Progress in multicomponent thermodiffusion studies in connection with the DCMIX space experiments

In multicomponent fluid mixtures, diffusive transport is not solely influenced by concentration gradients (Fickian diffusion), but also by temperature and pressure gradients (barodiffusion). Mass diffusion induced by temperature gradients is termed thermodiffusion, also known as thermal diffusion or the Soret effect. While barodiffusion is typically insignificant, except in geological contexts, thermodiffusion can be notably significant under non-equilibrium thermal conditions. Thermodiffusion is observed in gaseous, liquid, and solid mixtures, wherein mass diffusion flows are caused by temperature gradients. Its wide-ranging applications in fields such as uranium enrichment, oil recovery, nanotechnology, and biological macromolecule manipulation underscore its importance in various technological fields.

Over the years, extensive experimental and theoretical investigations have been conducted to gain a deeper understanding of the Soret effect, leading to significant advancements in the interpretation of binary mixtures. Over the past decade, the scientific focus has shifted toward ternary mixtures, which expand the scope of research to more realistic applications. It brought a new challenge.¹ Due to additional coupling between species resulting from cross-diffusion, the ternary system, even with a positive Soret coefficient of the denser component, can become unstable.^2,3 Sometimes instability can be difficult to recognize during a Soret experiment, as a hydrodynamically stable ternary system can become unstable under a certain class of initial conditions.⁴ Thus, experiments conducted in a convective-free environment are particularly helpful for the investigation of ternary mixtures and the validation of ground techniques.

Due to the relatively long duration of Soret's experiments, they require the utilization of orbital platforms that offer substantial microgravity time. Examples of these platforms include unmanned recoverable scientific vehicles, such as the European Retrievable Carrier (EURECA), the Russian FOTON-M, and Chinese Shijian satellite series, as well as the International Space Station (ISS). The first attempt to use the benefits of microgravity for measuring thermodiffusion in liquid mixtures dates back to 1992 and was associated with the EURECA mission. Two instruments were developed and utilized on orbit to measure thermodiffusion in liquid alloys⁵ and in 20 organic binary mixtures and aqueous solutions.⁶ 

In the 1990s, in order to explore the potential for the industrial use of space, ESA and its partners turned their attention on industry-related research for oil recovery. Two significant projects were initiated: the “Soret Coefficient in Crude Oil” (SCCO) and the “Diffusion Coefficient in Crude Oil” (DCCO). The projects targeted multicomponent (ternary and quaternary) mixtures of hydrocarbons under conditions close to the ones of natural oil reservoirs, i.e., at elevated pressures and temperatures.⁷ The first attempt to fly the SCCO experiment into a GAS (Get Away Special) canister^8,9 on the Space Shuttle was unsuccessful due to a computer failure. The first and only flight under the DCCO¹⁰ project in 2002 was out of luck. The diffusion hole in a membrane connecting the two chambers with ternary mixtures was blocked by a bubble.

The studies within the Soret Coefficient in Crude Oil (SCCO) project were continued with a new facility designed by ESA. The experimental setup of SCCO comprises six small cylindrical tubes, each containing 1.2 ml of fluid, divided into two halves that are linked by an initially open valve. During the experiment, the flat surfaces of each cylindrical compartment (half tube) are maintained at different temperatures, in order to induce thermodiffusion within the fluid. At the end of the mission, the valves in all tubes are closed separating each fluid sample into a “hot” and a “cold” compartment. The cells are returned to the ground, where the fluid composition in the separated compartments is analyzed, providing the thermodiffusion coefficients for each component present. For the first time, such an instrument was scheduled to fly on the Russian satellite “Foton-M1” (2002), but the launch was unsuccessful due to a rocket explosion. The instrument was rebuilt and reconfigured, and a subsequently flown on the Foton-M2 (2005) and Foton-M3 (2007) missions. The objective was to study a ternary mixture simulating two fractions of crude oil: incompressible and compressible. The experiments were conducted at a pressure of 35 MPa and a temperature of 333.15 K. The experimental results for the incompressible fraction (THN/IBB/C₁₂) were well processed.⁷ However, the experimental data for the compressible fraction (methane, n-butane, and n-dodecane) were lost during the post-flight gas chromatographic analysis of the samples.¹¹ 

