Giant fluctuations in diffusion processes

Brogioli, Doriano; Vailati, Alberto; Giglio, M.

doi:10.1088/0953-8984/12/8a/305

Cited by 18 publications

(30 citation statements)

References 9 publications

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“…Giglio and coworkers have measured the intensity of nonequilibrium fluctuations for negative Rayleigh numbers down to wave numbersq of order unity, both with ultra-low angle light-scattering experiments [22,23] and from quanti- tative analysis of shadowgraph images [52,53]. They actually measured the intensity of nonequilibrium concentration fluctuations in a liquid mixture.…”

Section: Interpretation Of Experimental Resultsmentioning

confidence: 99%

“…In practice I 0 (x) is calculated by averaging over many shadowgraph images, so that fluctuations cancel out and the resulting I 0 (x) contains only contributions from nonuniform illumination of the sample. From physical and geometrical optics one can demonstrate that the modulus squared of the two-dimensional Fourier transform of the shadowgraph signal, |i(q)| 2 , after taking an azimuthal average, can be expressed as [50,51,53]:…”

Section: Nonequilibrium Structure Factor Probed In Experimentsmentioning

confidence: 99%

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Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh–Bénard instability

Zárate

Sengers

2001

Physica A: Statistical Mechanics and its Applications

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Starting from the linearized fluctuating Boussinesq equations we derive an expression for the structure factor of fluids in stationary convection-free thermal nonequilibrium states, taking into account both gravity and finite-size effects. It is demonstrated how the combined effects of gravity and finite size causes the structure factor to go through a maximum value as a function of the wave number q. The appearance of this maximum is associated with a crossover from a q −4 dependence for larger q to a q 2 dependence for very small q. The relevance of this theoretical result for the interpretation of light scattering and shadowgraph experiments is elucidated. The relationship with studies on various aspects of the problem by other investigators is discussed. The paper thus provides a unified treatment for dealing with fluctuations in fluid layers subjected to a stationary temperature gradient regardless of the sign of the Rayleigh number R, provided that R is smaller than the critical value R c associated with the appearance of Rayleigh-Bénard convection.

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Section: Interpretation Of Experimental Resultsmentioning

confidence: 99%

Section: Nonequilibrium Structure Factor Probed In Experimentsmentioning

confidence: 99%

Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh–Bénard instability

Zárate

Sengers

2001

Physica A: Statistical Mechanics and its Applications

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“…We note that similar NE concentration fluctuations and, hence, NE Casimir forces, will also be present in liquid films with an isothermal concentration gradient or chemical-potential gradient [10,[42][43][44]. Hence, this kind of NE Casimir force may be ubiquitous in nature.…”

Section: Prl 115 035901 (2015) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 94%

Nonequilibrium Casimir-like Forces in Liquid Mixtures

2015

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In this Letter, we consider a liquid mixture confined between two thermally conducting walls subjected to a stationary temperature gradient. While in a one-component liquid nonequilibrium fluctuation forces appear inside the liquid layer, nonequilibrium fluctuations in a mixture induce a Casimir-like force on the walls. The physical reason is that the temperature gradient induces large concentration fluctuations through the Soret effect. Unlike temperature fluctuations, nonequilibrium concentration fluctuations are also present near a perfectly thermally conducting wall. The magnitude of the fluctuation-induced Casimir force is proportional to the square of the Soret coefficient and is related to the concentration dependence of the heat and volume of mixing. When large and long-range fluctuations are present, they will induce forces in confined fluids [1]. These are commonly referred to as Casimir-like forces in analogy to forces induced by vacuum fluctuations between two conducting plates [2,3]. A well-known example is the Casimir force induced by critical fluctuations in fluids [4][5][6][7]. Apart from critical systems, long-range correlations also exist in equilibrium systems with Goldstone modes [1] and in many nonequilibrium systems, where even longerrange correlations can exist [8][9][10][11].In this Letter, we consider a liquid mixture in a nonequilibrium steady state (NESS) between two parallel thermally conducting plates subjected to a uniform temperature gradient ∇T. In a liquid mixture a temperature gradient induces large concentration fluctuations through the Soret effect [12,13]. These nonequilibrium concentration fluctuations vary with the 4th power of the inverse of the wave number k of the fluctuations, just as the nonequilibrium temperature fluctuations in a one-component fluid [8,14]. However, there is a principal difference between the Casimir pressures induced by nonequilibrium concentration fluctuation and those induced by nonequilibrium temperature fluctuations. In thin fluid layers, fluctuations not only may induce a force on the walls, but also may introduce an effective potential inside the fluid layer causing a modification of the density or composition profile [15]. While in a one-component fluid nonequilibrium fluctuations induce the latter phenomenon yielding a rearrangement of the density profile [16], the purpose of the present Letter is to demonstrate that nonequilibrium concentration fluctuations induce an actual Casimir pressure on the walls directly.It is well known that in considering the dynamics of fluctuations around thermal equilibrium, nonlinear terms in the hydrodynamic equations serve to renormalize various terms in the linearized hydrodynamic equations [17][18][19][20][21][22][23][24].Here we show that in a NESS the nonlinear terms cause a most important renormalization of the nonequilibrium (NE) pressure or normal stresses in a binary fluid. To determine the nonequilibrium induced pressure in a liquid mixture, we need to consider the pressure p as a function of the fl...

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“…The presence of a concentration gradient puts the fluid in a nonequilibrium condition, characterized by the presence of a macroscopic diffusive mass flux [1]. Nonequilibrium fluctuations orders of magnitude larger than the equilibrium ones have been predicted theoretically [2][3][4][5][6][7] and reported experimentally [8][9][10][11] during diffusion between couples of ordinary miscible fluids. These nonequilibrium fluctuations are originated by thermally excited velocity fluctuations, which give rise to vortices at mesoscopic length scales displacing volumes of fluid in layers with different concentration.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium fluctuations during diffusion in liquid layers

Brogioli

Vailati

2017

Phys. Rev. E

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Theoretical analysis and experiments have provided compelling evidence of the presence of long-range nonequilibrium concentration fluctuations during diffusion processes in fluids. In this paper, we investigate the dependence of the features of the fluctuations from the dimensionality of the system. In three-dimensional fluids the amplitude of nonequilibrium fluctuations can become several orders of magnitude larger than that of equilibrium fluctuations. Notwithstanding that, the amplitude of nonequilibrium fluctuations remains small with respect to the concentration difference driving the diffusion process. By extending the theory to two-dimensional systems, such as liquid monolayers and bilayers, we show that the amplitude of the fluctuations becomes much stronger than in three-dimensional systems. We investigate the properties of the fronts of diffusion and show that they have a self-affine structure characterized by a Hurst exponent H = 1. We discuss the implications of these results for diffusion in liquid crystals and in cellular membranes of living organisms.

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Giant fluctuations in diffusion processes

Cited by 18 publications

References 9 publications

Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh–Bénard instability

Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh–Bénard instability

Nonequilibrium Casimir-like Forces in Liquid Mixtures

Nonequilibrium fluctuations during diffusion in liquid layers

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