Diffusion of hydrocarbons diluted in supercritical carbon dioxide

Mutual diffusion of six hydrocarbons (methane, ethane, isobutane, benzene, toluene or naphthalene) diluted in supercritical carbon dioxide ([Formula: see text]) is studied by molecular dynamics simulation near the Widom line, i.e., in the temperature range from 290 to 345 K along the isobar 9 MPa. The [Formula: see text] + aromatics mixtures are additionally sampled at 10 and 12 MPa and an experimental database with Fick diffusion coefficient data for those systems is provided. Taylor dispersion experiments of [Formula: see text] with benzene, toluene, n-dodecane and 1,2,3,4-tetrahydronaphthalene are conducted along the [Formula: see text] 10 MPa isobar. Maxwell-Stefan and Fick diffusion coefficients are analyzed, together with the thermodynamic factor that relates them. It is found that the peculiar behavior of the Fick diffusion coefficient of some [Formula: see text] mixtures in the extended critical region is a consequence of the thermodynamic factor minimum due to pronounced clustering on the molecular scale. Further, the strong dependence of the Fick diffusion coefficient on the molecular mass of the solute as well as the breakdown of the Stokes-Einstein relation near the Widom line are confirmed. Eleven correlations for the prediction of the Fick diffusion coefficient of [Formula: see text] mixtures are assessed. An alternative two-step approach for the prediction of the infinite dilution Fick diffusion coefficient of supercritical [Formula: see text] mixtures is proposed. It requires only the state point in terms of temperature and pressure (or density) as well as the molecular solute mass as input parameters. First, entropy scaling is applied to estimate the self-diffusion coefficient of [Formula: see text]. Subsequently, this coefficient is used to determine the infinite dilution Fick diffusion coefficient of the mixture, based on the finding that these two diffusion coefficients exhibit a linear relationship, where the slope depends only on the molecular solute mass.

Cross diffusion governs an oscillatory instability in a ternary mixture with the Soret effect

In a ternary mixture with the Soret effect, the interplay between cross-diffusion, thermodiffusion, and convection can lead to rich and complex dynamics including spatial patterns and oscillations. We present an experimental and three-dimensional numerical study of dynamic regimes in the toluene-methanol-cyclohexane ternary mixture with the Soret effect in the geometry of a thermogravitational column. An important feature of the system is that for the first component, toluene, the Soret and thermodiffusion coefficients have opposite signs, which triggers the oscillatory instability. Our experiments and numerical analysis show that the primary long-wave instability manifests itself in the form of a standing wave, and the secondary one emerges in the form of a swinging pattern. The computational model provides insight into the role of cross-diffusion coefficient D₁₂ in the emergence and development of oscillatory instability. This study demonstrates that the long-wave oscillatory instability in transverse direction occurs only within a limited range of the D₁₂ values and outside of this range it decays to a stationary pattern of either Turing-like or monotonic instability.

Variety of flow patterns in a liquid bridge subjected to a gas stream

We present an experimental and two-phase computational study of convection in a liquid bridge ([Formula: see text]) that develops under the action of a parallel gas flow. The study focuses on tracking the evolution of hydrothermal waves by increasing the applied temperature difference [Formula: see text] and the temperature of gas moving at the velocity [Formula: see text]. Our experiments revealed certain regularity in the change of oscillatory states with an increase in the control parameters. Above the instability threshold, the nonlinear dynamics passes through three oscillatory regimes, which are repeated in a somewhat similar way at higher values of the control parameters. They are periodic, quasi-periodic with two or three frequencies and multi-frequency state when the Fourier spectrum is filled with clusters of duplex, triplex or higher numbers of frequencies. Three-dimensional numerical simulation, complemented by a deep spectral analysis, sheds light on the evolution of the flow pattern observed in experiments. The developed methodology identified conditions for the existence of a multi-frequency regime such as the presence of a weak low-frequency mode that can modulate strong high-frequency modes, the existence of strong azimuthal modes with different wavenumbers and the [Formula: see text] mode, and the structured combination of peaks in the Fourier spectrum. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

Measurement of Diffusion of Atmospheric Gases in a Liquid Perfluoro Compound by Means of an Optical Technique

