Diffusion and thermodiffusion of the ternary system polystyrene + toluene + cyclohexane.

We have studied diffusion and thermodiffusion in the ternary system polystyrene + toluene + cyclohexane over the entire composition range of the binary solvent toluene + cyclohexane and for polymer concentrations up to 0.1 mass fractions by multi-color optical beam deflection. The polystyrene molar masses were 4.88 and 17.90 kg/mol. The inversion problem of the contrast factor matrix could be avoided by reasonable a priori assumptions about the diffusion eigenvectors. The fast mode of the bimodal dynamics is attributed to the interdiffusion of the two solvents at constant polymer concentration, whereas the slow mode is due to the diffusion of the polymer with respect to the binary solvent. The amplitude of the fast mode vanishes in the pure toluene and the pure cyclohexane limits of the mixed solvent. The amplitude of the slow mode increases with polymer concentration. The composition and temperature dependence of the slow diffusion eigenvalue, the hydrodynamic correlation length, and the Soret coefficient of the polymer reflect the transition from a good to a theta solvent with increasing cyclohexane content and with decreasing temperature. Due to cross diffusion, cyclohexane reverses its migration direction between the fast and the slow mode, leading to a positive thermodiffusion but a negative Soret coefficient. The polymer thermodiffusion coefficients during the slow mode vary by approximately a factor of two, depending on the solvent composition. Rescaling with the solvent viscosity collapses all data onto a single master curve with an extrapolated value of ηDT ≈ 6 × 10-15 Pa m2 K-1 in the dilute limit. This value is well known from various other binary polymer/solvent mixtures.

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.

Thermodiffusion of polymer solutions and colloidal dispersions in mixed solvents.

Two-color optical measurements of thermodiffusion in ternary mixtures frequently suffer from ill-conditioned contrast factor matrices, whose inversion leads to very large experimental errors. In this contribution, we show how the error amplification can be avoided in situations where a priori knowledge about the directions of the eigenvectors of the diffusion matrix is available. We present optical beam deflection experiments on solutions of the polymer polystyrene of Mw = 4880 g/mol in a mixed solvent of toluene and cyclohexane. In this system, the two diffusion eigenvalues differ by almost one order of magnitude. The large eigenvalue can be attributed to the interdiffusion of the two solvents and the small one to the polymer diffusion relative to the mixed solvent. The pre-selection of the eigenvectors renders the method stable against fluctuations of the experimental parameters. Both the diffusion and the Soret coefficients attributed to the two modes agree very well with the respective values of corresponding binary mixtures.

Nonlinearities in shadowgraphy experiments on non-equilibrium fluctuations in polymer solutions.

Giant thermal and solutal non-equilibrium fluctuations are observed in shadowgraphy experiments on liquid mixtures subjected to a temperature gradient. For large temperature differences, both the temperature and the composition dependence of the relevant thermophysical parameters and the nonlinear terms in the diffusion equation need to be taken into account, leading to a nonlinear concentration profile. For temperature differences exceeding the inverse of the Soret coefficient, in our example approximately 10 K, the usual data evaluation yields increasingly wrong diffusion and Soret coefficients that are off by almost a factor of two for a temperature difference of 50 K. A local model that treats the measured shadowgraph signal as a superposition of the contributions from every layer of the sample is able to capture the essential trend and yields a good agreement with experimental data. The results are important for the application of shadowgraphy as a tool for the measurement of Soret and diffusion coefficients, where large temperature gradients promise a good signal-to-noise ratio.

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.

Thermal and solutal non-equilibrium fluctuations in a polymer solution.

We have performed shadowgraphy experiments on a dilute polymer solution subjected to a temperature gradient in order to investigate simultaneous thermal and solutal non-equilibrium fluctuations (NEFs). The gravitational quenching of the NEFs at small q-vectors defines the thermal and solutal roll-off wavevectors, which can be extracted from both the static structure function and the time correlation functions. Both methods yield good agreement, and the ∼10% larger static solutal roll-off wavevector coincides with a similar observation reported in the literature. The thermal diffusivity of the solution and the diffusion, thermodiffusion, and Soret coefficients of the polymer can be obtained from the q-dependence of the relaxation times and from the thermal and solutal roll-off wavevectors without explicit knowledge of the optical contrast factors. This provides an alternative route for the measurement of diffusive transport coefficients, albeit with an unfavorable error propagation.

An Unreasonable Universality of the Thermophoretic Velocity.

Thermophoresis is the migration of dispersed molecules or particles in an inhomogeneous temperature field. It has been associated with various nonequilibrium phenomena ranging from stratified oil reservoirs to prebiotic evolution and the origin of life. The thermophoretic velocity is difficult to predict and appears almost random. We show that, in the case of strongly asymmetric mixtures with high molecular mass ratios of the solute to the solvent, it unexpectedly assumes a universal value once the trivial influence of the viscosity has been factored out. This asymptotic behavior is surprisingly universal and a general property of many highly asymmetric molecular mixtures ranging from organic molecules in n-alkanes to dilute solutions of high polymers. A quantitative explanation is provided on the basis of the asymmetric limit of the pseudoisotopic Soret effect.

