Shadowgraph Analysis of Non-equilibrium Fluctuations for Measuring Transport Properties in Microgravity in the GRADFLEX Experiment

Abstract

In a fluid system driven out of equilibrium by the presence of a gradient, fluctuations become long-ranged and their intensity diverges at large spatial scales. This divergence is prevented vertical confinement and, in a stable configuration, by gravity. Gravity and confinement also affect the dynamics of non-equilibrium fluctuations (NEFs). In fact, small wavelength fluctuations decay diffusively, while the decay of long wavelength ones is either dominated by buoyancy or by confinement. In normal gravity, from the analysis of the dynamics one can extract the diffusion coefficients as well as other transport properties. For example, in a thermodiffusion experiment one can measure the Soret coefficient. Under microgravity, the relaxation of fluctuations occurs by diffusion only and this prevents the determination of the Soret coefficient of a binary mixture from the study of the dynamics. In this work we propose an innovative self-referencing optical method for the determination of the thermal diffusion 2 ratio of a binary mixture that does not require previous knowledge of the temperature difference applied to the sample. The method relies on the determination of the ratio between the mean squared amplitude of concentration and temperature fluctuations. We investigate data from the GRADFLEX experiment, an experiment flown onboard the Russian satellite FOTON M3 in 2007. The investigated sample is a suspension of polystyrene polymer chains (MW=9,100g/mol, concentration 1.8wt%) in toluene, stressed by different temperature gradients. The use of a quantitative shadowgraph technique allows to perform measurements in the absence of delicate alignment and calibration procedures. The statics of the concentration and temperature NEFs are obtained and their ratio is computed. At large wave vectors the ratio becomes constant and is shown to be proportional to the thermal diffusion ratio of the sample.

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

“…We estimate as Ra s −10 4 the range of solutal Rayleigh numbers at which an acceleration in the dynamics associated to bouyancy is observable. Without gravity, c-NEFs exhibit the usual diffusive scaling with the standard Fickian diffusion coefficient for all wave numbers, as predicted by linearized fluctuating hydrodynamics [52] and observed in the GRADFLEX microgravity experiments [58][59][60].…”

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

“…The same gravitational stabilization of the fluctuations was shown to be present during timedependent isothermal diffusion processes [9][10][11][12], proving that nonequilibrium fluctuations are a general feature of diffusive processes, irrespective of the origin of the concentration gradient driving them. An additional mechanism breaking the scale invariance of the fluctuations at small wave vectors was predicted theoretically to be the finite size of the sample [13], a finding confirmed experimentally during the GRADFLEX experiment by the European Space Agency [14][15][16]. Recent experiments showed that finite-size effects also affect the dynamics of the fluctuations in the presence of gravity [17].…”

“…The power-law dependence led to the conclusion that the fluctuations are self-similar in a wide range of wave vectors, and to the argument that the fronts of diffusion are fractal (see, for example, the discussion in [26] and references therein). The analysis of experimental results obtained in microgravity confirmed the power-law behavior of the static structure factor of the fluctuations over a wide range of wave vectors, but it was not able to provide further insights about the fractal structure of the fronts of diffusion [14][15][16]. As pointed out by Alexander [27], a reliable experimental determination of the fractal dimension of rough surfaces is often prevented by the fact that the structures are not scale-invariant, but instead self-affine.…”

“…Such a confinement is necessarily present in the case of concentration gradients generated by the Soret effect. In this case, both theoretical models [13] and experiments performed under microgravity conditions [14,16] have shown that the quenching of the fluctuations occurs at wave vectors smaller than Q ≈ π/L. Recently, the effect of confinement has been shown to affect the dynamics of the fluctuations on Earth, too [17].…”

“…In the presence of gravity, the cutoff is of the order of a fraction of a millimeter [8]; microgravity experiments [14,16] extended this cutoff by roughly a factor 30. The power-law dependence led to the conclusion that the fluctuations are self-similar in a wide range of wave vectors, and to the argument that the fronts of diffusion are fractal (see, for example, the discussion in [26] and references therein).…”