Measurements of molecular and thermal diffusion coefficients in ternary 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.     

New thermal diffusion coefficient measurements for hydrocarbon binary mixtures: viscosity and composition dependency

New thermal diffusion coefficients of binary mixtures are measured for n-decane-n-alkanes and 1-methylnaphthalene-n-alkanes with 25 and 75 wt % at 25 degrees C and 1 atm using the thermogravitational column technique. The alkanes range from n-pentane to n-eicosane. The new results confirm the recently observed nonmonotonic behavior of thermal diffusion coefficients with molecular weight for binary mixtures of n-decane- n-alkanes at the compositions studied. In this work, the mobility and disparity effects on thermal diffusion coefficients are quantified for binary mixtures. We also show for the binary mixtures studied that the thermal diffusion coefficients and mixture viscosity, both nonequilibrium properties, are closely related.     

Prediction of thermodynamic, transport and vapor-liquid equilibrium properties of binary mixtures of ethylene glycol and water

Equilibrium and non-equilibrium molecular dynamics and Monte Carlo simulation techniques were applied to predict various thermodynamic, transport and vapor-liquid equilibrium properties of binary mixtures of ethylene glycol and water (EG-W) based on OPLS-AA and SPC/E force fields. The properties predicted include density, vaporization enthalpy, enthalpy of mixing, heat capacities, diffusion coefficients, shear viscosities, thermal conductivities, vapor-liquid coexistence isotherms and isobaric curves, and saturation vapor pressures. Good agreements with experimental data were obtained for most of these properties. Errors are mostly related to inaccuracy found in predictions of pure fluids; a correction to prediction of pure substance can systematically improve prediction for the mixture. This work suggests that OPLS-AA and SPC/E force fields using the common combining rules are transferable for predicting multiple physical properties of EG-W mixtures.     

Characterization of thermal diffusion of polystyrene in binary mixtures of THF/dioxane and THF/cyclohexane

The thermal diffusion coefficient (D_τ) was determined for three polystyrene standards of different molecular masses in binary mixtures of tetrahydrofuran/dioxane and tetrahydrofuran/cyclohexane of various compositions. The D_τ values were obtained by combining retention data from thermal field-flow fractionation measurements with diffusion data from dynamic light scattering experiments. In agreement with earlier work of Schimpf and Giddings, the thermal diffusion coefficient was found to be virtually independent of the molecular mass of the polymers. In the binary mixtures of tetrahydrofuran and dioxane, both good solvents for polystyrene, the D_τ value was approximately equal to the average of the D_τ values in the pure solvents, weighted according to the mole fractions of the solvents in the mixture. However, for polystyrene in binary mixtures of tetrahydrofuran and cyclohexane this linear behavior of the thermal diffusion phenomenon was not observed. The addition of cyclohexane to tetrahydrofuran has initially only a minor effect on the molecular and thermal diffusion coefficients of the polystyrene standards. Because cyclohexane is a theta solvent for polystyrene, the preferential solvation of polystyrene by tetrahydrofuran could be an explanation for these results. © 1996 John Wiley & Sons, Inc.     

Molecular and thermal diffusion coefficients of alkane-alkane and alkane-aromatic binary mixtures: effect of shape and size of molecules

New molecular and thermal diffusion coefficients of binary mixtures of normal decane-normal alkanes and methylnaphthalene-normal alkanes are measured at atmospheric pressure and T = 25 degrees C. The normal alkanes used in this work include nC5-nC20. Thermal diffusion coefficients were measured in a thermogravitational column. Molecular diffusion coefficients were measured using an open-ended capillary tube technique. Results show a significant effect of molecular shape and size on thermal and molecular diffusion coefficients. Molecular diffusion coefficients show a monotonic behavior in both aromatic-normal alkane and normal decane-normal alkane mixtures. Thermal diffusion coefficients reveal a nonmonotonic trend with molecular size in the normal decane-normal alkane mixtures. This is the first report of the nonmonotonic behavior in the literature. The data presented in this paper provide an accurate self-molecular diffusion coefficient for nC10 from binary data.     

