simulation shows that fluctuations of the binding energy in the surface layer play an important role in evaporation, thanks to which a significant contribution to the evaporated flux comes from atoms whose kinetic energy is of the same order of magnitude as the mean thermal energy. Such a mechanism of evaporation differs substantially from the traditional one [Ya. I. Frenkel’, Kinetic Theory of Liquids (Clarendon Press, Oxford, 1946)] based on the assumption that only those particles evaporate that have energies of the order of the binding energy, i.e., much larger than the mean thermal energy. The structure of the transitional layer between the bulk gas and liquid phases is investigated. Potential energy fluctuations and pairwise correlation functions in the bulk phases and transitional layer are calculated. The velocity distribution function of the atoms for evaporation into vacuum is found. Zh. éksp. Teor. Fiz. 111, 1328–1346 (April 1997)