Modeling and correction of image drift in dynamic shadowgraphy experiments.

The study of phoretic transport phenomena under non-stationary conditions presents several challenges, mostly related to the stability of the experimental apparatus. This is particularly true when investigating with optical means the subtle temperature and concentration fluctuations that arise during diffusion processes, superimposed to the macroscopic state of the system. Under these conditions, the tenuous signal from fluctuations is easily altered by the presence of artifacts. Here, we address an experimental issue frequently reported in the investigation by means of dynamic shadowgraphy of the non-equilibrium fluctuations arising in liquid mixtures under non-stationary conditions, such as those arising after the imposition or removal of a thermal stress, where experiments show systematically the presence of a spurious contribution in the reconstructed structure function of the fluctuations, which depends quadratically from the time delay. We clarify the mechanisms responsible for this artifact, showing that it is caused by the imperfect alignment of the sample cell with respect to gravity, which couples the temporal evolution of the concentration profile within the sample with the optical signal collected by the shadowgraph diagnostics. We propose a data analysis protocol that enables disentangling the spurious contributions and the genuine dynamics of the fluctuations, which can be thus reliably reconstructed.

Heterodyne dynamic light scattering for the characterization of particle dispersions.

Particle self-diffusivities in unimodal and bimodal aqueous dispersions are characterized by dynamic light scattering (DLS) applying a heterodyne detection scheme. For unimodal dispersions close to infinite dilution, it could be evidenced that pure homodyne conditions cannot be realized, leading to an increasing underestimation of diffusivity with a decreasing concentration. Even for bimodal dispersions and neglecting any local oscillator field, the coherent superposition of scattered light from different particle species hinders a clear assignment of the measured signals and their evaluation for diffusivity. In this case, the impact of a cross term on the determined diffusivities cannot be neglected. The results emphasize that the use of a heterodyne detection scheme in DLS experiments is a key aspect for an accurate determination of particle diffusivities in low-concentrated unimodal and bimodal dispersions.

Dynamics of non-equilibrium concentration fluctuations during free-diffusion in highly stratified solutions of glycerol and water.

We investigate the non-equilibrium fluctuations occurring during free diffusion between two solutions of glycerol and water with various concentration differences. The non-linearity of the system, determined by the strong stratification of the sample, requires introducing an interpretation model able to characterize the dependence of the correlation properties of the non-equilibrium fluctuations on the local thermophysical variables of the system. The proposed model allows us to characterize the dynamics of non-equilibrium fluctuations in the presence of a wide range of relaxation times determined by the strong stratification of the sample, at variance with the cumulant methods commonly used in dynamic light scattering experiments, which work well in the presence of a moderate dispersion of relaxation times.

Stabilized convection in a ternary mixture with two Soret coefficients of opposite sign.

We performed ground-based experiments on the sample polystyrene-toluene-cyclohexane in order to complement the experimental activities in microgravity conditions related to the ESA projects DCMIX4 and Giant Fluctuations. After applying a stabilizing thermal gradient by heating from above a layer of the fluid mixture, we studied over many hours the density variations in the bidimensional horizontal field by means of a Shadowgraph optical setup. The resulting images evidence the appearance of convective instability after a diffusive time associated with the binary molecular solvent consisting of toluene and cyclohexane, confirming the negative sign of the Soret coefficient of this mixture. After a larger diffusive time related to mass diffusion of the polystyrene in the binary solvent, convection was suppressed by the increasing stabilizing density gradient originated by the Soret-induced concentration gradient of the polymer. This is compatible with a positive sign of the Soret coefficient of the polymer in the binary solvent.

Mutual and Thermal Diffusivities as well as Fluid-Phase Equilibria of Mixtures of 1-Hexanol and Carbon Dioxide.

This work contributes to an improved understanding of the fluid-phase behavior and diffusion processes in mixtures of 1-hexanol and carbon dioxide (CO2) at temperatures around the upper critical end point (UCEP) of the system. Raman spectroscopy and dynamic light scattering were used to determine the composition at saturation conditions as well as Fick and thermal diffusivities. An acceleration of the Fick diffusive process up to CO2 mole fractions of about 0.2 was found, followed by a strong slowing-down approaching vapor-liquid-liquid equilibrium or critical conditions. The acceleration of the Fick diffusive process vanished at temperatures much higher than the UCEP. Experimental Fick diffusivity data were compared with predictions from equilibrium molecular dynamics simulations and excess Gibbs energy calculations using interaction parameters from the literature. Both theoretical methods were not able to predict that the thermodynamic factor is equal to zero at the spinodal composition, stressing the need for new methodologies under such conditions. Thus, new sets of temperature-dependent interaction parameters were developed for the nonrandom two-liquid model, which improve the prediction of the Fick diffusion coefficient considerably. The link between the Fick diffusion coefficient and the nonrandomness of the liquid phases is also discussed.