Recovered after the Foton M3 mission, the SCCO facility remained on the ground for a decade until it was decided to fly it on a Chinese satellite to study mixtures with supercritical CO₂. The QinetiQ company involved in instrument refurbishment, placed a contract to MRC ULB to conduct tests for leaktightness and compatibility with CO₂. Cells filled with CO₂ were leaking,¹² and it was decided to fly n-alkane mixtures at a pressure above 30 MPa. Using the approved cell design, a series of experiments were conducted on the Shijian satellite (SJ-10 mission).¹³ Measurements in two cells containing a ternary liquid mixture and a condensate gas demonstrated that the lightest and heaviest species exhibited a tendency to migrate relative to the remaining species toward the hot and cold regions, respectively. These trends were subsequently validated by molecular dynamics simulations.¹³ 

The SCCO design, however, has certain limitations: the need in returning the full experiment hardware with integrated cells, the requirement for a complex post-flight chemical analysis, and the number of experiments that are strictly limited by the number of flight cells.

Most of these limitations were eliminated in the frame of the SODI (Selectable Optical Diagnostics Instrument) facility, which was developed by ESA as a multipurpose tool, taking into account all requirements of thermodiffusion experiments in binary and ternary mixtures. The instrument's modular structure, comprising a CPU block that integrates electronics for controlling various sensors, mechanical actuators, thermoelectric modules, laser diodes, and cameras, enables its multi-functionality. Furthermore, external removable hard drives were employed for the collection of experimental data. The optical modules, designed in a horizontally elongated U-shape, were equipped with both one- and two-color reconfigurable interferometers. Moreover, a dedicated cell array was positioned in the opening space of the optical modules.

The SODI instrument played a pivotal role in the success of the consecutive IVIDIL (Influence VIbration on DIffusion in Liquids) and DCMIX (Diffusion Coefficients Measurement in Ternary Mixtures) projects. The latter project involved four experimental campaigns conducted on the ISS between 2010 and 2019, managed by the European Space Agency (ESA) in collaboration with Roscosmos¹⁴ and the Canadian Space Agency at an earlier stage.¹⁵ 

The outcomes of these projects extend beyond the plain measurement of transport properties as substantial fundamental knowledge has been gained. Aside from the measured coefficients, the projects yielded in numerous fundamental discoveries and breakthroughs throughout the stages of experiment preparation and result processing. These findings can be categorized into two groups: “generic” (global) and “experiment-dependent.” The generic results represent scientific advances related to the Soret experiment in ternary mixtures, irrespective of the specific ternary mixture. The experiment-dependent results also brought new and interesting findings but specific to the DCMIX mixture under consideration. In this paper, we put focus on generic results.

The convective stability of binary mixtures in ground experiments can be efficiently controlled in low-profile Soret cells. However, in the case of thermodiffusion in ternary mixtures, the stability becomes less predictable and unguided due to three different characteristic times. Moreover, gravitational instabilities cannot be ruled out in the presence of cross-diffusion. Additionally, the potentially destabilizing effects of the denser component migrating opposite to the temperature gradient cannot be excluded. The major part of the knowledge on thermodiffusion in ternary mixtures, available in the literature, has been acquired within the framework of the DCMIX project. This project included measurements conducted in a gravity-free environment on the ISS.

Four campaigns of the DCMIX experiment were targeting several different ternary mixtures, and three of them are depicted in Fig. 1. The first campaign SODI-DSC (DCMIX1) was fully dedicated to the ternary mixture comprising hydrocarbons from different families, tetralin–isobutylbenzene–n-dodecane. The chemical species represent the three major families of compounds found in crude oils: THN, IBB, and nC₁₂, respectively, for the families of naphthenic, aromatic, and aliphatic compounds. The selected systems involve three components and are away from the diluted limits. These ternary systems carry the main features of multicomponent systems, and the chemo-diffusion couplings characteristic of them arise as soon as more than two undiluted components diffuse. The DCMIX1 microgravity experiment was carried out in 2012 with the aim to establish a firm basis by investigating the so-called Fontainebleau benchmark system,¹⁶ whose binary pairs had already extensively been characterized before. For each system investigated during the DCMIX1 campaign aboard the ISS, several experimental runs were performed at a mean temperature of $T=298.15$ K. Inspired by the successful results of microgravity experiments, researchers extensively measured the Soret coefficients for the DCMIX1 system in ground laboratories. The measurements were carried out on a dense grid in the Gibbs composition triangle.¹⁷ Interestingly, isobutylbenzene changes its migration direction depending on the composition of the other two components. This sign change in a ternary mixture could potentially be attributed to the concept of thermophobicity, which was initially formulated for binary systems.^18,19

