Soret coefficients of the ternary mixture 1,2,3,4-tetrahydronaphthalene + isobutylbenzene + n-dodecane

Frame-invariant Fick diffusion matrices of multicomponent fluid mixtures

Extension of a description of mass diffusion in binary fluids based on Fick's law to multicomponent fluids requires introduction of diffusion matrices. A problem is that Fick diffusion matrices commonly adopted for multicomponent fluids depend on the velocity frame of reference. In this paper we show how one can define Fick diffusion matrices for multicomponent fluids that are frame invariant.

The Soret effect in ternary mixtures of water+ethanol+triethylene glycol of equal mass fractions: Ground and microgravity experiments

Measurements of the Soret and thermodiffusion coefficients of a symmetric ternary mixture with equal mass fractions of water, ethanol, and triethylene glycol have been performed by two-color optical beam deflection (2-OBD) and the thermogravitational column technique (TGC) in the laboratory and under microgravity conditions in the Selectable Optical Diagnostics Instrument (SODI) aboard the International Space Station. The results from all three experimental techniques agree within the experimental error bars, which result mainly from the inversion of the contrast factor matrices. TGC shows by far the lowest, 2-OBD the highest error amplification. The microgravity measurements are in between. The agreement with the microgravity results shows that thermosolutal convection could be well controlled in the 2-OBD experiments by a proper orientation of the temperature gradient. Despite the different condition numbers, the results are invariant under the choice of the independent compositions. Based on the orientation of the confidence ellipsoid in the ternary composition diagram, not all coefficients are equally affected by experimental errors. Although there are appreciable uncertainties for water and ethanol, the Soret and the thermodiffusion coefficients of triethylene glycol could be obtained with a good accuracy due to the favorable orientation of the confidence ellipsoid. We have found that water behaves thermophobic, corresponding to a positive Soret coefficient, whereas both ethanol and triethylene glycol are thermophilic with negative Soret coefficients. This resembles the behaviour of the binary system ethanol/water above the ethanol concentration of the sign change.

Soret forced Rayleigh scattering instrument for simultaneous detection of two-wavelength signals to measure Soret coefficient and thermodiffusion coefficient in ternary mixtures

We describe an instrument for the measurement of the Soret and thermodiffusion coefficients in ternary systems based on the transient holographic grating technique, which is called Soret forced Rayleigh scattering (SFRS) or thermal diffusion forced Rayleigh scattering (TDFRS). We integrated the SFRS technique and the two-wavelength detection technique, which enabled us to obtain two different signals to determine the two independent Soret coefficients and thermodiffusion coefficients in ternary systems. The instrument has been designed to read the mass transport simultaneously by two-wavelength lasers with wavelengths of λ = 403 nm and λ = 639 nm. The irradiation time of the probing lasers is controlled to reduce the effect of laser absorption to the sample with dye (quinizarin), which is added to convert the interference pattern of the heating laser of λ = 532 nm to the temperature grating. The result of the measurement of binary benchmark mixtures composed of 1,2,3,4-tetrahydronaphthalene (THN), isobutylbenzene (IBB), and n-dodecane (nC12) shows that the simultaneous two-wavelength observation of the Soret effect and the mass diffusion are adequately performed. To evaluate performance in the measurement of ternary systems, we carried out experiments on the ternary benchmark mixtures of THN/IBB/nC12 with the mass fractions of 0.800/0.100/0.100 at a temperature of 298.2 K. The Soret coefficient and thermodiffusion coefficient agreed with the ternary benchmark values within the range of the standard uncertainties (23% for the Soret coefficient of THN and 30% for the thermodiffusion coefficient of THN).

Dynamic analysis of the light scattered by the non-equilibrium fluctuations of a ternary mixture of polystyrene-toluene-n-hexane

Dynamic analysis of the light scattered by non-equilibrium fluctuations in a thermodiffusion experiment has been performed on a sample of polystyrene-toluene-n -hexane, at 0.9-49.55-49.55% mass fraction. Time decays of the non-equilibrium fluctuations have been obtained revealing the accurate detectability of three modes. The slowest mode has been attributed to the mass diffusion of the polymer into the binary solvent; the intermediate one to mass diffusion of the two molecular components of the solvent; finally, the fastest one has been attributed to the thermal diffusivity of the overall mixture. The two eigenvalues of the mass diffusion matrix have been evaluated with accuracy in the order of 1%. Neglecting cross-diffusion effects we obtain a simplified expression for the relative amplitude of the two mass diffusion modes, allowing a parameterized determination of polystyrene and toluene Soret coefficients in the ternary mixture. We suggest that a two wavelength shadowgraph experiment is needed for a complete determination of all the coefficients.

Analysis of multi-wavelength measurements of diffusive properties via dispersion dependence of optical properties

We suggest a novel approach to analyze the diffusive properties of mixtures using their optical dispersion relations. Two diagnostics are required to determine the thermodiffusion coefficients in a ternary mixture, e.g., two different wavelengths. The literature results on thermodiffusion experiments indicate that the choice of a pair of wavelengths affects the result of the sought-after thermodiffusion (Soret) coefficients somewhat, because the numerical values of the refractive index variation with the concentration (optical contrast factor ∂n/∂C) depend on the wavelength. The present study offers three main contributions. First, we show that the available measurements for the optical contrast factors and component separation caused by the Soret effect for the mixture tetralin-isobutylbenzene-n-dodecane can be described by the same type of Cauchy dispersion relation as the refractive index n=f(λ). Then, we discuss an algorithm for eliminating the two types of systematic errors from the reported measurements of contrast factors in order to elaborate new synthetic dispersion curves of the Cauchy type. Lastly, we create a general dispersion curve for the stationary component separation which merges the results obtained at different pairs of wavelengths and provides consistent Soret coefficients.

Diffusion in Multicomponent Liquids: From Microscopic to Macroscopic Scales

In spite of considerable research on the nature of aqueous alcohol mixtures that are characterized by microscopic inhomogeneity or incomplete mixing at the molecular level, transport properties have received little attention. We report the results of a study on diffusion in the ternary mixture of water with two alcohols, that is, water + methanol + ethanol, which is investigated on microscopic and macroscopic scales by means of molecular simulation and Taylor dispersion experiments. A novel protocol is developed for the comparison of mutual diffusion coefficients sampled by two fundamentally different approaches, which allows for their critical analysis. Because of complex intermolecular interactions, given by the presence of hydrogen bonding, the analysis of transport processes in this mixture is challenging for not only on the microscopic scale for simulation techniques but also on the macroscopic scale due to unfavorable optical properties. Binary limits of the Fick diffusion matrix are used for validation of the experimental ternary mixture results together with the verification of the validity of the phenomenological Onsager reciprocal relations. The Maxwell-Stefan diffusion coefficients and the thermodynamic factor are sampled by molecular simulation consistently on the basis of given force field models. The protocol for the comparison of the results from both approaches is also challenging because Fick diffusion coefficients of ternary mixtures depend on the frame of reference. Accordingly, the measured coefficients are transformed from the volume-averaged to the molar-averaged frame of reference, and it is demonstrated that both approaches provide not only similar qualitative behavior along two concentration paths but also strong quantitative agreement. This coordinated work using different approaches to study diffusion in multicomponent mixtures is expected to be a significant step forward for the accurate assessment of cross-diffusion.