The Soret effect of halobenzenes in n-alkanes: The pseudo-isotope effect and thermophobicities.

We have measured the Soret coefficients of three halobenzenes-fluoro-, chloro-, and bromobenzene-in n-alkanes ranging from hexane to hexadecane over the entire composition range at a temperature of 25 °C. With these new results, two semi-empirical models for the Soret effect, which are based on the pseudo-isotope effect and on the single-component thermophobicities, could significantly be expanded and put on a broader common experimental basis. In particular, for the longer alkanes, above decane, a simplified version of the pseudo-isotope effect yields a good description. In the dilute limit, the agreement of the chemical contributions to the Soret coefficient is perfect, but there are some unexplained systematic deviations at finite concentrations. We have used these Soret coefficients, together with the measurements of 1-bromonaphthalene in the n-alkanes, to expand the database for the thermophobicities of equimolar binary mixtures. Due to a vanishing mixing term in symmetric mixtures, the heats of transport computed from the Soret coefficients can be considered as differences in additive single component properties, the thermophobicities. This allows an ordering of the substances according to these numbers. In a binary mixture, the component with the higher thermophobicity migrates toward the cold side. With the new measurements, the database now contains 24 compounds with 107 out of 276 possible binary mixtures measured.

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.

Measurement of non-isothermal transport coefficients in a near-eutectic succinonitrile/(d)camphor mixture.

We have determined nonisothermal diffusive transport coefficients of a succinonitrile-(d)camphor mixture with a composition of c = 0.239 wt.-frac. (d)camphor at a temperature of 318.2 K, which is close to the eutectic point. The employed experimental techniques are optical beam deflection in a Soret cell and photon correlation spectroscopy. The diffusion coefficient is D = (1.43 ± 0.04) × 10-10 m2 s-1, the thermodiffusion coefficient is DT = (2.00 ± 0.06) × 10-12 m2 s-1 K-1, and the Soret coefficient is ST = (1.40 ± 0.02) × 10-2 K-1. Camphor migrates toward the lower and succinonitrile migrates toward the higher temperatures. While the diffusion coefficient is in good agreement with the literature, the Soret coefficient has been determined for the first time. Our analysis shows that a significant concentration shift can be established in the liquid mixture in the presence of a temperature gradient. The mixture has a negative separation ratio, which leads to convective instabilities if heated from above.

The Soret effect in ternary mixtures of water+ethanol+triethylene glycol of equal mass fractions: Ground and microgravity experiments.

Measurements of the Soret and thermodiffusion coefficients of a symmetric ternary mixture with equal mass fractions of water, ethanol, and triethylene glycol have been performed by two-color optical beam deflection (2-OBD) and the thermogravitational column technique (TGC) in the laboratory and under microgravity conditions in the Selectable Optical Diagnostics Instrument (SODI) aboard the International Space Station. The results from all three experimental techniques agree within the experimental error bars, which result mainly from the inversion of the contrast factor matrices. TGC shows by far the lowest, 2-OBD the highest error amplification. The microgravity measurements are in between. The agreement with the microgravity results shows that thermosolutal convection could be well controlled in the 2-OBD experiments by a proper orientation of the temperature gradient. Despite the different condition numbers, the results are invariant under the choice of the independent compositions. Based on the orientation of the confidence ellipsoid in the ternary composition diagram, not all coefficients are equally affected by experimental errors. Although there are appreciable uncertainties for water and ethanol, the Soret and the thermodiffusion coefficients of triethylene glycol could be obtained with a good accuracy due to the favorable orientation of the confidence ellipsoid. We have found that water behaves thermophobic, corresponding to a positive Soret coefficient, whereas both ethanol and triethylene glycol are thermophilic with negative Soret coefficients. This resembles the behaviour of the binary system ethanol/water above the ethanol concentration of the sign change.

Particle accumulation and depletion in a microfluidic Marangoni flow.

Thermosolutal and thermocapillary Marangoni convection at a liquid-gas interface in a microchannel structure of approximately 100 × 90 µm2 cross section creates a localized vortex that acts as a trap for micrometer and sub-micrometer sized tracer particles. Next to the vortex, depleted volumes appear that are entirely cleared of particles. This particle redistribution is caused by collisions of the tracers with the meniscus, which push the particles back onto the critical streamline with one particle radius distance to the meniscus. The streamlines between the meniscus and the critical streamline feed the depleted regions. Since the critical streamline depends on the particle radius, the effect leads to a particle fractionation according to their size. Diffusion allows only small particles to escape from the trap. Larger particles are permanently confined and their diffusion is rectified after every revolution at the meniscus, which produces a ratchet effect and increases the particle localization within the vortex.

Competition between phase transition and thermophoretic expansion of a transient poly(N-isopropylacrylamide) network.

