title: Correlations and scaling properties of nonequilibrium fluctuations in liquid mixtures.
abstract: 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=sqrt[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.
authors.affiliation: Energiespeicher- und Energiewandlersysteme, Universität Bremen, Wiener Straße 12, 28359 Bremen, Germany.
authors.forename: Doriano
authors.initials: D
authors.lastname: Brogioli
authors.affiliation: Laboratoire des Fluides Complexes et leurs Réservoirs-CNRS UMR5150, Université de Pau et des Pays de l'Adour, 64600 Anglet, France.|Centre National d'Etudes Spatiales (CNES), 2, Place Maurice Quentin, 75001 Paris, France.
authors.forename: Fabrizio
authors.initials: F
authors.lastname: Croccolo
authors.affiliation: Dipartimento di Fisica, Università degli Studi di Milano, I-20133 Milano, Italy.
authors.forename: Alberto
authors.initials: A
authors.lastname: Vailati