The next campaign, DCMIX2, targeted a highly non-ideal mixture of toluene–methanol–cyclohexane, known for a demixing gap formed between methanol and cyclohexane. Adding toluene as a component that facilitates mixing allowed for the formation of mixtures with different distances to the demixing zone. The system exhibits hydrodynamic instability over a wide range of compositions when subjected to a temperature difference and does not allow the measurement of the Soret coefficients in ground laboratories.²⁰ In 2014, an experimental campaign was conducted on the ISS providing an opportunity to further explore this system. The primary objective of the second campaign was to assess how the distance to the demixing zone influences the divergence in separation and the near-critical characteristics of diffusion. The analysis of the DCMIX2 ternary mixture in a given cell (cell 1) has established a linear dependence of the Soret coefficients on the mean temperature.²¹ Such a finding was reported for the first time for ternary mixtures. The examination of the cells with other compositions (i.e., cells 2, 4, 5) revealed an increase in the Soret coefficient toward the demixing zone by at least one order of magnitude.

Alongside the examination of the ternary mixture, the temperature dependence within the toluene/cyclohexane binary subsystem was investigated. Experiments conducted in the orbital laboratory revealed that the Soret coefficient of the toluene/cyclohexane system (⁠$C=0.40$⁠) in the temperature range under investigation is negative, and its absolute value $|ST|$ decreases with increasing temperature.²² These observations verified ground-based data for binaries that display a negative Soret coefficient, which were measured using thermal diffusion forced Rayleigh scattering (TDFRS).²³ Furthermore, examination of the orbital data yielded an intriguing result: a temperature-independent thermodiffusion coefficient, $DT$⁠, for this mixture.

The DCMIX3 mixture represents the first aqueous system containing water/ethanol/triethylene glycol. The large region of negative Soret coefficients over the ternary Gibbs triangle was expected since the binary subsystem water/ethanol exhibits a broad range of negative Soret coefficients.^24,25 When the DCMIX3 mixture was sent for the first time into space in 2014, one of the turbopump engines experienced a catastrophic failure, which led to the explosion of the Antares rocket and the loss of all cargo aboard. In 2016, the DCMIX3 mixture was successfully transported to the ISS. Due to the additionally availability of microgravity time, the mixture was subjected to complete testing at two different temperatures, 25 and 30 °C. This significantly exceeded the originally envisaged measurements at a single temperature only.²⁶ 

The most recent campaign, DCMIX4, launched to the ISS in late 2018, marked an exploratory mission as it represented the first attempt to investigate not only multicomponent but also complex fluids.^27,28 The complexity of the system arose from the presence of components with very different molecular masses and sizes. Among the mixtures studied, one involved the solution of C60 fullerene in tetralin–toluene solvent, while another complex fluid consisted of a solution of polystyrene in toluene–hexane solvent, serving as a model fluid with two well-separated mass diffusion timescales. The campaign included three additional mixtures similar to DCMIX2 at compositions that are closer to the demixing zone.

One of the main concerns for gravity-sensitive experiments is the effect of the microgravity disturbances (so-called g-jitter), inevitably present on the ISS due to the crew activity, trembling, docking events, or the station reboosting maneuvers.²⁹ Although the overall forces caused by disturbances are relatively small (ranging from $10−2$ to $10−6$ times the normal gravity), their cumulative impact cannot be ignored in long-duration experiments. The primary objective of the first experiment in the SODI on the ISS, the IVIDIL experiment, was to analyze and understand the effects of g-jitter.³⁰ 

The IVIDIL experiment provided the quantitative observations confirming that the daily onboard environment of the ISS does not perturb diffusion-controlled experiments. Experiments with two binary mixtures were reproducible on different days, even in different months, and thus in a different environment. This provided a separation of the components equivalent to that obtained from numerical simulations without perturbations or to ground results, when comparison was possible. These findings may not be applicable to fluid systems characterized by sharp density differences (e.g., gas/liquid interface) or to situations involving significant peak accelerations on the ISS.

