Fabrizio Croccolo

A light scattering study of non equilibrium fluctuations in liquid mixtures to measure the Soret and mass diffusion coefficient.

We use dynamic near field scattering to measure the dynamics of concentration non equilibrium fluctuations at the steady-state of Soret separation. The analysis reveals that above a threshold wave vector q(c), the dynamics is governed by diffusion while at smaller wave vectors, gravity dominates. From the measurements, we extract both the mass diffusion and the Soret coefficients. Comparing our results with literature data, we find good agreement confirming that the proposed experimental technique can be considered a sound approach for the study of thermodiffusion processes.

Use of dynamic schlieren interferometry to study fluctuations during free diffusion

We used a form of schlieren interferometry to measure the mean-squared amplitude and temporal autocorrelation function of concentration fluctuations driven by the presence of a gradient during the free diffusion of a urea solution into water. By taking and processing sequences of images separated in time by less than the shortest correlation time of interest, we were able to simultaneously measure dynamics at a number of different wave vectors. The technique is conceptually similar to the shadowgraph method, which has been used to make similar measurements, but the schlieren method has the advantage that the transfer function is wave-vector independent rather than oscillatory.

Effect of Gravity on the Dynamics of Nonequilibrium Fluctuations in a Free-Diffusion Experiment

Abstract:  Diffusion is commonly believed to be a homogeneous process at the mesoscopic scale, being driven only by the random walk of fluid molecules. On the contrary, very large amplitude, long wavelength fluctuations always accompany diffusive processes. 1–4 In the presence of gravity, fluctuations in a fluid containing a stabilizing gradient are affected by two different processes: diffusion, which relaxes them, and the buoyancy force, which quenches them. These phenomena affect both the overall amplitude of fluctuations and their time dependence. For the case of free diffusion, the time‐correlation function of the concentration fluctuations is predicted to exhibit an exponential decay with correlation time depending on the wave vector q. For large wave vector fluctuations, diffusion dominates, and the correlation time is predicted to be 1 / (Dq2). For small wave vector fluctuations, gravitational forces have time to play a significant role, and the correlation time is predicted to be proportional to q2. The effects of gravity and diffusion are comparable for a critical wave vector qc determined by fluid properties and gravity. We have utilized a quantitative dynamic shadowgraph technique to obtain the temporal correlation function of a mixture of LUDOX® TMA and water undergoing free diffusion. This technique allows one to simultaneously measure correlation functions achieving good statistics for a number of different wave vectors in a single measurement. Wave vectors as small as 70 cm−1 have been investigated, which is very difficult to achieve with ordinary dynamic light‐scattering techniques. We present results on the transition from the diffusive decay of fluctuations to the regime in which gravity is dominant.

High-pressure mass transport properties measured by dynamic near-field scattering of non-equilibrium fluctuations

High-pressure mass diffusion and Soret coefficients of the equimassic 1,2,3,4-tetrahydronaphthalene and n-dodecane binary mixture are obtained from dynamic light scattering analysis of concentration non-equilibrium fluctuations at the steady state of Soret-driven separation. A high-pressure shadowgraph set-up has been developed to investigate thermodiffusion in free medium from atmospheric pressure up to 20MPa. Results at atmospheric pressure show excellent agreement with benchmark values. High-pressure results for the mass diffusion coefficient confirm theoretical predictions by Leffler-Cullinan relation. Further calculation of the thermodiffusion coefficient allows also comparison with previous experimental results with, again, very good agreement.Graphical abstract

Quantitative Fourier analysis of schlieren masks: the transition from shadowgraph to schlieren

In a schlieren setup, a lens system forms an image of the refractive index fluctuations of a transparent sample onto a matrix detector while an intensity mask is positioned in the Fourier plane of a collecting lens to perform the required spatial filtering. In the absence of the mask, the resulting technique is that of a shadowgraph. The two methods provide different information about the refractive index of transparent fluids and can be used both for visualization purposes and scattering measurements. Here, we describe the effect of the intensity mask on the technique transfer function, i.e., its ability to detect different spatial frequencies and show how the special cases of shadowgraph, schlieren, and the transition between the two can be derived. We also present experimental data that agree well with our predictions.