Systematic study of the thermal diffusion in associated mixtures

We performed systematic temperature and concentration dependent measurements of the Soret coefficient in different associated binary mixtures of water, deuterated water, dimethyl sulfoxide (DMSO), methanol, ethanol, acetone, methanol, 1-propanol, 2-propanol, and propionaldehyde using the so-called thermal diffusion forced Rayleigh scattering method. For some of the associating binary mixtures such as ethanol/water, acetone/water, and DMSO/water, the concentration xw+/- at which the Soret coefficient changes its sign does not depend on temperature and is equal to the concentration xw x where the Soret coefficient isotherms intersect. For others such as 1-propanol/water, 2-propanol/water, and ethanol/DMSO, the sign change concentration is temperature dependent, which is the typical behavior observed for nonassociating mixtures. For systems with xw+/-=xw x, we found that xw+/- depends linearly on the ratio of the vaporization enthalpies of the pure components. Probably due to the similarity of methanol and DMSO, we do not observe a sign change for this mixture. The obtained results are related to structural changes in the fluid observed by nuclear magnetic resonance, mass spectrometric, and x-ray experiments in the literature. Furthermore, we discuss the influence of hydrophilic and hydrophobic interactions and the solubility on thermal diffusion behavior.     

On measurement of thermal diffusion coefficients in multicomponent mixtures

We investigate the steady-state separation of the individual components of an incompressible multicomponent liquid mixture in a narrow two-dimensional thermogravitational column. Analytic working equations for measuring thermal diffusion coefficients analogous to the existing equations for a binary mixture are derived. Similar to the binary results, we find that when compositional variation has negligible effect on fluid density and vertical diffusive flux can be ignored, molecular diffusion does not affect steady-state separation. However, when compositional effects on density are taken into account, molecular diffusion does affect the bulk convective flow and the steady-state separation of the components. There may be also two distinct trends in the velocity and separation profiles. With one or more negative thermal diffusion coefficients, there may be more than one convection cell resulting in oscillatory behavior of separation. The working equations presented can be used to measure thermal diffusion coefficients of multicomponent mixtures. Such measurements have not yet been reported in the literature.     

Correlation of the mutual diffusion coefficients of binary liquid mixtures

A correlative UNIDIF model for the mutual diffusion coefficients of binary liquid mixtures is developed using statistical thermodynamics and the absolute reaction rate theory. In this model, a mole fraction average of the logarithm of the pure-component limiting diffusion coefficients is taken as a reference term. The model expresses the excess part of the diffusion coefficient relative to this reference term in a form similar to that of a UNIQUAC equation which comprises two parts due to the combinatorial and residual contributions. The combinatorial part depends on the molecular sizes and shapes. The residual part includes two binary interaction parameters, which are obtained from data regression, for each binary mixture. Mutual diffusion coefficients of nonpolar+nonpolar, nonpolar+polar and polar+polar fluid mixtures are correlated in this study. Optimal binary interaction parameters are presented. Correlation results using the UNIDIF model for mutual diffusion coefficient are satisfactory and are superior to those from other methods.     

Thermal diffusion and molecular diffusion values for some alkane mixtures: a comparison between thermogravitational column and thermal diffusion forced rayleigh scattering

In the present work we studied the thermal diffusion behavior of n-decane in various alkanes by thermogravitational column (TC) technique and the thermal diffusion forced Rayleigh scattering (TDFRS) method. The investigated lighter alkanes compared to n-decane are n-pentane, n-hexane, n-heptane, n-octane, and the heavier ones are n-tetradecane, n-pentadecane, n-hexadecane, n-heptadecane, n-octadecane, and n-eicosane. The binary mixture n-decane/ n-pentane we investigated at several different concentrations; all other mixtures were only investigated at a mass fraction of 50%. Even for the volatile n-pentane/ n-decane mixture the deviations between the thermal diffusion coefficients determined by the different methods agreed within the error bars. Typically the agreement between the two methods was in the order of 5%. In comparison to recently published TC and TDFRS data we found deviations in the order of 30% up to 40%. We analyze and discuss the possible reasons for the discrepancies for the present and the past publications.     

Acoustic,viscometric and optical properties of binary mixtures of tetrahydrofuran with 1-propanol and 2-propanol

The values estimated from various mixing rules for the ultrasonic velocity, viscosity and refractive index have been compared with the respective values measured earlier at 293, 303, and 313?K over the entire mole fraction range of two binary mixtures of tetrahydrofuran (THF) with 1-propanol (1-p) and 2-propanol (2-p). There is an excellent agreement between the experimental values of ultrasonic velocity and of refractive index with the respective values obtained from the mixing rules. The mixing rules for viscosity provide values agreeing broadly with those obtained from experimental measurements. The relative merits and interrelations of these mixing rules are discussed.     