Translational and Rotational Diffusion Coefficients of Gold Nanorods Dispersed in Mixtures of Water and Glycerol by Polarized Dynamic Light Scattering.

Polarized dynamic light scattering (DLS) gives access to orientation-averaged translational and rotational diffusion coefficients of anisotropic particles dispersed in fluids in a single experiment. As the combination of both diffusivities contains information on the morphology of the particles, their simultaneous and accurate measurement for the same sample and thermodynamic state is beneficial for particle characterization. For nontransparent model suspensions of gold nanorods in water and water-glycerol mixtures, a scattering geometry in reflection direction was realized, which minimizes multiple scattering and allows using low laser powers to avoid laser heating. Furthermore, a heterodyne detection scheme was guaranteed by superimposing much stronger reference light to the scattered light. This ensures an unambiguous data evaluation and reduces the uncertainties for the rotational and the translational diffusivity, where the latter is accessible with smaller uncertainty. For the water-based suspensions, both diffusivities agree well with the stick hydrodynamic theory for rods and show an Andrade-type behavior in the studied temperature range from 271 to 323 K. The measured results for both diffusivities, particularly for the rotational diffusivity, indicate a breakdown of the stick boundary conditions for dynamic viscosities larger than 4 mPa·s.

Diffusivities in 1-Alcohols Containing Dissolved H2, He, N2, CO, or CO2 Close to Infinite Dilution.

The influence of the strength of intermolecular interactions on mass diffusive processes remains poorly understood for mixtures of associative liquids with dissolved gases. For contributing to a fundamental understanding of the interplay between liquid structures and mass diffusivities in such systems, dynamic light scattering, Raman spectroscopy, and molecular dynamics simulations were used in this work. As model systems, binary mixtures consisting of the gases hydrogen, helium, nitrogen, carbon monoxide, or carbon dioxide dissolved in ethanol, 1-hexanol, or 1-decanol were selected. Experiments and simulations were performed at macroscopic thermodynamic equilibrium close to infinite dilution of solute for temperatures between 303 and 423 K. The Fick diffusion coefficients and self-diffusivities of the gas solutes increase with increasing temperature, decreasing alkyl chain length of the 1-alcohols, and decreasing molar mass of the solutes except for helium and hydrogen showing the opposite behavior. The analysis of the liquid structure of the mixtures showed that the fraction of hydrogen-bonded alcohol molecules decreases with increasing alkyl chain length and temperature. From the obtained structure-property relationships, a new correlation was developed to predict mass diffusivities in binary mixtures consisting of n-alkanes or 1-alcohols with dissolved gases close to infinite dilution within 10% on average.

Simultaneous study of molecular and micelle diffusion in a technical microemulsion system by dynamic light scattering.

HYPOTHESIS: The application of dynamic light scattering (DLS) is well-established for measuring diffusion coefficients related to either molecular or translational micelle diffusion. The simultaneous determination of both transport properties should be feasible, but has not been reported in the literature yet. EXPERIMENTS: Different diffusion modes present in a microemulsion and selected subsystems consisting of a polyol mixture, a binary surfactant mixture, and carbon dioxide (CO2) were investigated systematically by DLS at temperatures of (314, 333, and 353) K and corresponding pressures of (10, 13, and 16) MPa. FINDINGS: Diffusion coefficients related to molecular and translational micelle diffusion could be measured simultaneously and increase with increasing temperature. From the translational diffusion coefficients, an increase in the hydrodynamic diameter of the micelles from their non-swollen to the CO2-swollen state being in agreement with literature data for the same and similar microemulsions was found. The effective diffusion coefficients related to the faster molecular diffusion process only observable in the presence of CO2 are not affected significantly by the surfactant. The time-dependent parts of the recorded intensity correlation functions related to molecular diffusion processes are heterodyne because the scattered light modulated by molecular concentration fluctuations is superimposed with light scattered by the micelles.

Influence of Liquid Structure on Fickian Diffusion in Binary Mixtures of n-Hexane and Carbon Dioxide Probed by Dynamic Light Scattering, Raman Spectroscopy, and Molecular Dynamics Simulations.