Characterization of anisotropic nano-particles by using depolarized dynamic light scattering in the near field.

Light scattering techniques are widely used in many fields of condensed and soft matter physics. Usually these methods are based on the study of the scattered light in the far field. Recently, a new family of near field detection schemes has been developed, mainly for the study of small angle light scattering. These techniques are based on the detection of the light intensity near to the sample, where light scattered at different directions overlaps but can be distinguished by Fourier transform analysis. Here we report for the first time data obtained with a dynamic near field scattering instrument, measuring both polarized and depolarized scattered light. Advantages of this procedure over the traditional far field detection include the immunity to stray light problems and the possibility to obtain a large number of statistical samples for many different wave vectors in a single instantaneous measurement. By using the proposed technique we have measured the translational and rotational diffusion coefficients of rod-like colloidal particles. The obtained data are in very good agreement with the data acquired with a traditional light scattering apparatus.

Concentration dependent refractive index of a binary mixture at high pressure

In the present work binary mixtures of varying concentrations of two miscible hydrocarbons, 1,2,3,4-tetrahydronaphtalene (THN) and n-dodecane (C12), are subjected to increasing pressure up to 50 MPa in order to investigate the dependence of the so-called concentration contrast factor (CF), i.e., (∂n/∂c)(p, T), on pressure level. The refractive index is measured by means of a Mach-Zehnder interferometer. The setup and experimental procedure are validated with different pure fluids in the same pressure range. The refractive index of the THN-C12 mixture is found to vary both over pressure and concentration, and the concentration CF is found to exponentially decrease as the pressure is increased. The measured values of the refractive index and the concentration CFs are compared with values obtained by two different theoretical predictions, the well-known Lorentz-Lorenz formula and an alternative one proposed by Looyenga. While the measured refractive indices agree very well with predictions given by Looyenga, the measured concentration CFs show deviations from the latter of the order of 6% and more than the double from the Lorentz-Lorenz predictions.

Note: Quasi-real-time analysis of dynamic near field scattering data using a graphics processing unit

We present an implementation of the analysis of dynamic near field scattering (NFS) data using a graphics processing unit. We introduce an optimized data management scheme thereby limiting the number of operations required. Overall, we reduce the processing time from hours to minutes, for typical experimental conditions. Previously the limiting step in such experiments, the processing time is now comparable to the data acquisition time. Our approach is applicable to various dynamic NFS methods, including shadowgraph, Schlieren and differential dynamic microscopy.

Slowing-down of non-equilibrium concentration fluctuations in confinement

Fluctuations in a fluid are strongly affected by the presence of a macroscopic gradient making them long-ranged and enhancing their amplitude. While small-scale fluctuations exhibit diffusive lifetimes, larger-scale fluctuations live shorter because of gravity, as theoretically and experimentally well-known. We explore here fluctuations of even larger size, comparable to the extent of the system in the direction of the gradient, and find experimental evidence of a dramatic slowing-down in their dynamics. We recover diffusive behaviour for these strongly-confined fluctuations, but with a diffusion coefficient that depends on the solutal Rayleigh number. Results from dynamic shadowgraph experiments are complemented by theoretical calculations and numerical simulations based on fluctuating hydrodynamics, and excellent agreement is found. The study of the dynamics of non-equilibrium fluctuations allows to probe and measure the competition of physical processes such as diffusion, buoyancy and confinement.

Note: Temperature derivative of the refractive index of binary mixtures measured by using a new thermodiffusion cell

A thermodiffusion cell is developed for performing Soret experiments on binary mixtures at high pressure and in the presence of a porous medium. The cell is validated by performing experiments at atmospheric pressure. The experiments are performed by applying different temperature gradients to binary mixtures in order to determine their thermal contrast factor. These measurements provide a first demonstration of the good reproducibility of this kind of measurements upon calibration.