We report on accurate measurements of Fickian diffusion coefficients in binary mixtures consisting of hydrofluoroether (a perfluoro compound of methoxy-nonafluorobutane or HFE-7100) with dissolved atmospheric gases CO₂, N₂, and O₂ in the limit of an infinite dilution of the gas. We show that the use of optical digital interferometry (ODI) allows the determination of diffusion coefficients of dissolved gases with relatively small standard uncertainties for this class of experiments. In addition, we illustrate the ability of an optical approach to determine the gas concentration. We compare the capacity of four mathematical models, singly used in the literature, to obtain diffusion coefficients by applying them to the processing of a large amount of experimental data. We quantify their systematic errors and standard uncertainties. The temperature behavior of the diffusion coefficients measured in the range of 10 to 40 °C is consistent with the behavior of the same gases in other solvents available in the literature.

Transport properties of n-ethylene glycol aqueous solutions with focus on triethylene glycol–water

Soret effect and diffusion in triethylene glycol (TEG)–water mixtures were investigated as a function of concentration at 25 °C by means of optical digital interferometry, with the use of a classical Soret cell. Diffusion D, thermal diffusion D T, and Soret S T coefficients are described for the full concentration range and an analysis is made individually for TEG–water mixture and within a series of n-ethylene glycol ( n-EG) aqueous systems. All coefficients decrease with increasing the concentration of TEG and n-EG. S T shows a change of sign with concentration, and this change is directly related to the ability of the n-EG molecule to establish hydrogen bonding with water. Diffusion and thermal diffusion coefficients present a plateau behavior with increasing concentration, showing the occurrence of changes in the preferential interactions in aqueous solution with concentration and meaning that, at high TEG composition, ether oxygens can be involved in the molecular interactions.

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.

A ternary mixture at the border of Soret separation stability

Ternary mixtures with the Soret effect are prone to triple-diffusive convection in a thermal field. The Soret coefficients of the toluene-methanol-cyclohexane mixture, measured in microgravity at a given composition [0.62-0.31-0.07] in mass fractions, showed that the net separation ratio, Ψ, the parameter responsible for the hydrodynamic stability in a gravity field is close to zero. Furthermore, the large cross-diffusion of toluene leads to a curious situation: the Soret coefficient S_T1 is positive while the thermodiffusion coefficient D_T1 is negative. The behavior of this ternary mixture on the border of stability, when Ψ is slightly negative or positive, is examined experimentally and numerically. The mixture is placed in an elongated cell between the differently heated walls. Depending on Ψ and the initial temperature of the liquid (mean temperature, linear profile or cold one), the evolution of concentration patterns are classified by four regimes. We observe the emergence of motionless, metastable, and convective patterns. In the case of Ψ > 0, it was found that cross-diffusion fluxes cause a temporarily unstable density pattern. The initially cold mixture at either Ψ sign shows dissimilar Soret separation in the upper and lower parts of the cell. It leads to the formation of a long-lived inverse density gradient at the upper part of the cell, which finally results in a motionless (Ψ > 0) or convective (Ψ < 0) pattern.

Diffusion of the carbon dioxide-ethanol mixture in the extended critical region

The effect of traces of ethanol in supercritical carbon dioxide on the mixture's thermodynamic properties is studied by molecular simulations and Taylor dispersion measurements. This mixture is investigated along the isobar p = 10 MPa in the temperature range between T = 304 and 343 K. Along this path, the mixture undergoes two transitions: First, the Widom line is crossed, marking the transition from liquid-like to gas-like conditions. A second transition occurs from the supercritical gas-like domain to a subcritical gas. The Widom line crossover entails inflection points for most of the studied properties, i.e. density, enthalpy, shear viscosity, Maxwell-Stefan and intradiffusion coefficients. On the other hand, the transition between the super- and subcritical regions is found to be generally smooth, an observation that is qualitatively confirmed by experimental Taylor dispersion measurements. Dedicated atomistic simulations show the presence of microheterogeneities due to ethanol self-association along the investigated path, which lead to the mixture's anomalous behavior in its extended critical region.