This study contributes to a fundamental understanding of how the liquid structure in a model system consisting of weakly associative n-hexane ( n-C6H14) and carbon dioxide (CO2) influences the Fickian diffusion process. For this, the benefits of light scattering experiments and molecular dynamics (MD) simulations at macroscopic thermodynamic equilibrium were combined synergistically. Our reference Fickian diffusivities measured by dynamic light scattering (DLS) revealed an unusual trend with increasing CO2 mole fractions up to about 70 mol %, which agrees with our simulation results. The molecular impacts on the Fickian diffusion were analyzed by MD simulations, where kinetic contributions related to the Maxwell-Stefan (MS) diffusivity and structural contributions quantified by the thermodynamic factor were studied separately. Both the MS diffusivity and the thermodynamic factor indicate the deceleration of Fickian diffusion compared to an ideal mixture behavior. Computed radial distribution functions as well as a significant blue-shift of the CH stretching modes of n-C6H14 identified by Raman spectroscopy show that the slowing down of the diffusion is caused by a structural organization in the binary mixtures over a broad concentration range in the form of self-associated n-C6H14 and CO2 domains. These networks start to form close to the infinite dilution limits and seem to have their largest extent at a solute-solvent transition point at about 70 mol % CO2. The current results not only improve the general understanding of mass diffusion in liquids but also serve to develop sound prediction models for Fick diffusivities.

Thermal, Mutual, and Self-Diffusivities of Binary Liquid Mixtures Consisting of Gases Dissolved in n-Alkanes at Infinite Dilution.

In the present study, dynamic light scattering (DLS) experiments and molecular dynamics (MD) simulations were used for the investigation of the molecular diffusion in binary mixtures of liquids with dissolved gases at macroscopic thermodynamic equilibrium. Model systems based on the n-alkane n-hexane or n-decane with dissolved hydrogen, helium, nitrogen, or carbon monoxide were studied at temperatures between 303 and 423 K and at gas mole fractions below 0.06. With DLS, the relaxation behavior of microscopic equilibrium fluctuations in concentration and temperature is analyzed to determine simultaneously mutual and thermal diffusivity in an absolute way. The present measurements document that even for mole gas fractions of 0.007 and Lewis numbers close to 1, reliable mutual diffusivities with an average expanded uncertainty ( k = 2) of 13% can be obtained. By use of suitable molecular models for the mixture components, the self-diffusion coefficient of the gases was determined by MD simulations with an averaged expanded uncertainty ( k = 2) of 7%. The DLS experiments showed that the thermal diffusivity of the studied systems is not affected by the dissolved gas and agrees with the reference data for the pure n-alkanes. In agreement with theory, mutual diffusivities and self-diffusivities were found to be equal mostly within combined uncertainties at conditions approaching infinite dilution of the gas. Our DLS and MD results, representing the first available data for the present systems, reveal distinctly larger mass diffusivities for mixtures containing hydrogen or helium compared to mixtures containing nitrogen or carbon monoxide. On the basis of the broad range of mass diffusivities of the studied gas-liquid systems covering about 2 orders of magnitude from about 10-9 to 10-7 m2·s-1, effects of the solvent and solute properties on the temperature-dependent mass diffusivities are discussed. This contributed to the development of a simple semiempirical correlation for the mass diffusivity of the studied gases dissolved in n-alkanes of varying chain length at infinite dilution as a function of temperature. The generalized expression requiring only information on the kinematic viscosity and molar mass of the pure solvent as well as the molar mass and acentric factor of the solute represents the database from this work and further literature with an absolute average deviation of about 11%.

Characterization of Water Solubility in n-Octacosane Using Raman Spectroscopy.

In this study, we demonstrate the ability of polarization-difference Raman spectroscopy (PDRS) to detect dissolved free water molecules in a n-octacosane (n-C28H58) liquid-rich phase, and thus to determine its solubility, at temperatures and pressures relevant to the Fischer-Tropsch synthesis. Our results for the pure alkane reveal thermal decomposition above a temperature of 500 K as well as an increase of gauche conformers of the alkane chains with an increase in temperature. For binary homogeneous mixtures, raw spectra obtained from two different polarization scattering geometries did not show a relevant signal in the OH stretching frequency range. In contrast, isotropic spectra obtained from the PDRS technique reveal a narrow and tiny peak associated with the dangling OH bonds. Over the complete range of temperatures and pressures, no signature of hydrogen-bonded water molecules was observed in the isotropic Raman scattering intensities. A thorough investigation covering a large range of temperatures and pressures using PDRS signals showed that the higher the fraction of gauche conformers of hydrocarbon, the higher the solubility of water. The proportion of gauche and trans conformers was found to be water-concentration-independent, and the intensity of the OH-dangling peak increased linearly with increasing the vapor partial pressure of water. Therefore, we established a relation between a relevant intensity ratio and the concentration of water obtained from SAFT calculations. Contrary to the results from relevant literature, the calibration factor was found to be temperature-independent between 424 and 572 K. The isotropic Raman scattering intensities are corrected in order to provide a better representation of the vibrational density of states. The influence of correction of the isotropic scattering intensities on the solubility measurements as well as on the analysis of the molecular arrangement is discussed.

