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

Spatial-temporal distribution, source identification, risk assessment and water quality assessment of trace elements in the surface water of typical tributary in Yangtze River delta, China

As China's first cross-province ecological compensation mechanism pilot area in the hinterland of the Yangtze River Delta, Xin'an River has been hotspot in the study of rational utilization of ecological resources, and the functional value of its ecosystem services has been widely concerned. As an important tributary of the upper reaches of Xin'an River, Fengle River may affect the whole basin. The spatial-temporal distributions, occurrence, water quality and risk assessment of trace elements were studied in Fengle River in three seasons. High element concentrations were found in the downstream. Traceability models results showed that the major sources of trace elements were related to different human activities. The water quality was worse downstream in the wet season, and was more suitable for irrigation in the dry season. Risk assessment results showed that Zn, Cu, Mn, Co, and As were able to pose the risk to the ecological environment and human.

Thermogravitational separation in porous vertical and horizontal cylindrical annular cells saturated by a binary mixture

In this paper, analytical and numerical studies of species separation in vertical and horizontal porous, cylindrical annular cells were presented. The binary fluid, saturating the porous medium, is a water-ethanol mixture. The thickness e of the horizontal and vertical columns is equal to [Formula: see text], where [Formula: see text] and [Formula: see text] are, respectively, the internal and the external radii. H is the height of the vertical cell, and the length of the horizontal cell. Constant temperatures, [Formula: see text] and [Formula: see text], were imposed on the inner and outer cylinders. Since an important species separation, in thermogravitational column (TGC), is obtained for [Formula: see text], the same assumption was made for the two configurations. The analytical solution was obtained using the parallel flow approximation for both configurations. The governing equations were solved numerically for 2D and 3D configurations using two different software (Comsol Multiphysics and a spectral collocation method with Gauss-Lobatto-Chebyshev points). Velocity, temperature, mass fraction fields and time to reach steady state were compared for the two configurations. The amount of species separated at the top or the bottom of each cell was also compared for each configuration.

Mass diffusion and Soret coefficient measurements of triethylene glycol/water binary mixtures by dynamic shadowgraphy

The investigation of the transport properties of binary fluid mixtures remains a topic of interest in relation to the more challenging studies of ternary mixtures. In fact, the study of the phase boundary limits of the Gibbs composition triangle can be the initial step for a more complete analysis of ternary mixtures. In this paper, we apply the dynamic shadowgraphy optical technique to study non-equilibrium fluctuations induced by the presence of a gradient of temperature and/or concentration in the triethylene glycol (TEG)/water system. These thermodiffusion and free-diffusion experiments aim at measuring the transport properties of samples of the studied system at different experimental conditions. We scan both the average temperature and the TEG concentration, which allows us investigating both positive and negative thermodiffusive behaviours. The obtained values of mass diffusion coefficient are consistent with data available in the literature in the range of temperature investigated in this study. The mass diffusion coefficient of the sample prepared at 0.7 w/w TEG concentration are characterised by shadowgraphy following the two proposed methods, exhibiting consistent results. An increase of the mass diffusion coefficient as a function of the average temperature is highlighted. On the other hand, the thermodiffusion coefficient appears to be independent of the average temperature of the sample at 0.3 w/w TEG concentration.

The Soret coefficients of the ternary system water/ethanol/triethylene glycol and its corresponding binary mixtures

Thermodiffusion in ternary mixtures is considered prototypic for the Soret effect of truly multicomponent systems. We discuss ground-based measurements of the Soret coefficient along the binary borders of the Gibbs triangle of the highly polar and hydrogen bonding ternary DCMIX3-system water/ethanol/triethylene glycol. All three Soret coefficients decay with increasing concentration, irrespective of the choice of the independent component, and show a characteristic sign change as a function of temperature and/or composition. With the exception of triethylene glycol/ethanol at high temperatures, the minority component always migrates toward the cold side. All three binaries exhibit temperature-independent fixed points of the Soret coefficient. The decay of the Soret coefficient with concentration can be related to negative excess volumes of mixing. The sign changes of the Soret coefficients of the binaries allow to draw far-reaching conclusions about the signs of the Soret coefficients of the corresponding ternary mixtures. In particular, we show that at least one ternary composition must exist, where all three Soret coefficients vanish simultaneously and no steady-state separation is observable.

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.

Limiting diffusion coefficients of [Formula: see text],[Formula: see text]-amino acids in water and in sodium chloride aqueous solutions at 298.15 K

Transport properties of model compounds in aqueous solutions such as amino acids can provide valuable information in order to understand the complex interactions in aqueous solutions as well as the protein stability in water and the relevant factors involved. Informations about the diffusion of amino acids in water and in aqueous solutions of sodium chloride are very scarce, especially for the 5-aminopentanoic acid and 6-aminohexanoic acid. In this study, limiting binary mutual diffusion coefficients at 298.15 K of 5-aminopentanoic and 6-aminohexanoic acids in aqueous solutions of NaCl 0.15 mol kg^-1, using the Taylor dispersion technique, were determined and the results compared with the limiting binary mutual diffusion coefficients for 2-aminopentanoic acid, and 2-aminohexanoic acid, obtained in the same experimental conditions. The discussion of the properties of the selected amino acids is centered on the positions of the ionic groups in the hydrocarbon chain and, in addition, we have discussed the effects of NaCl on their structures and properties. The data on diffusion properties are supported by ¹H, ¹³C and ²³Na NMR experiments, which we have obtained for 5-aminopentanoic and 6-aminohexanoic acids, in aqueous solution, also in the presence of NaCl.

Separation under thermogravitational effects in binary mixtures

In the present work, by using a parallelepipedic thermogravitational microcolumn, the temperature gradient influence on the stability of the flow has been examined, emphasizing mixtures with positive Soret coefficients. Experiments were conducted for DCMIX2 Toluene/Methanol and DCMIX3 Water/Ethanol binary subsystems because of their broad range of positive Soret values for high concentrations of methanol and ethanol, respectively. Two different mixtures have been studied here in order to confirm the thermogravitational stability of the mixtures. Experiments were compared with numerical simulations carried out using the open-source software platform OpenFOAM.

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.

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.

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.

Limiting values of diffusion coefficients of glycine, alanine, α-amino butyric acid, norvaline and norleucine in a relevant physiological aqueous medium

The side chain effect on transport in ionic aqueous salt solutions was investigated for [Formula: see text]-amino acids glycine, alanine, [Formula: see text]-amino butyric acid, norvaline, and norleucine --that together define a chemical homologous series based on the length of the characteristic side chain which increases from zero to four carbons, respectively. Binary mutual diffusion coefficients at infinitesimal concentration in aqueous solutions of NaCl (0.15 mol kg ^-1) are measured by means of Taylor dispersion technique for this series and significant differences were found against previous published results for identical systems in pure water. In this way, NaCl effect on the transport of each amino acid is thus assessed and discussed in terms of salting-out effects. Also, solvated Stokes hydrodynamic radii were computed for the series showing comparable results in water and NaCl solution. The new information should prove useful in the design and characterization of transport-controlled systems in physiological and pharmacological studies.

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.