2001
DOI: 10.1016/s0378-4371(01)00321-1
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Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh–Bénard instability

Abstract: 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 dep… Show more

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Cited by 34 publications
(32 citation statements)
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“…However, for the rest of this paper we shall neglect the presence of boundaries. Previous studies show that confinement affects both the amplitude [25,26] and the dynamics [27] of NE fluctuations at lateral wave numbers q L −1 . Hence, our current results are expected to be valid only for fluctuations with q large enough, while we leave for future publications a thorough investigation of confinement effects on NE fluctuations in ternary mixtures.…”
Section: Fluctuating Hydrodynamicsmentioning
confidence: 98%
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“…However, for the rest of this paper we shall neglect the presence of boundaries. Previous studies show that confinement affects both the amplitude [25,26] and the dynamics [27] of NE fluctuations at lateral wave numbers q L −1 . Hence, our current results are expected to be valid only for fluctuations with q large enough, while we leave for future publications a thorough investigation of confinement effects on NE fluctuations in ternary mixtures.…”
Section: Fluctuating Hydrodynamicsmentioning
confidence: 98%
“…(6) and (7), obtain expressions for the correlation functions of the two fluctuating concentrations. In general, such a procedure must include boundary conditions for the fluctuating fields which, as elucidated elsewhere [16,[25][26][27], modify the spatial and dynamical spectrum of NE fluctuations at small q. These confinement effects are a direct consequence of the nonequilibrium fluctuations having, generically, long spatial range [39].…”
Section: Bulk Solutionmentioning
confidence: 99%
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“…(3) the term dE T −mv µ dv µ does not depend on velocity in accordance with the definition of the total energy Eq. (2). So the entropy in Eq.…”
Section: Introductionmentioning
confidence: 97%
“…Mention can be made, for instance, of time dependent diffusion processes in binary liquid mixtures, where they are the principal mechanism leading to anomalously large fluctuations in concentration [1]. Also, the coupling between temperature and transverse-velocity fluctuations in the well known case of a horizontal fluid layer heated from below may be associated with a small convective heat transfer below the Rayleigh-Bénard instability [2]. It is natural to consider these kind of problems from the point of view of irreversible thermodynamics.…”
Section: Introductionmentioning
confidence: 99%