Nonlinear resonant coupling between shear and heat fluctuations in fluids far from equilibrium

Ronis, David; Procaccia, Itamar

doi:10.1103/physreva.26.1812

Cited by 128 publications

(68 citation statements)

References 17 publications

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“…In the limit g → 0, Eq. (12) reduces to the expression of the Rayleigh spectrum of a fluid subjected to a stationary temperature gradient, first obtained by Kirkpatrick et al [6], and subsequently reproduced by other investigators [7][8][9]. The nonequilibrium structure factor, as given by Eq.…”

Section: Linearized Fluctuating Boussinesq Equationsmentioning

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: Linearized Fluctuating Boussinesq Equationsmentioning

confidence: 99%

“…The original work of Kirkpatrick et al and of others [6,7,9] yielded an expression for the structure factor of a fluid in thermally nonequilibrium states without considering any gravity or boundary effects. Segrè at al.…”

Section: Introductionmentioning

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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“…This mechanism leads to the exponent -4 of Eq. (2), typical of nonequilibrium fluctuations in a bulk phase [16][17][18][19][20]15,[21][22][23][24]10,1].…”

Section: Resultsmentioning

confidence: 99%

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

2001

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We have studied the nonequilibrium fluctuations occurring at the interface between two miscible phases of a near-critical binary mixture during a free diffusion process. The small-angle static scattered intensity is the superposition of nonequilibrium contributions due to capillary waves and to bulk fluctuations. A linearized hydrodynamics description of the fluctuations allows us to isolate the two contributions, and to determine an effective surface tension for the nonequilibrium interface. As the diffuse interface thickness increases, we observe the cross-over of the capillary-wave contribution to the bulk one.OCIS: 240.6700, 290.5870

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“…Here, and in the rest of this paper, the plus and the minus sign are applied in eq. (14) in such a way thatD 1 <D 2 . Hence,D 1 will always represent the slowest diffusion mode andD 2 the fastest one.…”

Section: Diagonal Concentrationsmentioning

confidence: 99%

“…FHD has been later extended, among other developments, to equilibrium binary mixtures [13]. Both theoretical approaches are equivalent for systems in equilibrium, but FHD can be extended for dealing with fluctuations in non-equilibrium (NE) systems [14][15][16][17], while the Mountain method of arbitrary initial conditions cannot. Indeed, it has been the systematic application of FHD that allowed the investigation of fluctuations in systems out of (global) equilibrium.…”

Section: Introductionmentioning

confidence: 99%

Gravity effects on Soret-induced non-equilibrium fluctuations in ternary mixtures

Pancorbo¹,

Zárate²,

Bataller³

et al. 2017

Eur. Phys. J. E

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Abstract.We discuss the gravity effects on the dynamics of composition fluctuations in a ternary mixture around the non-equilibrium quiescent state induced by thermodiffusion when subjected to a stationary temperature gradient. We found that the autocorrelation matrix of concentration fluctuations can be expressed as the sum of two exponentially decaying concentration modes. Without accounting for confinement, we obtained exact analytical expressions for the two decay rates which, as a consequence of gravity, display a wave-number-dependent mixing. The stability of the quiescent solution is also examined, as a function of the two solutal Rayleigh numbers used to express the decay rates. After having discussed the dynamics of the two concentration modes, we calculate the corresponding amplitudes. Consequences for optical experiments are discussed.

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Nonlinear resonant coupling between shear and heat fluctuations in fluids far from equilibrium

Cited by 128 publications

References 17 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

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

Gravity effects on Soret-induced non-equilibrium fluctuations in ternary mixtures

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