Diffusion of Quinine with Ethanol as a Co-Solvent in Supercritical CO2

This study aims at contributing to quinine extraction using supercritical CO2 and ethanol as a co-solvent. The diffusion coefficients of quinine in supercritical CO2 are measured using the Taylor dispersion technique when quinine is pre-dissolved in ethanol. First, the diffusion coefficients of pure ethanol in the supercritical state of CO2 were investigated in order to get a basis for seeing a relative change in the diffusion coefficient with the addition of quinine. We report measurements of the diffusion coefficients of ethanol in scCO2 in the temperature range from 304.3 to 343 K and pressures of 9.5, 10 and 12 MPa. Next, the diffusion coefficients of different amounts of quinine dissolved in ethanol and injected into supercritical CO2 were measured in the same range of temperatures at p = 12 Mpa. At the pressure p = 9.5 MPa, which is close to the critical pressure, the diffusion coefficients were measured at the temperature, T = 343 K, far from the critical value. It was found that the diffusion coefficients are significantly dependent on the amount of quinine in a small range of its content, less than 0.1%. It is quite likely that this behavior is associated with a change in the spatial structure, that is, the formation of clusters or compounds, and a subsequent increase in the molecular weight of the diffusive substance.

Preliminary analysis of Diffusion Coefficient Measurements in ternary mIXtures 4 (DCMIX4) experiment on board the International Space Station

In the frame of the Diffusion Coefficient Measurements in ternary mIXtures 4 (DCMIX4) project the thermodiffusion experiments were conducted on the International Space Station (ISS) in the Selectable Optical Diagnostics Instrument (SODI) which is on orbit since 2009. We describe the results of the preliminary analysis of images downloaded during the execution of DCMIX4 in order to check the quality of the running experiments and, if needed, adjust the experiment parameters for the following runs. The quick analysis of raw data showed that they are meaningful and will allow to obtain the transport coefficients of examined ternary and binary mixtures.

European Space Agency experiments on thermodiffusion of fluid mixtures in space

This paper describes the European Space Agency (ESA) experiments devoted to study thermodiffusion of fluid mixtures in microgravity environment, where sedimentation and convection do not affect the mass flow induced by the Soret effect. First, the experiments performed on binary mixtures in the IVIDIL and GRADFLEX experiments are described. Then, further experiments on ternary mixtures and complex fluids performed in DCMIX and planned to be performed in the context of the NEUF-DIX project are presented. Finally, multi-component mixtures studied in the SCCO project are detailed.

Diffusion of methane in supercritical carbon dioxide across the Widom line

Diffusion of methane diluted in supercritical carbon dioxide is studied by experiment and molecular simulation in the temperature range from 292.55 to 332.85 K along the isobars 9.0, 12.5 and 14.7 MPa. Measurements of the Fick diffusion coefficient are carried out with the Taylor dispersion technique. Molecular dynamics simulation and the Green-Kubo formalism are employed to obtain Fick, Maxwell-Stefan and intradiffusion coefficients as well as shear viscosity. The obtained diffusion coefficients are on the order of 10-8 m2/s. The composition, temperature and density dependence of diffusion is analyzed. The Fick diffusion coefficient of methane in carbon dioxide shows an anomaly in the near-critical region. This behavior can be attributed to the crossing of the so-called Widom line, where the supercritical fluid goes through a transition between liquid-like and gas-like states. Further, several classical equations are tested on their ability to predict this behavior and it is found that equations that explicitly include the density are better suited to predict the sharp variation of the diffusion coefficient near the critical region predicted by molecular simulation.

Finite-size effects on pattern selection in immiscible fluids subjected to horizontal vibrations in weightlessness

A detailed numerical investigation of frozen wave pattern selection in finite rectangular containers under microgravity conditions is presented. The column growth cycle controlling mode transitions is described and the instability diagram showing selected wave number as function of the vibrational velocity is obtained. In contrast to the continuous monotonic dependence of pattern wave number on forcing predicted by linear inviscid theory in the limit of infinitely long containers, the pattern selection process in finite domains is characterized by solution branches that persist over discrete forcing intervals. We describe how properties of the selected frozen wave pattern, including the finite critical forcing value, depend on container length. In long containers, a transition from nearly symmetric to asymmetric columnar development is found at sufficiently high forcing values, with the loss of (approximate) reflection symmetry evident in the mean flow associated with the transient growth of the pattern. The effect of container height is considered separately, in the limit of both shallow and deep layers. Shallow layers suppress the development of long-wave perturbations leading to higher wave-number patterns whose growth may be associated with an asymmetric series of collisions between developing columns and container boundaries. In thick layers, lower pattern wave numbers are observed and, although the column growth is on average more regular, the final state is often asymmetric. Finally, we compare our results with the dependence on container aspect ratio Γ=L/2H predicted by inviscid theory. For Γ≳2, finite-size effects are reasonably weak and the numerically obtained thresholds are similar to but slightly higher than the theoretical values, most likely due to viscous effects. For Γ≲2, finite-size effects come to the fore and onset is significantly delayed.

