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

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 by 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 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.