Diffusion, thermal diffusion, and Soret coefficients and optical contrast factors of the binary mixtures of dodecane, isobutylbenzene, and 1,2,3,4-tetrahydronaphthalene

Thermodiffusive desalination

Desalination could solve the grand challenge of water scarcity, but materials-based and conventional thermal desalination methods generally suffer from scaling, fouling and materials degradation. Here, we propose and assess thermodiffusive desalination (TDD), a method that operates entirely in the liquid phase and notably excludes evaporation, freezing, membranes, or ion-adsorbing materials. Thermodiffusion is the migration of species under a temperature gradient and can be driven by thermal energy ubiquitous in the environment. Experimentally, a 450 ppm concentration drop was achieved by thermodiffusive separation when passing a NaCl/H2O solution through a single channel. This was further increased through re-circulation as a proof of concept for TDD. We also demonstrate via molecular dynamics and experiments that TDD in multi-component seawater is more amenable than in binary NaCl/H2O solutions. Numerically, we show that a scalable cascaded channel structure can further amplify thermodiffusive separation, achieving a concentration drop of 25000 ppm with a recovery rate of 10%. The minimum electric power consumption in this setup can be as low as 3 Whe m-3, which is only 1% of the theoretical minimum energy for desalination. TDD has potential in areas with abundant thermal energy but limited electrical power resources and can contribute to alleviating global freshwater scarcity.

Soret vector for description of multicomponent mixtures

The Soret effect describes the transport of constituent species in multicomponent mixtures that occurs due to a temperature gradient. This cross-coupling effect of heat and mass transfer has been successfully examined in binary liquid mixtures, while experiments with ternary mixtures are rare as they impose significant difficulties. We introduce a new and innovative concept, the Soret vector, for the characterization of Soret driven separation in ternary mixtures. The presentation of the component separation in the vector form offers several advantages: (i) to predict the Soret sign of a ternary mixture from knowledge of the Soret coefficients in binary subsystems; (ii) to control consistency of measured coefficients, this is especially important when results are obtained using different instruments and methods; (iii) to determine in which regions and which components cause the greatest separation; (iv) to identify the regions where the Soret separation is inaccessible for optical techniques or gravitationally unstable. We demonstrate these features by exploring ternary mixtures of different origins: (a) nearly ideal mixture composed by THN–IBB–nC12 when Soret coefficients in binary subsystems (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{T}^{bin}$$\end{document}STbin) are positive, (b) non-ideal mixture containing water and ethanol TEG–Wat–EtOH when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{T}^{bin}$$\end{document}STbin are positive and negative and (c) Tol–MeOH–Ch mixture containing demixing zone with positive and negative \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{T}^{bin}$$\end{document}STbin. Our approach provides a promising systematic framework for the future research of an important and challenging problem of thermodiffusion in multicomponent liquids.

Simultaneous determination of multiple transport properties over a wide range of temperatures and pressures from the analysis of non-equilibrium fluctuations by the shadowgraph method

The present work demonstrates that by the analysis of the dynamics of non-equilibrium fluctuations using the shadowgraph method, the thermal diffusivity, the Fick diffusion coefficient, the kinematic viscosity, and the Soret coefficient of a binary mixture can be determined from a single thermodiffusion experiment. The study was performed for a mixture consisting of equal masses of 1,2,3,4-tetrahydronaphthalene and n-dodecane in a newly developed shadowgraph apparatus at temperatures up to 373 K and pressures up to 40 MPa. The obtained results are mainly discussed in the light of their uncertainties at varying thermodynamic states for evaluating the benefits, drawbacks, and potentials of the apparatus. The Fick diffusion coefficient and the thermal diffusivity obtained with average expanded uncertainties of 2.8% and 6.6% agree with literature data and measurements for the same mixture taken by heterodyne dynamic light scattering. Current limitations of the method are reflected by the distinctly larger uncertainties of the kinematic viscosity and the Soret coefficient. Corresponding reasons and potential measures to overcome the limitations are discussed.

