Fluctuations in inhomogeneous and nonequilibrium fluids under the influence of gravity

Segrè, P. N.; Schmitz, Rudi; Sengers, J. V.

doi:10.1016/0378-4371(93)90252-y

Cited by 58 publications

(70 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Section 3 we review the derivation of the well-known expression for the structure factor of a fluid subjected to a stationary temperature gradient without taking into account the presence of boundaries, but including the effects of gravity. The relationship of the resulting expression for the effect of gravity with that obtained previously by Segrè et al [20] will be elucidated. In Section 4 we then consider the modifications to the nonequilibrium structure factor due to the finite height of the fluid layer.…”

Section: Introductionmentioning

confidence: 98%

“…Stricly speaking, in the expression (9) for the decay rates Ω ± (q) the temperature gradient ∇T 0 should be identified with the effective temperature gradient ∇T 0 + (αT 0 /c P )g, as shown by Segrè et al [20]. However, as mentioned in Section 2, the contribution (αT 0 /c P )g from the adiabatic temperature gradient is neglected in the Boussinesq approximation.…”

Section: Linearized Fluctuating Boussinesq Equationsmentioning

confidence: 99%

“…Segrè at al. extended the theory to include gravity effects, first in a onecomponent liquid [20] and then in a liquid mixture [21]. They predicted that gravity will cause the singular q −4 dependence of the structure factor to saturate at small values of q.…”

Section: Introductionmentioning

confidence: 99%

“…We note that in this paper the parallel and perpendicular directions are defined with respect to the horizontal plane, as done by most researchers in the field [8,26,27,31], but unlike the notation used by Segrè et al [20,21]. The Fourier transforms F 1 (ω, q) and F 2 (ω, q) of the random noise terms can be expressed as a function of the Fourier transforms of the random stress tensor and the random heat flow:…”

Section: Linearized Fluctuating Boussinesq Equationsmentioning

confidence: 99%

See 3 more Smart Citations

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

Zárate

Sengers

2001

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 98%

Section: Linearized Fluctuating Boussinesq Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Linearized Fluctuating Boussinesq Equationsmentioning

confidence: 99%

See 2 more Smart Citations

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

Zárate

Sengers

2001

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…Since the quiescent state is stable, any spontaneous fluctuation will eventually decay and our focus is on the dynamics of this non-equilibrium concentration fluctuations (c-NEFs). It has been theoretically known for some time [20,21] that, if confinement effects are neglected, the c-NEFs in this system decay exponentially with a well-defined decay time that depends on the (horizontal, perpendicular to gravity and the applied gradient) wave number q of the fluctuations as:τ (q) d+g =q…”

Section: Introductionmentioning

confidence: 99%

Confinement effect on the dynamics of non-equilibrium concentration fluctuations far from the onset of convection

et al. 2016

View full text Add to dashboard Cite

In a recent letter [C. Giraudet et al., Europhys. Lett. 111, 60013 (2015)] we reported preliminary data showing evidence of a slowing down of non-equilibrium fluctuations of the concentration in thermodiffusion experiments on a binary mixture of miscible fluids. The reason for this slowing down was attributed to the effect of confinement. Such tentative explanation is here experimentally corroborated by new measurements and theoretically substantiated by studying analytically and numerically the relevant fluctuating hydrodynamics equations. In the new experiments presented here, the magnitude of the temperature gradient is changed, confirming that the system is controlled solely by the solutal Rayleigh number, and that the slowing down is dominated by a combined effect of the driving force of buoyancy, the dissipating force of diffusion and the confinement provided by the vertical extension of the sample cell. Moreover, a compact phenomenological interpolating formula is proposed for easy analysis of experimental results.

show abstract

Thermal-Diffusion Driven Concentration Fluctuations in a Polymer Solution

Sengers

Gammon

Zárate

2002

Computational Studies, Nanotechnology, and Solution Thermodynamics of Polymer Systems

View full text Add to dashboard Cite

Fluctuations in inhomogeneous and nonequilibrium fluids under the influence of gravity

Cited by 58 publications

References 37 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

Confinement effect on the dynamics of non-equilibrium concentration fluctuations far from the onset of convection

Thermal-Diffusion Driven Concentration Fluctuations in a Polymer Solution

Contact Info

Product

Resources

About