Fickian Diffusion in Ternary Mixtures Composed by 1,2,3,4-Tetrahydronaphthalene, Isobutylbenzene, and n-Dodecane

Stabilized convection in a ternary mixture with two Soret coefficients of opposite sign

We performed ground-based experiments on the sample polystyrene-toluene-cyclohexane in order to complement the experimental activities in microgravity conditions related to the ESA projects DCMIX4 and Giant Fluctuations. After applying a stabilizing thermal gradient by heating from above a layer of the fluid mixture, we studied over many hours the density variations in the bidimensional horizontal field by means of a Shadowgraph optical setup. The resulting images evidence the appearance of convective instability after a diffusive time associated with the binary molecular solvent consisting of toluene and cyclohexane, confirming the negative sign of the Soret coefficient of this mixture. After a larger diffusive time related to mass diffusion of the polystyrene in the binary solvent, convection was suppressed by the increasing stabilizing density gradient originated by the Soret-induced concentration gradient of the polymer. This is compatible with a positive sign of the Soret coefficient of the polymer in the binary solvent.

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.

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.

Do ternary liquid mixtures exhibit negative main Fick diffusion coefficients?

Measured main Fick diffusion coefficients are throughout positive. However, they may appear to be negative after transformation to the molar reference frame, if the excess volume is significant and the experimental uncertainties of the cross diffusion coefficients are large.

Interplay of structure and diffusion in ternary liquid mixtures of benzene + acetone + varying alcohols

The Fick diffusion coefficient matrix of ternary mixtures containing benzene + acetone + three different alcohols, i.e., methanol, ethanol, and 2-propanol, is studied by molecular dynamics simulation and Taylor dispersion experiments. Aiming to identify common features of these mixtures, it is found that one of the main diffusion coefficients and the smaller eigenvalue do not depend on the type of alcohol along the studied composition path. Two mechanisms that are responsible for this invariant behavior are discussed in detail, i.e., the interplay between kinetic and thermodynamic contributions to Fick diffusion coefficients and the presence of microscopic heterogeneities caused by hydrogen bonding. Experimental work alone cannot explain these mechanisms, while present simulations on the molecular level indicate structural changes and uniform intermolecular interactions between benzene and acetone molecules in the three ternary mixtures. The main diffusion coefficients of these ternary mixtures exhibit similarities with their binary subsystems. Analyses of radial distribution functions and hydrogen bonding statistics quantitatively evidence alcohol self-association and cluster formation, as well as component segregation. Furthermore, the excess volume of the mixtures is analyzed in the light of intermolecular interactions, further demonstrating the benefits of the simultaneous use of experiment and simulation. The proposed framework for studying diffusion coefficients of a set of ternary mixtures, where only one component varies, opens the way for further investigations and a better understanding of multicomponent diffusion. The presented numerical results may also give an impulse to the development of predictive approaches for multicomponent diffusion.

Mutual diffusion governed by kinetics and thermodynamics in the partially miscible mixture methanol + cyclohexane

To gain an understanding of the transport and thermodynamic behavior of the highly non-ideal mixture methanol + cyclohexane, three complementary approaches, i.e. experiment, molecular simulation and predictive equations, are employed. The temperature and composition dependence of different diffusion coefficients is studied around the miscibility gap at ambient pressure. On the one hand Fick diffusion coefficients are measured experimentally by interferometric probing and on the other hand Maxwell-Stefan diffusion coefficients and intradiffusion coefficients are sampled by equilibrium molecular dynamics simulation at five temperatures below the upper critical temperature of ∼319 K. The spinodal curve is determined from extrapolation of the experimental Fick diffusion coefficient data and compared to predictions from excess Gibbs energy models. It is found that these models are not capable to correctly describe the activity coefficients over the whole composition range of the studied mixture. Thus, different parameter sets for a modified Wilson model are used for calculations of the thermodynamic factor, which is needed to transform Maxwell-Stefan into Fick diffusion coefficients and vice versa. Further, predictive equations for the Maxwell-Stefan diffusion coefficient, which are based on intradiffusion coefficients, are compared to simulation results. Using different approaches provides a clearer understanding of the relations between kinetic and thermodynamic properties contributing to the diffusion behavior of partially miscible mixtures.

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).

The effect of alcohols as the third component on diffusion in mixtures of aromatics and ketones

The Fick diffusion coefficient matrix of three ternary mixtures composed of an aromatic (benzene), a ketone (acetone) and one of three different alcohols (methanol, ethanol or 2-propanol) is investigated with laboratory and numerical work.

Isothermal molecular diffusion in mixtures containing toluene, cyclohexane and methanol

The Taylor dispersion technique has been used for measuring ternary mutual diffusion coefficients for mixtures of cyclohexane-toluene-methanol, corresponding to the mixtures under study on the International Space Station (ISS) within the scope of the project DCMIX2 (second series of the experiment Diffusion Coefficients in Mixtures). Five ternary systems with different composition of cyclohexane-toluene-methanol were investigated in order to accurately obtain the mass diffusion coefficients, contributing to a better understanding of the isothermal molecular diffusion in conjunction with the coupled flows of solutes occurring in such fluid systems. Current standardized protocols for carrying out an experience are also examined to understand if the experimental conditions may be ill conditioning the final results.

Theoretical models for the thermo-gravitational separation process in porous media filled by N-component mixtures

The aim of this work is to present a theoretical analysis of the separation of an N-component mixture. In this study, two analytical models explaining the thermo-gravitational separation of components in N-component mixtures for vertical cavity filled by a porous medium are presented and assessed. The basic state and the separation are expressed in terms of the separation ratio, and the Lewis, cross-diffusion and Rayleigh numbers. Our computational analysis confirms that, for the given values of the mass fractions, thermodiffusion can be measured with a thermo-gravitational column, strongly supporting the experimentally determined transport coefficients.

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.

Development of a high-pressure set-up for measurements of binary diffusion coefficients in supercritical carbon dioxide

We present the development of a high-pressure apparatus for measurements of diffusion coefficients in supercritical fluids. The Taylor dispersion method has been adapted to conduct experiments at the pressures up to 25.0 MPa. In order to test the developed set-up, binary diffusion coefficients D at infinite dilution in supercritical carbon dioxide have been measured for a reference system, benzene, at temperatures in the range of 309.50-319.95 K. The effects of flow velocity, number of consecutive injections and absorbance at different wave numbers on the diffusion coefficient have been analysed. The obtained diffusion coefficients are of the order of 10^-8 m ²/s and in excellent agreement with the available literature data.