Dynamics of Non Equilibrium Fluctuations in Free Diffusion

Fluctuations in a fluid in macroscopic equilibrium state have been widely investigated both theoretically and experimentally since the first decades of the 20th century. The most used experimental technique has been light scattering due to the direct access to sample structure factor, which is the fundamental tool to describe fluctuations in fluids.
In the latest decades attention has moved to the fluctuations in fluids driven outside thermodynamic equilibrium by an applied macroscopic gradient. Both simple fluids and fluid mixtures have been investigated by applying a vertical, stabilizing, uniform temperature gradient to a horizontal slab of sample, which is the simplest way to generate non-equilibrium fluctuations, and the static structure factor has been investigated by light scattering techniques. The earliest experiments showed the strong divergence with a power law in the fluctuations intensity as the wave vector was decreased, in net contrast with the equilibrium behavior in which the intensity was measured to be -independent. The divergence resulted in a strong increase of the scattering intensity for the smallest observable scattering angles in some case as large as 3 or 4 orders of magnitude.
The refinement of optical techniques and in particular the acquired ability to investigate smaller wave vectors, let scientists detect the stabilizing effect of gravity on the fluctuations, which was that of making the intensity constant for wave vectors smaller than a critical value related to fluid properties and gravity. Moreover theory was further developed to account for time-dependent gradients like that of the free diffusion experiment in which a mixture is mechanically prepared with an initial strong concentration gradient and mass diffusion relaxes the system to the homogeneous state.
The dynamics of non-equilibrium fluctuations have been studied by the theoretical point of view and it was derived that the temporal correlation function of fluctuations should be an exponential decay with characteristic time depending on the wave vector. For wave vectors larger than the critical value , the time constant should be the usual diffusive one, which has been experimentally tested.
For wave vectors smaller than the critical value the time constant should be limited by the effect of gravity, but no experimental check was available since none had been able to apply any dynamic technique for wave vectors smaller than typical critical values, of the order of .
The subject of this thesis is the experimental investigation of the dynamics of non-equilibrium fluctuations in free diffusion processes, where two miscible fluids are put in contact and mass diffusion relaxes the initial strong concentration gradient to the homogeneous state. To get access to the temporal correlation function at wave vectors smaller than the critical ones for our samples, a new processing has been used, in fact we have applied the structure factor approach to get a statistical procedure that can be applied to images grabbed through a shadowgraph or a Schlieren or other optical techniques. The development of this procedure led to the writing of a custom-made software able to extract the temporal correlation function of the investigated sample out of the images.
Experiments have been performed on free-diffusing samples and the temporal correlation function of non-equilibrium fluctuations have been recovered as a function of the wave vector showing the non-diffusive decay behavior below the critical wave vector thus confirming for the first time theoretical predictions and giving evidence that the temporal correlation function of non-equilibrium fluctuations is an exponential decay within experimental accuracy.
Other experiments are foreseen as a development of this work to investigate the dynamics of non-equilibrium fluctuations in different diffusive processes like that of a single fluid under the effect of a temperature gradient or a binary mixture in the same conditions to analyze the behavior of both thermal and concentration fluctuations. Moreover it will be very much interesting to analyze the dynamics when analogous experiments will be performed in a micro-gravity environment, like in the GRADFLEX experiment that is scheduled to be flown on the Foton M3 Russian vector.
The dynamical technique here introduced is well suited to study the dynamics of slow processes, therefore future experiments can be foreseen on gels or glass-like systems.