Mutual and Thermal Diffusivities as well as Fluid-Phase Equilibria of Mixtures of 1-Hexanol and Carbon Dioxide

This work contributes to an improved understanding of the fluid-phase behavior and diffusion processes in mixtures of 1-hexanol and carbon dioxide (CO₂) at temperatures around the upper critical end point (UCEP) of the system. Raman spectroscopy and dynamic light scattering were used to determine the composition at saturation conditions as well as Fick and thermal diffusivities. An acceleration of the Fick diffusive process up to CO₂ mole fractions of about 0.2 was found, followed by a strong slowing-down approaching vapor-liquid-liquid equilibrium or critical conditions. The acceleration of the Fick diffusive process vanished at temperatures much higher than the UCEP. Experimental Fick diffusivity data were compared with predictions from equilibrium molecular dynamics simulations and excess Gibbs energy calculations using interaction parameters from the literature. Both theoretical methods were not able to predict that the thermodynamic factor is equal to zero at the spinodal composition, stressing the need for new methodologies under such conditions. Thus, new sets of temperature-dependent interaction parameters were developed for the nonrandom two-liquid model, which improve the prediction of the Fick diffusion coefficient considerably. The link between the Fick diffusion coefficient and the nonrandomness of the liquid phases is also discussed.

Diffusivities in 1-Alcohols Containing Dissolved H2, He, N2, CO, or CO2 Close to Infinite Dilution

The influence of the strength of intermolecular interactions on mass diffusive processes remains poorly understood for mixtures of associative liquids with dissolved gases. For contributing to a fundamental understanding of the interplay between liquid structures and mass diffusivities in such systems, dynamic light scattering, Raman spectroscopy, and molecular dynamics simulations were used in this work. As model systems, binary mixtures consisting of the gases hydrogen, helium, nitrogen, carbon monoxide, or carbon dioxide dissolved in ethanol, 1-hexanol, or 1-decanol were selected. Experiments and simulations were performed at macroscopic thermodynamic equilibrium close to infinite dilution of solute for temperatures between 303 and 423 K. The Fick diffusion coefficients and self-diffusivities of the gas solutes increase with increasing temperature, decreasing alkyl chain length of the 1-alcohols, and decreasing molar mass of the solutes except for helium and hydrogen showing the opposite behavior. The analysis of the liquid structure of the mixtures showed that the fraction of hydrogen-bonded alcohol molecules decreases with increasing alkyl chain length and temperature. From the obtained structure-property relationships, a new correlation was developed to predict mass diffusivities in binary mixtures consisting of n-alkanes or 1-alcohols with dissolved gases close to infinite dilution within 10% on average.

Cylindrical flowing-junction cell for the investigation of fluctuations and pattern-formation in miscible fluids

We describe a flowing-junction cell with cylindrical symmetry suitable to investigate fluctuations and pattern formation at the diffusing interface between two miscible phases of a liquid mixture. The continuous outflow of the remixed fluid through a thin slit located at the midheight of the sample allows the preparation of an initially sharp interface. The system can be used in both gravity-stable and unstable conditions. In the stable case, the denser liquid is on the bottom of the cell and mass diffusion is the only active process for remixing the two liquids. Once the flow is stopped, one can investigate nonequilibrium fluctuations during free-diffusion in a binary mixture or double diffusive instabilities in multicomponent mixtures. Two horizontal transparent windows allow vertical mapping of the fluid flow by using shadowgraphy. In the unstable condition, with the denser fluid on top, stopping the radial flow at the interface gives rise to a Rayleigh-Taylor instability, which drives the denser liquid toward the bottom of the cell. The fact that the cell can maintain the system in the unstable condition shows that it is suitable to perform experiments under microgravity conditions. With respect to other free-diffusion cells, the proposed configuration has the advantage that the interface is extremely stable and flat, and that the experiments can be repeated by just flowing the cell with fresh liquids.

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).

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.