To monitor the ambient conditions on the ISS, several acceleration sensors were mounted inside the Microgravity Science Glovebox (MSG), where the SODI was housed. Throughout the IVIDIL and DCMIX experiments, data from the nearest sensor, accessible on the PIMS NASA website, were downloaded and analyzed by the Prof. Ruiz team.^31–35 This undertaking not only facilitated the detection of orbital adjustments, dockings, and undockings but also enabled precise environmental control during periods of experiment activity. Signal analyses revealed that the restrictive conditions for the ISS were not fully met, particularly within the low-frequency range. Therefore, an accurate surveillance of the acceleration levels during experiments is necessary to ensure a correct interpretation of the experimental results.

Here, we illustrate a couple of key examples highlighting the significance of such work. In certain IVIDIL runs where strong vibrations were imposed, some results were found to be in contradiction to those predicted by numerical simulations. A detailed analysis of the accelerometer signals revealed that the third harmonic exhibited greater intensity than the operating frequency.^36,37 This unexpected finding indicates that the mechanical unit generating translational harmonic vibrations during various IVIDIL runs behaves as a nonlinear system, distributing energy anomalously. This behavior is likely attributed to a misalignment of the rotor axis.

Another example is the occurrence of a sudden shift in the camera during DCMIX3. Sensor data analysis revealed the origin: a short, low-frequency jitter on the MSG within the timeframe under consideration.³² The cause of this shaking remains undetermined, but it is likely that a slow-moving object collided with the MSG.

Optical digital interferometry (ODI), as employed in the Brussels laboratory^43,44 and utilized in the SODI instrument aboard the ISS for the IVIDIL^30,45–47 and the DCMIX^{20,26–28,48} experiments, yields a 2D-projection, integrated along the direction of the optical axis, of the refractive index distribution over the entire cross section of a Soret cell mounted in a Mach–Zehnder interferometer. The method is based on a phase-stepping technique, whereby the 2D-refractive index landscape is reconstructed from five consecutive phase-shifted interferometric fringe images using Hariharan's algorithm.^48,49 The essential data processing steps are illustrated in Fig. 2. An alternative method is based on filtering of individual images in the Fourier domain for the reconstruction of the phase and refractive index maps.⁵⁰ 

Significantly less detail is obtained by optical beam deflection (OBD), where only the refractive index gradient on the optical axis through the center of the cell is recorded.^{24,25,51–53} Nevertheless, when combined with appropriate solutions of the thermodiffusion equation, both ODI and OBD yield information that is highly comparable, allowing for the determination of the two diffusion eigenvalues from the transient signals and the Soret coefficients from the steady-state amplitudes at long times. In Ref. 54, it has been demonstrated how the SODI 2D image data can be converted to equivalent 1D OBD signals. Similar to the Fourier transform technique, this method proves particularly useful in situations where the SODI image stacks suffer from laser or phase instabilities that prevent the evaluation by means of temporal phase-stepping algorithms. Since the method focuses on the center of the cell, unfavorable image distortions near the cell boundary are of less concern. In addition to ODI and OBD, also the transient holographic grating technique of thermal diffusion forced Rayleigh scattering (TDFRS) with two-color detection has been proposed for ternary mixtures.⁵³ Despite markedly disparate diffusion lengths and time scales, the data interpretation and evaluation are strikingly analogous to those of OBD experiments.

A common issue in the assessment of experiments on ternary mixtures arises from a poor condition number of the solutal contrast factor matrix $Nc¯¯$⁠. This leads to a significant error amplification along a specific direction in the (⁠$c1,c2$⁠) concentration space. This is a fundamental mathematical property of the transformation. It affects all optical techniques, and also methods based on the simultaneous detection of, e.g., refractive index and density as in TGC, in a very similar way. It can be mitigated by selecting appropriate detection wavelengths, and suitable sample compositions within the ternary Gibbs triangle.²⁹ In particular, the latter has carefully been observed for the DCMIX experiments. For a detailed overview of the selected mixture compositions for the DCMIX experiments, please refer to Fig. 1. Experience has shown that the TGC experiments in a laboratory setting with simultaneous detection of refractive index and density frequently yield more favorable condition numbers of the solutal contrast factor matrix than comparable all-optical experiments.

