Propagating modes in a binary liquid mixture under thermal stress

Evaluation of the shadowgraph method for the determination of mutual and thermal diffusivities

The present work provides a systematic study on the influence of sample properties and experimental conditions on the reliable accessibility of Fick or mutual diffusion coefficients D11 and thermal diffusivities a in binary liquid mixtures using the shadowgraph method. For this, mixtures with varying magnitudes of the Soret coefficient ST and their optical contrast factors were studied at a temperature of 298.15 K and pressures between (0.1 and 0.65) MPa with varying magnitudes and orientations of the applied temperature and concentration gradients ∇T and ∇c. Experimental signals obtained in these investigations were analyzed with respect to the intensities of the signal contributions from non-equilibrium fluctuations (NEFs) in concentration and temperature, and the reliability of the determined D11 and a data was assessed by comparison to literature data. Larger signal intensities from NEFs and, therefore, a more reliable determination of diffusivities were given for sufficiently large magnitudes of ST, the optical contrast factors, and the applied ∇T and ∇c. At very small fluid layer thicknesses L ≤ 0.30 mm, the associated reduction of signal statistics outweighing the expected increase of signal intensities at larger magnitudes of ∇T and ∇c as well as the influence of confinement imposed limitations for the determination of diffusivities in some cases. Furthermore, an influence of the mixture composition on signal intensities from concentration-NEFs was identified, where too small mole fractions of one component can hinder the determination of D11 in mixtures with small magnitudes of the optical contrast factor (∂n/∂c)T,p.

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.

Fick diffusion coefficients probed by the shadowgraph method considering confinement and advection

The present work contributes to the development of the shadowgraph method for its routine application for an accurate determination of the Fick diffusion coefficient D₁₁ of binary fluid mixtures. In this context, measurement and data evaluation strategies for thermodiffusion experiments where confinement and advection are potentially present are elaborated by studying two binary liquid mixtures with positive and negative Soret coefficients, i.e., 1,2,3,4-tetrahydronaphthalene/n-dodecane and acetone/cyclohexane. For obtaining accurate D₁₁ data, the dynamics of non-equilibrium fluctuations in concentration is analyzed considering recent theory by data evaluation procedures that are demonstrated to be suitable for different experimental configurations.

Staggered scheme for the compressible fluctuating hydrodynamics of multispecies fluid mixtures

We present a numerical formulation for the solution of nonisothermal, compressible Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical method is the use of staggered grid momenta along with a finite volume discretization of the thermodynamic variables to solve the resulting stochastic partial differential equations. The key advantages of the numerical scheme are that it significantly simplifies the discretization of diffusive and stochastic momentum fluxes into a more compact form, and it provides an unambiguous prescription of boundary conditions involving pressure. The staggered grid scheme more accurately reproduces the equilibrium static structure factor of hydrodynamic fluctuations in gas mixtures compared to a collocated scheme described previously by Balakrishnan et al. [Phys. Rev. E 89, 013017 (2014)1539-375510.1103/PhysRevE.89.013017]. The numerical method is tested for ideal noble gases mixtures under various nonequilibrium conditions, such as applied thermal and concentration gradients, to assess the role of cross-diffusion effects, such as Soret and Dufour, on the long-ranged correlations of hydrodynamic fluctuations, which are also more accurately reproduced compared to the collocated scheme. We numerically study giant nonequilibrium fluctuations driven by concentration gradients and fluctuation-driven Rayleigh-Taylor instability in gas mixtures. Wherever applicable, excellent agreement is observed with theory and measurements from the direct simulation Monte Carlo method.

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.

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.

Mass diffusion and Soret coefficient measurements of triethylene glycol/water binary mixtures by dynamic shadowgraphy

The investigation of the transport properties of binary fluid mixtures remains a topic of interest in relation to the more challenging studies of ternary mixtures. In fact, the study of the phase boundary limits of the Gibbs composition triangle can be the initial step for a more complete analysis of ternary mixtures. In this paper, we apply the dynamic shadowgraphy optical technique to study non-equilibrium fluctuations induced by the presence of a gradient of temperature and/or concentration in the triethylene glycol (TEG)/water system. These thermodiffusion and free-diffusion experiments aim at measuring the transport properties of samples of the studied system at different experimental conditions. We scan both the average temperature and the TEG concentration, which allows us investigating both positive and negative thermodiffusive behaviours. The obtained values of mass diffusion coefficient are consistent with data available in the literature in the range of temperature investigated in this study. The mass diffusion coefficient of the sample prepared at 0.7 w/w TEG concentration are characterised by shadowgraphy following the two proposed methods, exhibiting consistent results. An increase of the mass diffusion coefficient as a function of the average temperature is highlighted. On the other hand, the thermodiffusion coefficient appears to be independent of the average temperature of the sample at 0.3 w/w TEG concentration.