Temperature dependence of Soret and diffusion coefficients for toluene-cyclohexane mixture measured in convection-free environment

We report on the measurement of diffusion (D), Soret (S(T)), and thermodiffusion (D(T)) coefficients in toluene-cyclohexane mixture with mass fraction of toluene 0.40 onboard of the International Space Station. The coefficients were measured in the range of the mean temperatures between 20 °C and 34 °C. The Soret coefficient is negative within the investigated temperature range and its absolute value |S(T)| decreases with increasing temperature. The diffusion coefficient for this system increases with temperature rising. For comparison, the temperature dependence of diffusion coefficient was measured in ground laboratory using counter-flow cell technique and revealed a good agreement with microgravity results. A non-direct comparison of the measured onboard Soret coefficients with different systems indicated a similar trend for the temperature dependent behavior. Unexpected experimental finding is that for this system the thermodiffusion coefficient D(T) does not depend on temperature.

Concentration dependent refractive index of CO2/CH4 mixture in gaseous and supercritical phase

Carbon dioxide (CO2)/methane (CH4) binary mixtures are investigated at pressure values up to 20 MPa at 303 K in order to investigate the pressure dependence of the optical concentration contrast factor, ∂n/∂c(P,T), through gaseous and supercritical phase. Refractive index is measured by means of a Michelson interferometer. Refractivities of the mixtures are found in good agreement with Lorentz-Lorenz predictions after density calculations by means of the AGA8-DC92 equation of state. Experimental polarizabilities of pure fluids are compared to quantum calculations of monomers and dimers for each pressure; it results that the quantity of dimers is small in the investigated thermodynamic conditions. Finally, by extending our experimental database with numerical simulations, we evidence that ∂n/∂cP,T presents a critical enhancement similar to heat capacity.

Nonequilibrium fluctuation-induced Casimir pressures in liquid mixtures

In this article we derive expressions for Casimir-like pressures induced by nonequilibrium concentration fluctuations in liquid mixtures. The results are then applied to liquid mixtures in which the concentration gradient results from a temperature gradient through the Soret effect. A comparison is made between the pressures induced by nonequilibrium concentration fluctuations in liquid mixtures and those induced by nonequilibrium temperature fluctuations in one-component fluids. Some suggestions for experimental verification procedures are also presented.

Investigation of Fickian diffusion in the ternary mixtures of water-ethanol-triethylene glycol and its binary pairs

We present a comprehensive experimental study of isothermal Fickian diffusion in the ternary and binary liquid mixtures of water, ethanol, and triethylene glycol over the entire ternary composition space. 21 ternary mixtures inside the composition triangle have been investigated by means of the Taylor dispersion technique and 30 binary mixtures by Taylor dispersion and/or optical beam deflection in a Soret cell. The scalar binary diffusion coefficient has been determined along all three binary boundaries of the composition space and compared with estimations based on the Stokes-Einstein relation using stick or slip boundary conditions. The four elements of the ternary diffusion matrix and the diffusion eigenvalues were determined over a large portion of the composition triangle. The pseudo-binary diffusion coefficients obtained in Taylor dispersion experiments with either one of the two independent concentrations kept constant are comparable to the two diffusion eigenvalues. One of the two off-diagonal elements of the diffusion matrix is of the same order as the diagonal ones and, hence, not negligible, whereas the other one is approximately one order of magnitude smaller. Where available, our results compare well with literature data. The investigated compositions also comprise the five compositions that are scheduled for microgravity experiments in the ESA DCMIX3 project.

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

In this work, the transport coefficients of the ternary mixtures of the diffusion coefficient measurements in ternary mixtures 1 project were determined. The analyzed ternary mixtures are formed by 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane (nC12) at different compositions. In all cases, the analysis was carried out at 25 °C. The thermodiffusion coefficients were measured by a new thermogravitational column, and the molecular diffusion coefficients were determined by the sliding symmetric tubes technique. Finally, the Soret coefficients were ascertained from the measurements of the thermodiffusion and molecular diffusion coefficients. In addition, two new quantitative correlations which enable the prediction of the thermodiffusion and Soret coefficients of a ternary mixture are presented. The comparison between the experimental and the predicted data shows a good agreement. The presented results help to complete the lack of experimental data in ternary mixtures. In addition, this work improves the fundamental understanding of multicomponent mixtures.