The error amplification caused by the transformation from the refractive index to the concentration space is not uniform. An isotropic error in the refractive index changes transforms into an elongated ellipse for the concentration changes with the major axis, the one with the high uncertainty, along one of the right-singular vectors of $Nc¯¯$⁠. Along its minor axis, as defined by the second right-singular vector, the error ellipse remains narrow with uncertainties comparable to those observed in binary mixtures. Figure 3 in Ref. 21 depicts the error ellipses for different temperatures are shown for the two independent Soret coefficients of the DCMIX2 system. The orientation of the error ellipse in concentration space is unknown a priori. It depends on the investigated system and on the detection wavelengths. Its projections onto the axes of the Gibbs triangle define the accuracy with which the three individual concentration changes and, thus, the Soret coefficients can be determined. Figure 3 (right) shows this situation for one of the DCMIX3 mixtures consisting of equal mass fractions of water, ethanol, and triethylene glycol.⁵⁵ The error ellipse is derived from simulations incorporating realistic isotropic random noise on the measured refractive index and contrast factor data. The orientation of the ellipse allows for a significantly more accurate determination of the Soret coefficient of triethylene glycol than for the other two components. In addition to the SODI microgravity experiment, ground-based OBD and TGC data are included, which fall onto the same ellipse and, thus, agree with the microgravity results within their respective error bars.

For a long time, the reliability of published Soret and thermodiffusion coefficients and the accuracy of measurement techniques were uncertain even for binary mixtures. In 1999, researchers from five European laboratories met in Fontainebleau and initiated a coordinated study of three binary mixtures (nC₁₂, IBB, THN), known as the Fontainebleau benchmark systems.¹⁶ A decade later, a similar problem arose with ternary mixtures, which are much more complex.

In October 2013, during the DCMIX project workshop in Mondragon Unibertsitatea, it was decided to consolidate individual efforts to establish a benchmark for ternary mixtures under both ground and microgravity conditions. The selected mixture was one of those studied in the DCMIX1 campaign: THN–IBB–nC₁₂ at a mass concentration of 0.80–0.10–0.10 and at 25 °C. The participants and the benchmark point are depicted in Fig. 4 (left). One year later, at the XI International Meeting on Thermodiffusion (IMT 11) in Bayonne, France, six teams from five institutions presented their individual results, which were collectively reviewed to determine the final values.⁵⁶ 

Using different experimental techniques, four teams^42,57–59 presented results derived from ground-based experiments, and the other teams^42,50,59,60 processed the results of the same dataset obtained from an experiment conducted under microgravity conditions. Two teams participated in both options.^42,59 The obtained results are summarized in Fig. 4 (right). At a first glance, relatively large error bars and moderate agreement between measurements suggest that a complete picture is not emerging. For better understanding of the discrepancy between ground results, the specific way of the error propagation in the Soret experiment has to be considered, see Sec. VI C. Through this systematic study, sources of error were identified and all teams converged to common benchmark values, validating the current and future experimental methods.⁵⁶ The comparison of microgravity and ground results and the understanding of their differences will advance the knowledge of ternary mixtures.

In a Soret cell, the behavior of the system is predominantly influenced by this minute net separation ratio (⁠$ψ1≈−ψ2$⁠), rather than by cross-diffusion.⁴ The density profiles generated by the two components during Soret separation practically cancel each other out, and the stability of the system is controlled only by the thermal field, see Fig. 5 (left). Such a system exists in a metastable state. When the initial perturbations are minimal, the separation progresses monotonically toward a steady state, allowing the Soret coefficients to be measured. However, in the presence of significant perturbations in the system, the system undergoes convective fingering, leading to stationary convection that prevents the measurement of the Soret coefficients.

When this mixture is placed in a thermogravitational column, the system dynamics heavily rely on the value of cross-diffusion.^2,3 Figure 5 illustrates different types of instability emerging at various values of $D12$ observed in the experiments and supported by numerical simulations. When $D12$ varies within the range of $(0.9−2.4)×10−9$ m²/s, the system passes from Turing like instability to oscillatory instability in the form of standing waves and then to monotonic instability.

