Nondiffusive decay of gradient-driven fluctuations in a free-diffusion process

Croccolo, Fabrizio; Brogioli, Doriano; Vailati, Alberto; Giglio, M.; Cannell, David S.

doi:10.1103/physreve.76.041112

Cited by 78 publications

(189 citation statements)

References 51 publications

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“…Further theoretical [7] and experimental [8] investigation showed that on Earth, the scale invariance of the fluctuations is broken by the force of gravity, which stabilizes long-wavelength fluctuations and thus prevents their divergence. 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].…”

Section: Introductionmentioning

confidence: 94%

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

2016

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Diffusion in liquids is accompanied by nonequilibrium concentration fluctuations spanning all the length scales comprised between the microscopic scale a and the macroscopic size of the system, L. Up to now, theoretical and experimental investigations of nonequilibrium fluctuations have focused mostly on determining their mean-square amplitude as a function of the wave vector. In this work, we investigate the local properties of nonequilibrium fluctuations arising during a stationary diffusion process occurring in a binary liquid mixture in the presence of a uniform concentration gradient, ∇c 0 . We characterize the fluctuations by evaluating statistical features of the system, including the mean-square amplitude of fluctuations and the corrugation of the isoconcentration surfaces; we show that they depend on a single mesoscopic length scale l = √ aL representing the geometric average between the microscopic and macroscopic length scales. We find that the amplitude of the fluctuations is very small in practical cases and vanishes when the macroscopic length scale increases. The isoconcentration surfaces, or fronts of diffusion, have a self-affine structure with corrugation exponent H = 1/2. Ideally, the local fractal dimension of the fronts of diffusion would be D l = d − H , where d is the dimensionality of the space, while the global fractal dimension would be D g = d − 1. The transition between the local and global regimes occurs at a crossover length scale of the order of the microscopic length scale a. Therefore, notwithstanding the fact that the fronts of diffusion are corrugated, they appear flat at all the length scales probed by experiments, and they do not exhibit a fractal structure.

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Section: Introductionmentioning

confidence: 94%

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

2016

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“…The optical technique we employed is known as Near-Field Scattering [36][37][38][39][40][41][42][43][44][45] by means of a shadowgraph setup [46][47][48]. The shadowgraph optical setup involves a low coherence light source (Super Lumen Diodes, Broad Lighter S680) connected with a single-mode fiber whose output is collimated by an achromatic doublet lens ( f = 15 cm, φ = 5 cm).…”

Section: Methodsmentioning

confidence: 99%

“…The dynamic near-field imaging technique has been shown to provide direct access to the structure function of the sample for all the wave vectors in the optical system by means of a statistical analysis of differences of images. Details of the dynamic analysis can be found elsewhere [46,47,49,50]. Here we just recall the working equation that is used to fit experimental data: …”

Section: Dynamic Near-field Imagingmentioning

confidence: 99%

“…In this case, we apply double-frame differential analysis [49,47,46,[50][51][52] in order to extract both the static structure factor and the temporal correlation function. Since this processing requires a heavy computational effort, we make use of custom-made software in the CUDA/C++ language, taking advantage of the parallelization capabilities of a graphic board (Nvidia, TESLA C2050).…”

Section: Dynamic Near-field Imagingmentioning

confidence: 99%

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Mass transport properties of the tetrahydronaphthalene/n-dodecane mixture measured by investigating non-equilibrium fluctuations

Croccolo

Scheffold

Bataller

2013

Comptes Rendus. Mécanique

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We present preliminary near-field light scattering (NFS) data concerning the analysis of the static power spectrum and of the relaxation time constant as a function of the wave vector for non-equilibrium fluctuations (NEFs). The goal of these measurements is to obtain information about the Soret and the mass diffusion coefficients of a binary mixture undergoing thermodiffusion. In particular, we show how the interaction between NEFs and the gravity force gives rise to a critical wavelength that provides additional information about the Soret coefficient. We suggest that a quantitative analysis can be performed by means of this non-invasive optical technique. In our setup, the sample is monitored parallel to the imposed temperature gradient, thus being insensitive to the refractive index profile along the vertical axis, while at the same time we are able to detect the light scattered by the refractive index fluctuations in horizontal planes. We select a shadowgraph layout for the NFS setup due to the extremely small wave vectors we aim to analyze. From a double-frame differential analysis of the acquired images, we obtain both the static power spectrum and the dynamics of NEFs. As a proof-of-principle experiment, we present Soret and diffusion coefficient data on a liquid mixture of tetrahydronaphthalene/n-dodecane.

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“…Just to give some examples close to our experience: fluid properties like the mass diffusion coefficient of binary mixtures, 1 the Soret coefficient, [1][2][3][4][5] phenomena like non-equilibrium fluctuations [6][7][8][9][10][11][12][13] have been extensively studied through techniques such as Mach-Zehnder interferometry, 1 static and dynamic light scattering, 10,11,[14][15][16][17] beam deflection, [2][3][4][5] shadowgraph 6, 8-10, 12, 13 and other scattering in the near field (SINF) techniques. 11,12,[18][19][20][21] In most of the aforementioned cases one needs to know a priori the dependence of the refractive index of the liquid under analysis on the relevant parameter (concentration, temperature, etc.)…”

Section: Introductionmentioning

confidence: 99%

Concentration dependent refractive index of a binary mixture at high pressure

Croccolo

Arnaud

Bégué

et al. 2011

The Journal of Chemical Physics

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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.

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Nondiffusive decay of gradient-driven fluctuations in a free-diffusion process

Cited by 78 publications

References 51 publications

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures

Mass transport properties of the tetrahydronaphthalene/n-dodecane mixture measured by investigating non-equilibrium fluctuations

Concentration dependent refractive index of a binary mixture at high pressure

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