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.

Stability of a stationary plane-parallel flow of a ternary fluid between two vertical plates maintained at constant different temperatures

The linear stability of a steady convective flow of a ternary mixture placed between differently heated vertical rigid plates is studied. The applied temperature gradient induces concentration gradients due to the Soret effect. The analysis is done for the case when separation ratios of ternary mixture, i.e., Soret coefficients, have different signs but the net separation ratio is negative. The stability maps in terms of the Grashof number and net separation ratio are obtained and discussed for monotonic and oscillatory modes of instability. The previous results for long-wave instability of a binary mixture were recovered in the limit when one of the Soret coefficients tends to zero. For finite-wavelength perturbations the previous results were extended by discovering the oscillatory instability.

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.

Onset and non-linear regimes of Soret-induced convection in binary mixtures heated from above

The paper deals with the investigation of the onset and non-linear regimes of convection of liquid binary mixtures with negative Soret effect heated from above. The linear stability of a convectionless state in a horizontal layer is studied by the numerical solution of the linearized problem on the temporal evolution of small perturbations of the unsteady base state. Non-linear regimes of convection are investigated by the numerical solution of the non-linear unsteady equations for a horizontally elongated rectangular cavity. The calculations are performed for water-ethanol and water-isopropanol liquid mixtures and for colloidal suspensions. The dependences of the instability onset time and wave number of the most dangerous perturbations on the solutal Rayleigh number (gravity level) obtained by a linear stability analysis and non-linear calculations are found to be in a very good agreement. A favorable comparison with the existing experimental and numerical data is presented.

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.

Experimental study on dynamics of coherent structures formed by inertial solid particles in three-dimensional periodic flows

We present experimental results obtained under normal gravity on the dynamics of solid particles in periodic oscillatory thermocapillary-driven flows in a non-isothermal liquid bridge made of decane. Inertial particles of different densities and in the size range approximately 0.75-75 μm are able to form stable coherent structures (particle accumulation structures, or PASs). Two image processing techniques were developed and successfully applied to compute time required for an ensemble of particles to form a structure. It is shown that the formation time grows with the decrease of the Stokes number. The observations indicate the probable irrelevance of the memory term for these experiments. Two types of PAS were observed-single (SL-I) and double-loop (SL-II)-which sometimes co-existed. Only large or very dense particles may form an SL-II type structure. A number of novel features of the system were perceived. In some cases, intermittently stable structures emerged (their dynamics is characterized by alternating time intervals during which a structure exists and is destroyed). Whereas in most experiments we observed a conventional symmetric and centered PAS, there were cases when a long-term stable asymmetric structure appeared. Experiments wherein two different types of PAS-forming particles were used simultaneously revealed the destructive role of collisions between the particles on formation of structures.

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.

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.

Interfacial pattern selection in miscible liquids under vibration

We explore the peculiar behaviour of an interface between two miscible liquids of similar (but non-identical) viscosities and densities under horizontal vibration with a frequency less than 25 Hz. Significant differences in the structure of the formed patterns were found between microgravity and ground experiments. In a gravity field, a spatially periodic saw-tooth frozen structure is generated in the interface which dissipates at long times. By contrast, under the low gravity conditions of a parabolic flight, the long lived pattern consists of a series of vertical columns of alternating liquids.

Wall-generated pattern on a periodically excited miscible liquid/liquid interface

We present a new generic type of pattern generated by bounding walls on the interface between miscible liquids in a horizontally vibrated cell. The pattern is observed in laboratory experiments and numerical simulations below and above the frozen-wave instability threshold. At the threshold, a competition develops between the new "fish-spine" pattern and frozen waves, while above the threshold these two kinds of patterns may coexist in spatially separated domains. We propose a theoretical model for the formation mechanism of the fish-spine pattern and its spreading along the interface.

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.