The connection between the Soret separation in ternary and binary systems is established due to the equal applicability of the Soret vector concept to binary mixtures. As common examples, we can consider binary mixtures without and with a change in the sign of the Soret coefficient over the composition space. Figure 6(b) presents the composition dependence of the Soret vector (shown along the horizontal axis) of the Tol–Chex binary mixture. The Soret coefficient is negative, indicating that toluene, the heavier component, migrates to the hot side. Consequently, the red side of the vector aims to increasing the toluene content. Another example is the toluene–methanol mixture. The Soret coefficient exhibits a sign change at the toluene mass fraction of $cTol$ = 0.78 kg/kg, as shown in Fig. 6(c). Toluene, being a heavier component, migrates to the hot side in the concentration range with the negative Soret coefficient, with the red side of the vector directed toward its increase. Conversely, in the concentration range where the Soret sign is positive, toluene moves to the cold side, and thus, the blue side of the vector is directed toward the increase in toluene.

The length of the vector is defined by the values of the Soret coefficients. However, since their typical magnitude is very small, making the vector barely visible on the full concentration scale, it is advisable to draw the vectors with an appropriate magnification.

The developed vector representation is utilized to depict the complete Soret separation in a ternary mixture, as illustrated in Fig. 7. This figure integrates all the binary and ternary measurements of the most extensively studied mixture of THN–IBB–nC₁₂.¹⁷ The plot indicates that the Soret vector undergoes a smooth change across the concentration space, exhibiting the behavior of a vector field. This consistency between the binary and ternary separations provides a foundation for qualitative predictions of the latter from the former.

Let us analyze the formation of ternary vectors from their knowledge in binary subsystems. Upon transitioning from the THN–nC₁₂ subsystem to THN–IBB, the vector undergoes a 60° rotation from its original position, as illustrated in the accompanying diagram on the right side of Fig. 7. Both binary vectors exhibit a similar orientation, with the blue side oriented toward the lower right corner. Consequently, the sign of the Soret coefficient for THN in ternary space in the vicinity of the vertex remains the same as in the binary case, namely, positive. Furthermore, in the THN–nC₁₂ system, the vectors are longer than those observed on the other side, which indicates a significant decrease in the Soret coefficient of THN as it approaches the THN–IBB mixture.

The same pattern of matching and rotation applies to the other corners of the Gibbs triangle. The situation in the left corner mirrors that of the right corner discussed earlier. However, near the upper corner, the Soret vectors in IBB–nC₁₂ and THN–IBB show opposite directions with respect to the apex. The hypothesis presented suggests that the Soret coefficient of IBB also undergoes a change in sign from positive to negative along the path from IBB–nC₁₂ to THN–IBB, with the vector undergoing a rotation of 120° along the path. Given that the Soret vectors of the IBB–nC₁₂ and THN–IBB mixtures have similar lengths on both sides at the upper part, it can be surmised that this occurs in the middle of the ternary space when the contents of THN and nC₁₂ are nearly equal. The visualization of the Soret vector field within a ternary mixture on the Gibbs triangle provides valuable insights. By observing the positioning of Soret vectors of binary subsystems along the triangle's sides, we gain a clearer understanding of their collective behavior within the ternary mixture. For more detailed information about the construction of the ternary Soret vector in systems where binary subsystems exhibit sign changes, refer to Ref. 62. The validation of this novel concept, and in particular, the presented results for the THN–IBB–nC₁₂ mixture, was made possible by data on ternary mixtures obtained in the DCMIX experiments conducted in microgravity environments,⁴⁸ as well as complementary ground research.^17,58

In summary, the visual representation of the Soret vector field on the Gibbs triangle offers several advantages: (i) to predict the Soret sign of a ternary mixture from knowledge of the Soret coefficients in binary subsystems; (ii) to ascertain which components are responsible for the greatest degree of separation in different regions of the triangle; (iii) to control the consistency of coefficients measured using different techniques; and (iv) to identify the regions where the Soret separation is inaccessible for optical techniques or gravitationally unstable.

The ternary DCMIX3-system water/ethanol/triethylene glycol (H₂O/ETH/TEG) differs from the other DCMIX mixtures by its strong polarity and tendency for hydrogen bonding. As with the other DCMIX systems, the space experiments on the DCMIX3 ternaries have been complemented by extensive ground-based measurements,^25,63,64 which together have provided a comprehensive picture of the Soret effect in this peculiar system.