Contribution to the benchmark for ternary mixtures: Measurement of the Soret, diffusion and thermodiffusion coefficients in the ternary mixture THN/IBB/nC12 with 0.8/0.1/0.1 mass fractions in ground and orbital laboratories

We have determined the Soret (ST), diffusion (D, and thermodiffusion (DT) coefficients in a ternary mixture of tetralin-isobutylbenzene-n-dodecane with a composition of 0.80/0.10/0.10 by mass fraction at a temperature of 298K. The Soret coefficients were measured in the microgravity experiment DCMIX1 and on the ground by optical digital interferometry (ODI) using two lasers with different wavelengths. The values of the Soret coefficients were determined from the stationary separation of the components using two- and six-parameter fits. The diffusion coefficients were independently measured using the Taylor Dispersion Technique in the ground laboratory, and the thermodiffusion coefficients were derived from known ST and matrix D. The processing of the data from the DCMIX experiment conducted on the International Space Station is discussed in detail. The multi-user design of the on-board instrument causes perturbations in the component separation. Several recommendations are suggested for improving the quality of the microgravity results. For example, we demonstrated that the tomography reconstruction of the 3-D concentration field allows to restore the underestimated component separation resulting from the spatial non-linearity of the temperature field. Furthermore, to avoid errors in component separation due to mass exchange between the working liquid volume and the expansion volume at the top of the cell, we suggest considering the evolution of the separation only in the lower half of the cell. The results of this study displayed reasonable quantitative agreement between the microgravity and ground experiments.

Contribution to the benchmark for ternary mixtures: Measurement of the Soret and thermodiffusion coefficients of tetralin+isobutylbenzene+n-dodecane at a composition of (0.8/0.1/0.1) mass fractions by two-color optical beam deflection

Within the framework of an international benchmark test we have performed measurements of the Soret and thermodiffusion coefficients of the organic ternary mixture (0.8/0.1/0.1 mass fraction) of 1,2,3,4-tetrahydronaphthaline (THN), isobutylbenzene (IBB) and n -dodecane (n C12) at 298.15K by means of a two-color optical beam deflection technique (OBD). The data evaluation procedure is based on a least squares fitting routine for an approximate analytical solution for the Soret cell problem. The condition number of the contrast factor matrix and standard error propagation are used for an error estimation for the measured Soret and thermodiffusion coefficients. The Soret coefficients obtained are S (') T(THN) = (1.20±0.09)×10(-3) K^-1, S (') T(IBB) = (- 0.34±0.14)×10(-3) K^-1, and S (') T(nC12) = (- 0.86±0.06)×10(-3) K^-1 and the corresponding thermodiffusion coefficients are D (') T(THN) = (0.72±0.26)×10(-12) m^2(s K)^-1, D (') T(IBB) = (- 0.22±0.42)×10(-12) m^2(s K)^-1, and D (') T(nC12) = (- 0.50±0.16)×10(-12) m^2(s K)^-1. These results will be used as ground-based reference data for the DCMIX project, where thermodiffusion experiments of ternary mixtures are measured in a microgravity environment aboard the International Space Station (ISS).

Investigation of Fickian diffusion in the ternary mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane

We present a comprehensive analysis of experimental results obtained for Fickian diffusion in the benchmark ternary liquid mixture of 1,2,3,4-tetrahydronaphthalene, isobutylbenzene, and dodecane (nC12) with equal mass fractions. Isothermal diffusion coefficients have been measured by two independent experimental methods: by Taylor dispersion technique, and by a counter flow cell fitted with an optical interferometry device. The experimental diffusion matrices have been critically analyzed regarding the Onsager reciprocal relations, for which we introduce a matrix asymmetry index s(2) that is independent of the frame of reference and the component order.