内压与液体混合物的超额焓

本文在前文提出的通用液体混合模型的基础上, 对其中某些近似假设和混合规则进行了合理的修正, 从而得到了一个液体混合物的超额焓与组分内压间的关系式。对于正常液体混合物, 式中有两个可调的修正系数, 对于醇-烃混合物, 则有三个可调参数。对十六个二元液体混合物的计算结果表明, 关系式不仅能准确地描述一般液体混合物的超额焓随浓度的变化规律, 而且亦适用于具有S型H^E-x曲线的复杂液体混合物。     

Dependence of thermal diffusion factor of binary mixtures to the thermodynamic state by NEMD simulation

In this paper, we investigate the dependence of thermal diffusion factor and thermal conductivity to the temperature, density and mole fraction in Lennard–Jones binary mixtures of isotopes, noble gases and SF₆–noble gases by non-equilibrium molecular dynamics simulations.The results for the isotopic mixtures indicated that the density has a crucial effect on the dependence of thermal diffusion factor on the temperature. For isotope system at low density, thermal diffusion factor increased with temperature then remains constant at higher temperatures and the slope of thermal diffusion factor vs. temperature is positive while at higher density, thermal diffusion factor decreased with temperature and then fluctuate. For noble gas mixtures, thermal diffusion factor reduces with increasing of temperature and remain constant at high temperatures. For SF₆–Ar system, thermal diffusion factor has a negative slope and reduced with increasing of temperature, but remain nearly constant at high temperatures. For Xe–SF₆ thermal diffusion factor changed sign and the slope of thermal diffusion factor vs. temperature was negative. The results also show that thermal conductivity increases with temperature for all systems.The dependence of thermal diffusion factor to mole fraction of heavier component also investigated. The inverse of thermal diffusion factor versus mole fraction of heavier component is linear for isotope mixtures at thermodynamic conditions: (a) Low temperature, large mass ratio and all densities. (b) High temperature, large mass ratio and low densities. For Ne–Kr mixture, the inverse of thermal diffusion factor shows a linear dependence to the mole fraction of heavier component in moderate temperatures and all densities. For SF₆–Ar and Xe–SF₆ mixtures, the inverse of thermal diffusion factor has linear behaviour at moderate temperatures and low density and high temperature and low density, respectively.     

Ambipolar diffusion in two-temperature multicomponent plasmas

A recent formulation of multicomponent diffusion in multitemperature gas mixtures [J. D. Ramshaw, J. Non-equilib. Thermodyn. 18. 121 (1993)] is applied to ambipolar diffusion in two-temperature multicomponent plasmas in zero magnetic field. Simplifications chic to the small electron muss are systematically exploited. A general expression is derived for the ambipolar electric field E. In the special case where the electron and heavy-particle temperatures are equal, this expression reduces to a result previously obtained using a self-consistent effective binary diffusion (SCEBD) approximation [J. D. Ramshaw and C. H. Chang,Plasma Chem. Plasma Process.11. 395 (1991)]. When thermal diffusion due to electrons is neglected, the heavy particles are shown to diffuse precisely as they would in the same E field if the electrons were entirely removed from the system. Finally, the SCEBD approximation for ambipolar diffusion in multicomponent plasmas is generalized to the case, of unequal electron and heavy-particle temperatures.     

Liquid densities at high pressures

Aalto et al. recently proposed a model for compressed liquid densities. The model was found more accurate than the Hankinson–Brobst–Thomson (HBT) and Chang–Zhao models. However, the pressure region of the data studied was limited to 200 bar maximum. In this work, the recently developed liquid density model is extended to high pressures. The equation describing the pressure dependence of liquid density is reformulated and the required parameters are optimized using a database containing 7478 data points for 31 pure hydrocarbons; maximum pressure in this data set is 8000 bar. The average absolute deviation (AAD) between these data and the recommended model is 0.4636%. A comparison to the results obtained with the HBT and Chang–Zhao models for the same data set shows that the new model is clearly more accurate in the extended pressure range, as well. The revised model is also tested in predicting liquid densities for mixtures; 84 different combinations of mixing rules are studied. The evaluation of the mixing rules is carried out using two compilations of experimental data: the first one contains 6712 points for 47 binary and two ternary mixtures, and the second 3582 points for 11 methane+alkane mixtures. In addition, the predictions are tested with a data set of 1119 points for other miscellaneous mixtures. No binary interaction parameters are used. With the recommended mixing rules, the AAD percentage is 0.5824% for the first set of data. If one simply adopts the mixing rules recommended for the HBT model, the AAD value for the same data set becomes 0.7482%.     

Application of a generalized van der Waals equation of state to several nonpolar mixtures

A generalized van der Waals equation of state, applied recently (Nguyen Van Nhu and Kohler, 1995) to the calculation of excess properties and phase equilibria for the mixture methane + ethane, is now extended to several nonpolar binary mixtures.Improved mixing rules for the van der Waals attractive term and for the correction term are proposed. With these mixing rules, the equation gives good agreement for vapour-liquid and liquid-liquid equilibria over a large temperature range for 29 binary mixtures. The agreement of mixture volumes and cross second virial coefficients is also satisfactory.     