The Soret coefficients of the three corresponding binary mixtures all show a characteristic decrease with increasing concentration, regardless of the choice of the independent component, with a sign change from positive to negative. In the dilute limits, the minority component always shows thermophobic behavior, i.e., it migrates toward the cold side. Another feature common to all three binaries is a temperature-independent fixed point of $ST$ at a certain concentration, where the concentration-dependent curves of $ST(c)$ all intersect. For TEG/H₂O, the fixed point corresponds to a positive Soret coefficient, for TEG/ETH to a negative one, and for ETH/H₂O it occurs exactly at the sign change composition, i.e., $ST$ vanishes at the fixed point.

The characteristic sign changes of $ST$ of the binary mixtures along the boundaries of the ternary Gibbs triangle in combination with the DCMIX3 microgravity measurement and supporting ground experiments on the ternary mixtures allowed for the construction of a qualitative and partially quantitative map of the three Soret coefficients over the ternary composition diagram,^55,63 as shown in Fig. 8.

The construction of the sign-map of $ST$ in Fig. 8 was made possible because of the knowledge of $ST$ along the binary borders and, in particular, a point in the center of the ternary diagram, marked as (2) in Fig. 8 (left). The latter was measured during the DCMIX3 campaign as sample 3 in the selectable optical diagnostics instrument (SODI) aboard the ISS and additionally on ground by means of two-color optical beam deflection (2-OBD) and the thermogravitational column (TGC) technique.⁵⁵ 

The colored regions in Fig. 8 show the approximate regions with thermophilic behavior, i.e., negative Soret coefficients, of TEG (green), ETH (orange), and H₂O (magenta). The boundary lines of these regions demarcate the compositions where the corresponding Soret coefficients are zero. Due to the conservation of mass, these three boundaries must intersect in one singular point, where the Soret coefficients of all three components vanish simultaneously. Figure 8 (right) illustrates the OBD mapping of a narrow region of the composition space in order to identify the precise locus of the singular point with vanishing component separation in the presence of a temperature gradient.⁶³ 

Despite all efforts, the inversion problem of the contrast factor matrix ultimately prevents the accuracy for ternary mixtures from reaching the significantly better quality level known from the binaries. A study was conducted on the thermodiffusion of asymmetric systems, which consisted of a larger entity, such as a polymer or colloid, dispersed in a binary mixture of small molecules. This study was motivated by one of the DCMIX4 samples, which was a polymer in a mixed solvent. The system consisted of polystyrene (⁠$Mw=4.88 kg/mol$⁠) at $c=0.04$ dissolved in a symmetric mixture of toluene and cyclohexane.⁶⁵ It was inspired by and similar to the mixture flown in cell 5 of the DCMIX4 campaign.²⁷ The thermodiffusion dynamics in these systems, as observed in both the SODI microgravity experiment and in OBD laboratory experiments, revealed two distinct time constants that are linked to the two diffusion eigenvalues, as illustrated in Fig. 9 (left).

A plausible a priori assumption, which has been proven correct in Ref. 65, is the assignment of the slow mode to the polymer diffusion with respect to the mixed solvent of constant composition. The fast mode is indicative of the interdiffusion of the two solvents at constant polymer concentration. The identification of the two diffusion modes essentially fixes the directions of the diffusion eigenvectors in both the ternary Gibbs triangle and in the 2D space of the independent concentrations $c1$ and $c2$⁠. In Ref. 65, it is shown how this additional information can be used for the separation of the ternary problem into two independent binary ones, thus circumventing the disadvantageous inversion of the ternary contrast factor matrix. Consequently, the elongated error ellipse is reduced to a more circular shape and the Soret coefficients of all three components can be determined with an accuracy of a few percent, as known for typical binary mixtures. A direct consequence of this mode separation is the existence of a strong cross-diffusion coefficient $D21$⁶⁵ and different signs of the thermodiffusion and Soret coefficient of cyclohexane. Starting from the homogeneous state, cyclohexane initially migrates toward the cold side. Subsequently, it reverses its migration direction toward the hot side, where it accumulates during the steady state.⁶⁶ 

The DCMIX project has played a crucial role in advancing our understanding of thermodiffusion in ternary mixtures, and microgravity experiments have played a pivotal role in this regard. Experiments conducted in microgravity established the most crucial experimental foundations, which were subsequently reinforced by a multitude of ground-based experiments. The systems in orbit included hydrocarbons (DCMIX1), highly non-ideal mixtures (DCMIX2), hydrogen-bonding systems (DCMIX3), and an exploratory campaign (DCMIX4). We present the generic outcomes achieved in connection with four DCMIX experimental campaigns.

