Nonequilibrium fluctuations during diffusion in liquid layers

Brogioli, Doriano; Vailati, Alberto

doi:10.1103/physreve.96.012136

Cited by 5 publications

(18 citation statements)

References 67 publications

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“…In these simulations, we use parameters from Setup B (see Table I), φ = 1, and start with a uniform system where we colored the particles in the middle third of the domain green. For Quasi2D (BD-q2D) we follow the evolution to time T q2D = 1.505 · 10 5 , and for True2D (BD-t2D) we follow the evolution to T t2D = 2 · For True2D we see the development of "colossal" fluctuations, the magnitude of which is comparable to the mean as predicted by linearized FHD [22]. Interestingly, however, the very fact that fluctuation are not small compared to the mean invalidates the linearized FHD theory used to predict the colossal fluctuations in the first place, as we demonstrate numerically in Section VI B 2.…”

Section: Color Gradientmentioning

confidence: 83%

“…2 and associated discussion in [22]. The contribution from the compressibility of the fluid in the plane of confinement has not yet been evaluated because the theoretical calculations in [22] are based on the Saffman mobility kernel for membranes [2], which assumes that the flow is incompressible in the plane of the membrane.…”

Section: B Giant Non-equilibrium Fluctuationsmentioning

confidence: 99%

“…In this section we study giant fluctuations in the presence of density and/or color gradients for a Quasi2D colloidal suspension confined to a planar interface, and compare to a True2D system such as a thin film in vacuum [21,22]. We begin by considering a density gradient, and then consider a color gradient in the absence of a density gradient.…”

Section: B Giant Non-equilibrium Fluctuationsmentioning

confidence: 99%

“…This means that the ensemble-averaged concentration in a system where the diffusing particles are strongly correlated by hydrodynamics (e.g., two-dimensional thin smectic films [23]), will look indistinguishable from the ensemble average in a system where the diffusing particles are uncorrelated (e.g., diffusion in a solid). But if one examines the magnitude of the nonequilibrium fluctuations, the hydrodynamic correlations are revealed through an unexpected power-law dependence of the structure factor on the wavenumber [22]. Third, collective fluctuations can couple bi-directionally to the motion of each particle and therefore renormalize transport coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…= χ 0 predicted by the Stokes-Einstein relation(22), the long-time slope gives a smaller long-time Mean square displacement of a tagged particle in a Quasi2D ideal gas of density φ = 1, computed from the equilibrium MSD (filled black circles), as well as the nonequilibrium average displacement of a particle pulled by a force F = 1 (empty squares). Error bars indicate one standard deviation confidence intervals.…”

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confidence: 99%

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Hydrodynamic fluctuations in quasi-two dimensional diffusion

Peláez¹,

Usabiaga²,

Panzuela³

et al. 2018

J. Stat. Mech.

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We study diffusion of colloids on a fluid-fluid interface using particle simulations and fluctuating hydrodynamics. Diffusion on a two-dimensional interface with three-dimensional hydrodynamics is known to be anomalous, with the collective diffusion coefficient diverging like the inverse of the wavenumber. This unusual collective effect arises because of the compressibility of the fluid flow in the plane of the interface, and leads to a nonlinear nonlocal convolution term in the diffusion equation for the ensemble-averaged concentration. We extend the previous hydrodynamic theory to account for a species/color labeling of the particles, as necessary to model experiments based on fluorescent techniques. We study the magnitude and dynamics of density and color density fluctuations using a novel Brownian dynamics algorithm, as well as fluctuating hydrodynamics theory and simulation. We find that hydrodynamic coupling between a single tagged particle and collective density fluctuations leads to a reduction of the long-time self-diffusion coefficient, even for an ideal gas of non-interacting particles. This unexpected finding demonstrates that density functional theories that do not account for thermal fluctuations are incomplete even for ideal systems. Using linearized fluctuating hydrodynamics theory, we show that for diffusion on a fluid-fluid interface, nonequilibrium fluctuations of the total density are small compared to the equilibrium fluctuations, but fluctuations of color density are giant and exhibit a spectrum that decays as the inverse cubed power of the wavenumber. We confirm these predictions through Brownian dynamics simulations of diffusive mixing with two indistinguishable species. We also examine nonequilibrium fluctuations in systems with two-dimensional hydrodynamics, such as thin smectic films in vacuum. We find that nonequilibrium fluctuations are colossal and comparable in magnitude to the mean, and can be accurately modeled using numerical solvers for the nonlinear equations of fluctuating hydrodynamics. * Electronic address: donev@courant.nyu.edu

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Section: Color Gradientmentioning

confidence: 83%

Section: B Giant Non-equilibrium Fluctuationsmentioning

confidence: 99%

Section: B Giant Non-equilibrium Fluctuationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Hydrodynamic fluctuations in quasi-two dimensional diffusion

Peláez¹,

Usabiaga²,

Panzuela³

et al. 2018

J. Stat. Mech.

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Giant Fluctuations Induced by Thermal Diffusion in Complex Liquids

Vailati

Philipp

Bataller

et al. 2020

Microgravity Sci. Technol.

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The GRADFLEX experiment of ESA has shown that under microgravity conditions a stationary thermodiffusion process is accompanied by giant non-equilibrium fluctuations with size as large as the size of the sample. In the presence of small concentration gradients, the features of the non-equilibrium fluctuations can be described by means of linearized hydrodynamics. However, the linear models are not suitable to describe most cases of applicative interest, such as fluctuations induced by large gradients and under non-stationary conditions. Moreover, presently the investigation of non-equilibrium fluctuations has mainly involved single component fluids and binary mixtures, but recently transport processes in ternary mixtures have attracted increasing interest due to the experiments performed on the International Space Station in the framework of the DCMIX project of ESA. The Giant Fluctuations (NEUF-DIX) project of ESA will investigate non-equilibrium fluctuations during diffusive processes occurring in complex multi-component mixtures, where one of the components is a macromolecule, such as a polymer, a colloid or a protein. Important objectives will be the exploration of the features of the fluctuations under non-ideal conditions, such as large gradients, transient processes, and concentrated samples, and the understanding of how the fluctuations affect the interactions between macromolecules. The project involves the development of a dedicated facility, consisting of an array of shadowgraph optical instruments working in parallel, each one equipped with a thermal gradient cell. Here we outline the design concept of the facility and the results of performance tests performed on a breadboard to evaluate the suitability of the designed instrument to carry out scientific measurements of non-equilibrium concentration fluctuations in space.

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