Benchmark values for the Soret, thermodiffusion and molecular diffusion coefficients of the ternary mixture tetralin+isobutylbenzene+n-dodecane with 0.8-0.1-0.1 mass fraction

With the aim of providing reliable benchmark values, we have measured the Soret, thermodiffusion and molecular diffusion coefficients for the ternary mixture formed by 1,2,3,4-tetrahydronaphthalene, isobutylbenzene and n-dodecane for a mass fraction of 0.8-0.1-0.1 and at a temperature of 25°C. The experimental techniques used by the six participating laboratories are Optical Digital Interferometry, Taylor Dispersion technique, Open Ended Capillary, Optical Beam Deflection, Thermogravitational technique and Sliding Symmetric Tubes technique in ground conditions and Selectable Optical Diagnostic Instrument (SODI) in microgravity conditions. The measurements obtained in the SODI installation have been analyzed independently by four laboratories. Benchmark values are proposed for the thermodiffusion and Soret coefficients and for the eigenvalues of the diffusion matrix in ground conditions, and for Soret coefficients in microgravity conditions.

Soret separation in a binary liquid mixture near its critical temperature

The values of transport coefficients near a critical point are typically enhanced compared to the values in the classical region far away from a critical point. We report on the impact of the asymptotic behavior of the mass diffusion near the critical region on the Soret separation of the components in a model binary mixture. Concentration patterns are numerically investigated in the case of a spatially varying temperature. The Soret separation in ordinary mixture leads to the establishing of a linear concentration distribution in a steady state. The presence of the critical point redistributes the concentration field, it creates a thin layer with sharp concentration change at the critical region which can be seen as a horizontal plateau on vertical profiles. Large concentration gradients are established across this layer. The analysis showed that the kinetic of the separation significantly depends on whether the critical temperature is inside or outside of the applied temperature region, which is T(cold) ≤ T ≤ T(hot). Critical separation road is suggested for the case when T(cr) is located inside this region, T(cold) ≤ T(cr) ≤ T(hot).

Experimental and numerical analysis of mass transfer in a binary mixture with Soret effect in the presence of weak convection

One of the targets of the experiment IVIDIL (Influence Vibrations on Diffusion in Liquids) conducted on-board ISS was to study the response of binary mixtures to vibrational forcing when the density gradient results from thermal and compositional variations. Compositional variations were created by the Soret effect and can strengthen or weaken the overall density gradient and, consequently, the response to vibrational forcing. We present the results of two experimental runs conducted on-board ISS in the frame of the experiment IVIDIL for low and strong vibrational forcing. The experimental observations revealed that a significant mean flow is set within 2 minutes after imposing vibrations and later in time it varies weakly and slowly due to the Soret effect. A mathematical model has been developed to compute the thermal and concentration fields in the experiment IVIDIL and verify the accuracy of picture processing based on the classical approach used in non-convective systems with the Soret effect. The effect of temperature and concentrations perturbations by joint action of vibrational convection and Soret effect on long time scale are carefully examined. The model demonstrates that image processing used for non-convective systems is suitable for the systems with vibration-affected thermodiffusion experiment.

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.

New flow regimes generated by mode coupling in buoyant-thermocapillary convection

We report on a new nonlinear dynamics occurring in a confined cylindrical column filled with fluid (liquid bridge) and heated from above. We demonstrate and analyze the novel oscillatory flow state created by the interaction of two hydrothermal waves of different origins: one propagates vertically from the cold towards the hot side (m=0) and another is traveling in the azimuthal direction (m=1). Their interaction leads to an exotic flow structure: during a part of the oscillation period the resulting wave propagates in a given azimuthal direction, whereas during the rest of the period it moves in the opposite direction. A new bimodal flow regime is found to exist over a parameter range where these modes have comparable influence. The phase diagrams, obtained by three-dimensional nonlinear simulations, are reported. They shed light on the instability mechanism and criteria of the existence of novel states.

Experimental evidence of thermal vibrational convection in a nonuniformly heated fluid in a reduced gravity environment

We report experimental evidence of convection caused by translational vibration of nonuniformly heated fluid in low gravity. The theory of vibrational convection in weightlessness is well developed but direct experimental proof has been missing. An innovative point of the experiment is the observation of a temperature field in the front and side views of the cubic cell. In addition, particle tracing is employed. The evolution of this field is studied systematically in a wide range of frequencies and amplitudes. The flow structures reported in previous numerical studies are confirmed. The transition from four-vortex flow to the pattern with three vortices is observed in the transient state.