The ability to obtain high-quality results on orbit was exemplified by IVIDIL, the first experiment conducted within the SODI, which examined a binary solution. In order to ensure the correct interpretation of the onboard experimental results, an accurate surveillance of the acceleration levels during experiments is necessary. The procedure for monitoring g-jitter and ambient conditions on the ISS has been developed as an integral component of the DCMIX project.

The processing of a substantial quantity of data from the ISS in general presents a significant challenge. Thermodiffusion experiments have demonstrated that the analysis of data involving ternary mixtures is more complex than originally anticipated. In the course of the project, a set of methodologies for effectively handling these raw datasets has been developed in a collaborative effort.

The revelation and insight gained into the asymmetric nature of error propagation in the Soret experiment have significantly contributed to the understanding of the results obtained from the ISS. Moreover, the recognition of the significance of the condition number has not only facilitated the selection of appropriate samples for DCMIX mixtures but will also provide valuable guidance for sample selection in ground-based experiments.

The establishment of the first benchmark for the Soret coefficients in a ternary mixture is a result of the collective efforts of the topical team members, who employed a range of experimental techniques in ground laboratories and microgravity conditions. The capacity to quantify and account for the propagation of errors in Soret experiments was a pivotal element in the development of the final values. This benchmark in ternary mixtures provides a foundation for future research.

One of the generic results is the discovery of the existence of different signs between the Soret and thermal diffusion coefficients, which was facilitated by data obtained on the ISS. Recently, the possibility of this phenomenon occurring in asymmetric ternary mixtures has been observed. In the DCMIX2 mixture, this phenomenon arises due to significant cross-diffusion, which can also result in the emergence of various types of instability in conventional laboratory setups.

Given the complexity of the analysis of ternary mixtures and the necessity to connect ternary and binary Soret coefficients, a straightforward and graphical representation, designated the Soret vector, was proposed. On the Gibbs triangle, the Soret vector field serves as a foundation for qualitative predictions of ternary Soret separation from its values at the binary borders and also assesses the consistency of ternary and binary separations. Another significant aspect of the Soret vector is that it facilitates the identification of regions where Soret separation is either inaccessible for optical techniques or where it is gravitationally unstable.

The knowledge of $ST$ along binary borders, in conjunction with microgravity measurements at several ternary points (DCMIX3), enabled the creation of a qualitative and partially quantitative map of the Soret coefficients within the ternary Gibbs triangle. Moreover, the analysis revealed a singular point at which the Soret coefficients of all three components vanish simultaneously.

In asymmetric ternary mixtures, two distinct time constants can be identified, each linked to a diffusion eigenvalue. The slow mode is attributed to polymer diffusion, while the fast mode reflects solvent interdiffusion. These modes facilitate the determination of diffusion eigenvectors in both the ternary Gibbs triangle and 2D concentration space. This approach facilitates the separation of the ternary problem into two independent binary ones, thereby eliminating the unfavorable inversion of the ternary contrast factor matrix.

It is also noteworthy that the DCMIX project has facilitated the formation of a robust international scientific team with expertise in the study of multicomponent mixtures. The tests conducted on the ISS constituted a pivotal motivating factor.

The authors would like to thank all the members of the DCMIX Topical Team for their comprehensive discussions, which contributed to the success of the project. The work of M.M.B. and V.S. is supported by the Basque Government under the MMASINT project (KK-2023/00041 Elkartek programme) and Research Group Programme IT1505-22 and PID2020-115086 GB-C33 financed by MCIN/AEI of the Spanish Government. W.K. wants to thank the German Aerospace Center DLR (Grant Nos. 50WM2147 and 50WM2444).

The authors have no conflicts to disclose.

V. Shevtsova: Conceptualization (equal); Resources (equal); Writing – original draft (equal); Writing – review & editing (equal). W. Köhler: Conceptualization (equal); Resources (equal); Writing – original draft (equal); Writing – review & editing (equal). M. M. Bou-Ali: Conceptualization (equal); Resources (equal); Writing – original draft (equal); Writing – review & editing (equal). A. Mialdun: Conceptualization (equal); Resources (equal); Writing – original draft (equal); Writing – review & editing (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.