The effect of corrugation of pore wall on the thermal diffusion in nanopores by molecular dynamics simulations

In this work we have studied the effect of corrugation on the thermal diffusion (soret effect) in isotopic and non-isotopic fluid mixtures confined in a slit pore. We used a boundary driven non-equilibrium molecular dynamics to simulate thermal diffusion in Lennard–Jones (LJ) binary mixtures confined in structureless Steele 10-4-3 and atomistic Lennard–Jones pore walls. The results showed that for the isotopic mixture thermal diffusion factor for both wall types agrees and the corrugation of the LJ wall has no effect in isotopic mixture. However, for non-isotopic mixture confined in atomistic LJ pore the component with stronger attraction adsorbs more to the wall than the structureless Steele wall. The effect of corrugation of pore wall on the thermal diffusion is noticeable in narrow slit pore and mixture with large difference in molecular attraction parameter of components.     

Vapor–liquid equilibrium measurement and modeling for the difluoromethane + pentafluoroethane + propane ternary mixture

Vapor–liquid equilibrium data for the difluoromethane (R32) + pentafluoroethane (R125) + propane (R290) ternary mixture were measured at 5 isotherms between 263.15 K and 323.15 K. The measurement was carried out using a circulation-type apparatus recently developed, which was validated with binary mixtures. With binary interaction parameters obtained for the three corresponding binary mixtures, VLE modeling and prediction were performed for the ternary mixture using the Peng–Robinson equation of state with the classical mixing rules and MHV1 mixing rules. Hou's group contribution model for VLE of new refrigerant mixtures was further tested with the experimental data for the ternary system. The predicted pressure and vapor phase composition were compared with experimental ones.     

Thermodynamic consistency of high pressure ternary mixtures containing a compressed gas and solid solutes of different complexity

A thermodynamic consistency test applicable to high pressure binary gas–solid mixtures is extended to ternary mixtures containing a compressed gas and two solid solutes. A high pressure mixture containing carbon dioxide as solvent and two chemically similar solutes (2,3 dimethylnaphthalene and 2,6 dimethylnaphthalene) and a high pressure mixture containing carbon dioxide as solvent and two chemically different solutes (capsaicin and β-carotene), are considered in the study. Several sets of isothermal solubility data for binary and ternary mixtures are considered in the study. The Peng–Robinson equation of state with the mixing rules of Wong and Sandler have been employed for modeling the solubility of the solid in the case of binary mixtures, while the classical van der Waals mixing rules were used for modeling the ternary mixtures containing two solid solutes. Then the proposed thermodynamic consistency test has been applied. The results show that the thermodynamic test for ternary mixtures can be applied with confidence determining consistency or inconsistency of the experimental data used.     

Calculation of the binary diffusion second virial coefficient

Calculations of the first density correction to the binary diffusion coefficient are presented for several mixtures. These calculations are based on the classical kinetic theory for mixtures developed by Bennett and Curtiss. The theoretical predictions agree well with experimental data.     

Thermal diffusion forced Rayleigh scattering setup optimized for aqueous mixtures

We developed a thermal diffusion forced Rayleigh scattering (TDFRS) setup operating at a writing wavelength of 980 nm, which corresponds to an absorption band of water with an absorption coefficient of approximately 0.5 cm(-1). Therefore, aqueous mixtures require no dye to convert the light into heat energy. Especially for aqueous system with a complex phase behavior such as surfactant systems, the addition of a water soluble dye can cause artifacts. The infrared-TDFRS (IR-TDFRS) setup has been validated for water/ethanol mixtures with water weight fractions c = 0.5-0.95 and in a temperature range between T = 15 degrees C to T = 35 degrees C. Comparison with literature data shows an excellent agreement. The addition of a small amount (c(dye) approximately 10(-6) wt) of adsorbing dye at the writing wavelength allows also the investigation of organic mixtures. We investigated the three binary mixtures of dodecane, isobutylbenzene, and 1,2,3,4-tetrahydronaphthalene at a weight fraction of c = 0.5 at a temperature of 25 degrees C and found good agreement with the Soret coefficients, which had been obtained in a benchmark test under the same conditions. Therefore, the presented setup is suitable for the investigation of the thermal diffusion behavior in aqueous and organic mixtures, and in the case of aqueous systems, the addition of a dye can be avoided.