The modern structurator: increased performance for calculating the structure function

The autocorrelation function is a statistical tool that is often combined with dynamic light scattering (DLS) techniques to investigate the dynamical behavior of the scattered light fluctuations in order to measure, for example, the diffusive behavior of transparent particles dispersed in a fluid. An alternative approach to the autocorrelation function for the analysis of DLS data has been proposed decades ago and consists of calculating the autocorrelation function starting from difference of the signal at different times by using the so-called structure function. The structure function approach has been proven to be more robust than the autocorrelation function method in terms of noise and drift rejection. Therefore, the structure function analysis has gained visibility, in particular in combination with imaging techniques such as dynamic shadowgraphy and differential dynamic microscopy. Here, we show how the calculation of the structure function over thousands of images, typical of such techniques, can be accelerated, with the aim of achieving real-time analysis. The acceleration is realized by taking advantage of the Wiener-Khinchin theorem, i.e., by calculating the difference of images through Fourier transform in time. The new algorithm was tested both on CPU and GPU hardware, showing that the acceleration is particularly large in the case of CPU.

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.

Simultaneous determination of multiple transport properties over a wide range of temperatures and pressures from the analysis of non-equilibrium fluctuations by the shadowgraph method

The present work demonstrates that by the analysis of the dynamics of non-equilibrium fluctuations using the shadowgraph method, the thermal diffusivity, the Fick diffusion coefficient, the kinematic viscosity, and the Soret coefficient of a binary mixture can be determined from a single thermodiffusion experiment. The study was performed for a mixture consisting of equal masses of 1,2,3,4-tetrahydronaphthalene and n-dodecane in a newly developed shadowgraph apparatus at temperatures up to 373 K and pressures up to 40 MPa. The obtained results are mainly discussed in the light of their uncertainties at varying thermodynamic states for evaluating the benefits, drawbacks, and potentials of the apparatus. The Fick diffusion coefficient and the thermal diffusivity obtained with average expanded uncertainties of 2.8% and 6.6% agree with literature data and measurements for the same mixture taken by heterodyne dynamic light scattering. Current limitations of the method are reflected by the distinctly larger uncertainties of the kinematic viscosity and the Soret coefficient. Corresponding reasons and potential measures to overcome the limitations are discussed.

Mixed Oscillation Flow of Binary Fluid with Minus One Capillary Ratio in the Czochralski Crystal Growth Model

This work presented a series of three-dimensional unsteady numerical simulations on the characteristics of the mixed oscillation flows of binary mixture in a Czochralski crystal growth model. The silicon-germanium melt is investigated and the capillary ratio is minus one. The simulation results showed that, for the special capillary ratio, the thermal and solutocapillary forces are imposed in opposite directions and counteract each other. With the effect of buoyancy, the balance between the capillary forces is disturbed. Mixed with the forced convection driven by rotation, the capillary-buoyancy convection is complex. The basic mixed flow streamlines are presented as various rolling cells. The directions of the rolls are dependent on the combinations of surface and body forces. With the increase of temperature gradient, the basic flow stability is broken, and the oscillations occur. The crucible rotation has an effective influence on the stability enhancement. However, affected by the crystal rotation, the critical condition experiences an increase to a turning point, and then undergoes a sharp reduction to zero. Once the instability is incubated, the surface oscillations are analyzed. For the three-dimensional steady flow, only spatial oscillations are observed circumferentially, and the surface patterns of spokes, rosebud, and pulsating ring are obtained. For the unsteady oscillation flow, the spiral hydrosoultal waves, rotating waves, and superimposition of spirals and spokes are observed, and the oscillation behaviors are also discussed.

Coupled non-equilibrium fluctuations in a polymeric ternary mixture

We investigate by dynamic shadowgraphy the non-equilibrium fluctuations at the steady state of a thermodiffusion experiment in a polymeric ternary mixture of polystyrene-toluene-n-hexane. The structure function of the refractive index reveals the existence of quite different decay times, thus requiring the analysis of a wide range of correlation times. This is related to the simultaneous presence of three distinct decay modes corresponding to (from fastest to slowest) the relaxation of temperature fluctuations, of the concentration fluctuations of the mixed solvent, and of the concentration fluctuations of the polymer in the binary solvent. An investigation of the decay times at the corresponding diffusive regimes provides a measurement of the thermal diffusivity and the two eigenvalues of the mass diffusion matrix of the ternary mixture. Similar experiments were performed in the past but here, to suppress the confinement effect and obtain a more direct comparison with the theory, a thicker sample is studied. Moreover, also a faster camera is used allowing the experimental observation of faster modes, like the propagative ones. The experimental values of the decay times are eventually compared with those predicted by different available theories. Finally, we present a more complete theoretical model to describe the non-equilibrium fluctuations in the bulk of a ternary mixture at the steady state of a thermodiffusion experiment.

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

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

European Space Agency experiments on thermodiffusion of fluid mixtures in space

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