Aqueous solutions of highly entangled ultra-high molar mass ( 2.4×106 g/mol) poly(N-isopropylacrylamide) (PNIPAM) have been subjected to an inhomogeneous temperature field by selective heating of a single embedded gold nanoparticle (GNP) by means of a focused laser beam. Randomly distributed tracer GNPs are trapped in the meshes of the transient entanglement network and serve as tracers for the monitoring of the network deformation field. Because of the positive Soret coefficient of PNIPAM in water, the viscoelastic polymer network is expanded by thermophoretic forces pointing away from the hot center. Close to the heated GNP the thermoresponsive polymer solution crosses the binodal and the network contracts, which is made visible by an inward motion of tracer GNPs, which are randomly embedded in the polymer network and not illuminated by the laser beam. Within a thin transition zone the network contraction and the competing thermophoretic network expansion cancel out in the steady state. There is, however, no cancellation during the transients due to the different time scales of both mechanisms. The network within the crossover region first undergoes an expansion that is followed by a slower contraction. From the global expansion and contraction, the local strain (stretching and compression) of the transient network can be calculated. Due to the long disentanglement times, corresponding to long lifetimes of the meshes of the network, the whole process is fully reversible.

[Mucinous adenocarcinoma of the Urachus: A Case Report]. / Muzinöses Adenokarzinom des Urachus--Ein Fallbericht.

Urachal carcinoma is a rare form of cancer. It often is diagnosed incidentally, like in our case report, because its cardinal symptom also occurs in a number of other urological diseases. We report the case of a 26-year-old man with a mucinous adenocarcinoma of the urachus. The carcinoma was removed via partial cystectomy with umbilical tumour excision.

Soret, thermodiffusion, and mean diffusion coefficients of the ternary mixture n-dodecane+isobutylbenzene+1,2,3,4-tetrahydronaphthalene.

We have investigated thermodiffusion in ternary mixtures of dodecane (nC12), isobutylbenzene (IBB), and 1,2,3,4-tetrahydronaphthalene (THN) by means of two-color optical beam deflection over the entire ternary composition space. The Soret and the thermodiffusion coefficients S(T,i)'(c1,c2) and D(T,i)'(c1,c2), respectively, have been determined for all three components i and fitted by smooth approximating polynomials in the independent concentrations c1 (nC12) and c2 (THN). Both the Soret and the thermodiffusion coefficient are negative for nC12 and positive for THN over all compositions. In case of IBB, they change sign, being negative for THN-rich and positive for nC12-rich mixtures. Both the positive and negative signs and the sign change are in agreement with qualitative predictions based on the recently introduced thermophobicity concept [S. Hartmann et al., Phys. Rev. Lett. 109, 065901 (2012); J. Chem. Phys. 141, 134503 (2014)]. For isothermal diffusion, a mean diffusion coefficient D̄ but neither the diffusion matrix nor its eigenvalues could be determined.

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.

Forced Phase Separation by Laser-Heated Gold Nanoparticles in Thermoresponsive Aqueous PNIPAM Polymer Solutions.

We have investigated the formation, growth, and dissolution dynamics of aggregates of the thermoresponsive polymer poly(N-isopropylacrylamide) (PNIPAM) that form around laser heated gold nanoparticles (GNPs). The aggregates show an initial rapid growth followed by a slow long-term tail that is caused by the temperature dependent induction time until phase separation sets in. The maximum aggregate radius is determined by the distance from the GNP where the temperature crosses the binodal. Melting and evaporation of the GNP can be identified as characteristic steps in the aggregate size as a function of the heating laser power. After prolonged exposure, the polymer concentration inside the aggregate increases considerably. GNPs get immobilized at the perimeter, and a stepwise increase of the laser power results in onionskin-like growth shells. After switching the laser off, the system returns to the homogeneous phase and the growth shells are radially repelled by the high osmotic pressure within the volume previously occupied by the aggregate.

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.

Contribution to the benchmark for ternary mixtures: Measurement of the Soret and thermodiffusion coefficients of tetralin+isobutylbenzene+n-dodecane at a composition of (0.8/0.1/0.1) mass fractions by two-color optical beam deflection.

Within the framework of an international benchmark test we have performed measurements of the Soret and thermodiffusion coefficients of the organic ternary mixture (0.8/0.1/0.1 mass fraction) of 1,2,3,4-tetrahydronaphthaline (THN), isobutylbenzene (IBB) and n -dodecane (n C12) at 298.15K by means of a two-color optical beam deflection technique (OBD). The data evaluation procedure is based on a least squares fitting routine for an approximate analytical solution for the Soret cell problem. The condition number of the contrast factor matrix and standard error propagation are used for an error estimation for the measured Soret and thermodiffusion coefficients. The Soret coefficients obtained are S (') T(THN) = (1.20±0.09)×10(-3) K^-1, S (') T(IBB) = (- 0.34±0.14)×10(-3) K^-1, and S (') T(nC12) = (- 0.86±0.06)×10(-3) K^-1 and the corresponding thermodiffusion coefficients are D (') T(THN) = (0.72±0.26)×10(-12) m^2(s K)^-1, D (') T(IBB) = (- 0.22±0.42)×10(-12) m^2(s K)^-1, and D (') T(nC12) = (- 0.50±0.16)×10(-12) m^2(s K)^-1. These results will be used as ground-based reference data for the DCMIX project, where thermodiffusion experiments of ternary mixtures are measured in a microgravity environment aboard the International Space Station (ISS).