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'.

Diffusion in liquid mixtures.

The understanding of transport and mixing in fluids in the presence and in the absence of external fields and reactions represents a challenging topic of strategic relevance for space exploration. Indeed, mixing and transport of components in a fluid are especially important during long-term space missions where fuels, food and other materials, needed for the sustainability of long space travels, must be processed under microgravity conditions. So far, the processes of transport and mixing have been investigated mainly at the macroscopic and microscopic scale. Their investigation at the mesoscopic scale is becoming increasingly important for the understanding of mass transfer in confined systems, such as porous media, biological systems and microfluidic systems. Microgravity conditions will provide the opportunity to analyze the effect of external fields and reactions on optimizing mixing and transport in the absence of the convective flows induced by buoyancy on Earth. This would be of great practical applicative relevance to handle complex fluids under microgravity conditions for the processing of materials in space.

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 DT, and Soret ST 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. ST 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.

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.

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.

Do ternary liquid mixtures exhibit negative main Fick diffusion coefficients?

Experimental data on Fick diffusion coefficients of ternary and higher mixtures depend on the reference frame; those which are in common use are associated with the average velocity either with respect to volume, mass or mole number. In this study, the dependence of diffusion coefficients on the reference frame is thoroughly analyzed for three ternary mixtures of different types. The first one, tetralin-isobutylbenzene-dodecane, can almost be considered as ideal, the second one, cyclohexane-toluene-methanol, exhibits liquid-liquid phase separation and the third one, water-ethanol-triethylene glycol, contains three associating species and is also strongly non-ideal. Experimental diffusion coefficient data sampled in the volume reference frame are transformed to the molar and mass reference frames. The required partial molar volumes are derived from present density measurements. Four additional mixtures are considered along a single or two composition paths. A highlight of this study is the existence of a strong similarity of the main diffusion coefficients in the volume and mass reference frames for all considered mixtures. When the excess volume is small, the coefficients in the molar reference frame are also similar. However, for the mixture with a large excess volume (containing water), the diffusion coefficients in the molar reference frame differ significantly, even indicating negative main diffusion coefficients. It is shown that negative main diffusion coefficients appear due to relatively large experimental uncertainties of cross diffusion coefficients, which are propagated and amplified by frame transformation.

Measurement of Soret coefficients in a ternary mixture of toluene-methanol-cyclohexane in convection-free environment.

We report on the measurement of Soret (ST) coefficients in the ternary system toluene (T)-methanol (M)-cyclohexane (Ch) onboard the International Space Station in the experiment selectable optical diagnostic instrument/DCMIX2 (Diffusion Coefficients Measurement in ternary mIXtures). Nine experiments were conducted in the range of mean temperatures between 298.15 K and 306.15 K in the mixture with composition 0.62 (T)-0.31 (M)-0.07 (Ch) in mass fractions. A linear dependence of the Soret coefficients on temperature was established for the ternary mixture. It has also been found that, over considered range of mean temperatures, the Soret coefficients of toluene are small and positive, while the Soret coefficients for methanol are negative and, at least, two times larger. The present work also presents a comprehensive study of possible methodologies to process raw data from the Soret experiment in ternary mixtures. All the experiments were processed by seven different schemes and two of them were identified as the most reliable. We also investigate the error propagation and explain the reasons for the discrepancy of the results obtained by different schemes.

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.

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.

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

We report the Fickian diffusion coefficients in 20 ternary mixtures formed by 1,2,3,4-tetrahydronaphthalene (THN), isobutylbenzene (IBB) and n-dodecane (nC12) measured by the Taylor dispersion technique at 298.1 K and atmospheric pressure. Four diffusion coefficients of the ternary mixtures were measured along six concentration paths starting on one binary subsystem and moving toward the other one. We found expressions for the diffusion matrix of a ternary mixture approaching to the binary limits. The measured diffusion coefficients were thoroughly verified by comparison with the theoretical asymptotic behavior. The main diffusion coefficients vary smoothly over the entire concentration space and D11 is always larger than D22. One of the two cross-diffusion coefficients is of the same order of magnitude as the main ones and, hence, not negligible, whereas the other one is close to zero. The investigated mixtures also comprise compositions that were examined in microgravity experiments in the ESA DCMIX1 project.

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.

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.

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.

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

We have measured the Soret (S(T)), diffusion (D), and thermal diffusion (D(T)) coefficients of the three binary benchmark mixtures of dodecane (C12), isobutylbenzene, and 1,2,3,4-tetrahydronaphthalene at T = 25°C for at least five different concentrations each, covering the entire binary composition range. The two different optical techniques employed, optical beam deflection and optical digital interferometry, are in good to excellent agreement. Additionally, we have carefully measured the optical contrast factors (∂n/∂c)(p, T) and (∂n/∂T)(p, c). If the temperature and composition dependence of the mixture density is taken into account, both the Lorentz-Lorenz (LL) and the Looyenga (LO) equations give reasonable predictions of (∂n/∂c)(p, T). In case of (∂n/∂T)(p, c), only the LO equation yields good predictions in case of constant molecular polarizabilities α(i) of the pure compounds. If the apparent temperature dependence of α(i) is explicitly taken into account, excellent predictions are obtained both from the LL and the LO equations.

A comprehensive study of diffusion, thermodiffusion, and Soret coefficients of water-isopropanol mixtures.

We report on the measurement of diffusion (D), thermodiffusion (D(T)), and Soret (S(T)) coefficients in water-isopropanol mixtures by three different instrumental techniques: thermogravitational column in combination with sliding symmetric tubes, optical beam deflection, and optical digital interferometry. All the coefficients have been measured over the full concentration range. Results from different instruments are in excellent agreement over a broad overlapping composition (water mass fraction) range 0.2 < c < 0.7, providing new reliable benchmark data. Comparison with microgravity measurements (SODI/IVIDIL (Selected Optical Diagnostic Instrument/Influence of VIbration on DIffusion in Liquids)) onboard the International Space Station and with literature data (where available) generally gives a good agreement. Contrary to theoretical predictions and previous experimental expectations we have not observed a second sign change of S(T) at low water concentrations.