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

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.

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.

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.

A lattice Boltzmann study of particle settling in a fluctuating multicomponent fluid under confinement

We present mesoscale numerical simulations based on the coupling of the fluctuating lattice Boltzmann method for multicomponent systems with a wetted finite-size particle model. This newly coupled methodologies are used to study the motion of a spherical particle driven by a constant body force in a confined channel with a fixed square cross section. The channel is filled with a mixture of two liquids under the effect of thermal fluctuations. After some validations steps in the absence of fluctuations, we study the fluctuations in the particle's velocity at changing thermal energy, applied force, particle size, and particle wettability. The importance of fluctuations with respect to the mean settling velocity is quantitatively assessed, especially in comparison with unconfined situations. Results show that the expected effects of confinement are very well captured by the numerical simulations, wherein the confinement strongly enhances the importance of velocity fluctuations, which can be one order of magnitude larger than what expected in unconfined domains. The observed findings underscore the versatility of the proposed methodology in highlighting the effects of confinement on the motion of particles in the presence of thermal fluctuations.

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.

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.

Propagating modes in a binary liquid mixture under thermal stress

Nonequilibrium temperature and concentration fluctuations inside a binary liquid mixture under the action of a temperature gradient relax back to equilibrium either due to conduction and diffusion at large wave numbers, or due to the quenching determined by gravity at small wave numbers. We investigate the dynamics of nonequilibrium fluctuations in a binary liquid mixture of polystyrene and toluene heated from above under stationary conditions in a thermodiffusion experiment. We show that the strong gravitational stabilization at small wave numbers determines the appearance of propagating modes of nonequilibrium fluctuations as detected through the structure function of shadowgraph images. The propagating modes are the combined effect of temperature and velocity nonequilibrium fluctuations induced by the buoyancy force. The experimental results are in good agreement with a fluctuating hydrodynamics theroretical model including the coupling of fluctuations of velocity, temperature and concentration.

Dynamic analysis of the light scattered by the non-equilibrium fluctuations of a ternary mixture of polystyrene-toluene-n-hexane

Dynamic analysis of the light scattered by non-equilibrium fluctuations in a thermodiffusion experiment has been performed on a sample of polystyrene-toluene-n -hexane, at 0.9-49.55-49.55% mass fraction. Time decays of the non-equilibrium fluctuations have been obtained revealing the accurate detectability of three modes. The slowest mode has been attributed to the mass diffusion of the polymer into the binary solvent; the intermediate one to mass diffusion of the two molecular components of the solvent; finally, the fastest one has been attributed to the thermal diffusivity of the overall mixture. The two eigenvalues of the mass diffusion matrix have been evaluated with accuracy in the order of 1%. Neglecting cross-diffusion effects we obtain a simplified expression for the relative amplitude of the two mass diffusion modes, allowing a parameterized determination of polystyrene and toluene Soret coefficients in the ternary mixture. We suggest that a two wavelength shadowgraph experiment is needed for a complete determination of all the coefficients.

Gravity effects on Soret-induced non-equilibrium fluctuations in ternary mixtures

We discuss the gravity effects on the dynamics of composition fluctuations in a ternary mixture around the non-equilibrium quiescent state induced by thermodiffusion when subjected to a stationary temperature gradient. We found that the autocorrelation matrix of concentration fluctuations can be expressed as the sum of two exponentially decaying concentration modes. Without accounting for confinement, we obtained exact analytical expressions for the two decay rates which, as a consequence of gravity, display a wave-number-dependent mixing. The stability of the quiescent solution is also examined, as a function of the two solutal Rayleigh numbers used to express the decay rates. After having discussed the dynamics of the two concentration modes, we calculate the corresponding amplitudes. Consequences for optical experiments are discussed.

Non-local fluctuation phenomena in liquids

Fluids in non-equilibrium steady states exhibit long-range fluctuations which extend over the entire system. They can be described by non-equilibrium thermodynamics and fluctuating hydrodynamics that assume local equilibrium for the thermophysical properties as a function of space and time. The experimental evidence for the consistency between this assumption of local equilibrium in the equations and the non-local fluctuation phenomena observed is reviewed.

Microgravity in a thin film: How confinement kills gravity

Fluctuations in the presence of concentration gradients are long-ranged and decay diffusively for small spatial scales. At larger scales fluctuations are influenced by gravity and confinement. The confinement in the direction of the concentration gradient couples to gravity generating a slowing down that ends up in a diffusion-like behavior of fluctuations of size comparable to the vertical extension of the sample. The resulting enhanced diffusion coefficient depends on the solutal Rayleigh number of the system. For small (in modulus) values of the solutal Rayleigh number the apparent diffusion coefficient tends towards the normal one and a simple diffusive behavior is obtained. This is quite similar to what happens in microgravity conditions when the solutal Rayleigh number is drastically reduced because of the reduction of g by about 6 orders of magnitude. Experiments are shown for positive and negative solutal Rayleigh numbers smaller (in modulus) than 1000. The effect of the confinement on the statics is also investigated. Comparison with microgravity data obtained through the GRADFLEX project is performed.