Capillary-to-bulk crossover of nonequilibrium fluctuations in the free diffusion of a near-critical binary liquid mixture

Cicuta, Pietro; Vailati, Alberto; Giglio, M.

doi:10.1364/ao.40.004140

Cited by 22 publications

(26 citation statements)

References 27 publications

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“…In 2D fluids, the equivalent of the 3D surface tension is the "line tension," which can originate from the presence of separated phases in the liquid mono-or bilayer; in this case, the lines separating the domains tend to minimize the length of the borders. In our case, we consider miscible fluids, in which the gradient of concentration is relatively small; in analogy with 3D fluctuations [61,62], line tension effects generated by small concentration gradients are negligible.…”

Section: Mathematical Model Of the Nonequilibrium Fluctuationsmentioning

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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Section: Mathematical Model Of the Nonequilibrium Fluctuationsmentioning

confidence: 99%

Nonequilibrium fluctuations during diffusion in liquid layers

Brogioli

Vailati

2017

Phys. Rev. E

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“…Simulations [33] and experiments [34,35] probing the Saffman-Taylor instability led to the conclusions that no interfacial tension exists between miscible fluids; in particular, the observation of a fractal-like interface between two miscible fluids was attributed to a vanishing interfacial energy cost, i.e., to Γ e ¼ 0 [34,35]. This has to be contrasted with experiments and simulations on miscible fluids probing capillary waves [14,15,36], the shape of drops and menisci [13,16,17,37,38], and that of patterns in hydrodynamic instabilities [18,[27][28][29][39][40][41], which all claimed the existence of an effective interfacial tension. The sign of Γ e is also debated.…”

Section: Introductionmentioning

confidence: 98%

“…Here, κ is the Korteweg or square gradient parameter, δ the thickness of the interface, and Δφ is expressed in terms of a difference in volume fraction, e.g., between a solute and the solvent for molecular fluid [13][14][15][16], or between polymer or colloidal suspensions and their solvent for complex fluids [17,18]. Clearly, the interfacial tension described by Eq.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium Interfacial Tension in Simple and Complex Fluids

et al. 2016

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Interfacial tension between immiscible phases is a well-known phenomenon, which manifests itself in everyday life, from the shape of droplets and foam bubbles to the capillary rise of sap in plants or the locomotion of insects on a water surface. More than a century ago, Korteweg generalized this notion by arguing that stresses at the interface between two miscible fluids act transiently as an effective, nonequilibrium interfacial tension, before homogenization is eventually reached. In spite of its relevance in fields as diverse as geosciences, polymer physics, multiphase flows, and fluid removal, experiments and theoretical works on the interfacial tension of miscible systems are still scarce, and mostly restricted to molecular fluids. This leaves crucial questions unanswered, concerning the very existence of the effective interfacial tension, its stabilizing or destabilizing character, and its dependence on the fluid's composition and concentration gradients. We present an extensive set of measurements on miscible complex fluids that demonstrate the existence and the stabilizing character of the effective interfacial tension, unveil new regimes beyond Korteweg's predictions, and quantify its dependence on the nature of the fluids and the composition gradient at the interface. We introduce a simple yet general model that rationalizes nonequilibrium interfacial stresses to arbitrary mixtures, beyond Korteweg's small gradient regime, and show that the model captures remarkably well both our new measurements and literature data on molecular and polymer fluids. Finally, we briefly discuss the relevance of our model to a variety of interface-driven problems, from phase separation to fracture, which are not adequately captured by current approaches based on the assumption of small gradients.

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“…These questions are currently lively debated, as the result of systematic experimental investigations performed in the last years by several groups, who employed various experimental strategies, ranging from probing capillary waves by light scattering [8][9][10] , to observing the shape of drops [11][12][13] and menisci 14 , and studying hydrodynamic instabilities 15,16 . The interest in this topic is not purely academic: the existence of an effective surface tension, in spite of its transient character, is of great relevance in many fields, from geodynamics to polymer physics and multiphase flow, and has implications in a large number of practical applications.…”

Section: Introductionmentioning

confidence: 99%

Off-equilibrium surface tension in miscible fluids

Truzzolillo

Cipelletti

2017

Soft Matter

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The interfacial tension between immiscible fluids is responsible for a wealth of every-day phenomena, from the spherical shape of small drops and bubbles to the ability to walk on water of many insects. More than a century ago, physicist and mathematician D. Korteweg postulated the existence of an effective interface tension for miscible fluids, whenever a composition gradient exists, as encountered, e.g., in many flow geometries. In this mini-review, we discuss experimental work performed in the last decades that demonstrates the existence of a positive effective interface tension in a variety of systems, from molecular, near-critical liquids to complex fluids such as polymer solutions and colloidal suspensions. The various experimental strategies that have been deployed are discussed, together with their advantages and limitations. Finally, some of the key theoretical questions still open are outlined.

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Capillary-to-bulk crossover of nonequilibrium fluctuations in the free diffusion of a near-critical binary liquid mixture

Cited by 22 publications

References 27 publications

Nonequilibrium fluctuations during diffusion in liquid layers

Nonequilibrium fluctuations during diffusion in liquid layers

Nonequilibrium Interfacial Tension in Simple and Complex Fluids

Off-equilibrium surface tension in miscible fluids

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