Non-equilibrium concentration fluctuations in superparamagnetic nanocolloids.

We investigate non-equilibrium concentration fluctuations during the free diffusion of a colloidal suspension against pure water. We investigate Fe2O3 superparamagnetic nanocolloids with sizes between 1 and 10 nm by means of a shadowgraph apparatus to determine the mixture mass diffusion coefficient and kinematic viscosity. The experiments were performed in three distinct conditions: Experiment 1 is without any magnetic field; Experiment 2 with a vertical magnetic field; Experiment 3 after turning off the magnetic field. We found no correlation between the kinematic viscosity coefficient and the external magnetic field. Conversely, we found that the mass diffusion coefficient decreases in the presence of the external magnetic field and slowly rebounds after the magnetic field was turned off.

Confinement effect on the dynamics of non-equilibrium concentration fluctuations far from the onset of convection.

In a recent letter (C. Giraudet et al., EPL 111, 60013 (2015)) we reported preliminary data showing evidence of a slowing-down of non-equilibrium fluctuations of the concentration in thermodiffusion experiments on a binary mixture of miscible fluids. The reason for this slowing-down was attributed to the effect of confinement. Such tentative explanation is here experimentally corroborated by new measurements and theoretically substantiated by studying analytically and numerically the relevant fluctuating hydrodynamics equations. In the new experiments presented here, the magnitude of the temperature gradient is changed, confirming that the system is controlled solely by the solutal Rayleigh number, and that the slowing-down is dominated by a combined effect of the driving force of buoyancy, the dissipating force of diffusion and the confinement provided by the vertical extension of the sample cell. Moreover, a compact phenomenological interpolating formula is proposed for easy analysis of experimental results.

Diffusivities of Ternary Mixtures of n-Alkanes with Dissolved Gases by Dynamic Light Scattering.

Theoretical approaches suggest that dynamic light scattering (DLS) signals from low-molecular-weight ternary mixtures are governed by fluctuations in temperature as well as two individual contributions from fluctuations in concentration that are related to the eigenvalues of the Fick diffusion matrix. Until now, this could not be proven experimentally in a conclusive way. In the present study, a detailed analysis of DLS signals in ternary mixtures consisting of n-dodecane (n-C12H26) and n-octacosane (n-C28H58) with dissolved hydrogen (H2), carbon monoxide (CO), or water (H2O) as well as of n-C12H26 or n-C28H58 with dissolved H2 and CO is given for temperatures up to 523 K and pressures up to 4.1 MPa. Thermal diffusivities of pure n-C12H26 and n-C28H58 as well as thermal and mutual diffusivities of their binary mixtures being the basis for the ternary mixtures with dissolved gas were studied for comparison purposes. For the investigated ternary mixtures, three individual signals could be distinguished in the time-resolved analysis of scattered light intensity by using photon correlation spectroscopy (PCS). For the first time, it could be evidenced that these signals are clearly associated with hydrodynamic modes. In most cases, the fastest mode observable for ternary mixtures is associated with the thermal diffusivity. The two further modes obviously related to the molecular mass transport are observable on different time scales and comparable to the modes associated with the concentration fluctuations in the respective binary mixtures. Comparison of the experimental data with results from molecular dynamics simulations revealed very good agreement.

Non-equilibrium fluctuations induced by the Soret effect in a ternary mixture.

We present, based on fluctuating hydrodynamics, the theory of concentration fluctuations in a ternary mixture subjected to a stationary temperature gradient, so that composition gradients are present due to thermal diffusion (Soret effect). We neglect gravity and confinement (boundary conditions) but consider a completely generic diffusion matrix, including cross-diffusion effects. We find, as in the case of binary mixtures, an important non-equilibrium enhancement of the concentration fluctuations, which is proportional to the square of the gradient and inversely proportional to the fourth power of the fluctuations wave number, q(-4). The results of this paper are expected to be asymptotically correct for fluctuations of large q, while for shorter q gravity and confinement effects need to be incorporated. Comparison with previous work in the topic is included.