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Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Benard instability

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Ortiz de Zárate Leira, José María and Sengers, Jan V. (2001) Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Benard instability. Physica A-statistical mechanics and its applications, 300 (1-2). pp. 25-52. ISSN 0378-4371

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Official URL: http://dx.doi.org/10.1016/S0378-4371(01)00321-1


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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 cause 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-Benard convection.


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© 2001 Elsevier Science B.V
The authors acknowledge some valuable discussions with G. Ahlers, D.S. Cannell, T.R. Kirkpatrick, R. Pérez Cordón and M.G. Velarde. The research at the University of Marylandis supportedby the Chemical Sciences, Geosciences andBiosciences Division of the OIce of Basic Energy Sciences of the US Department of Energy under Grant No. DE-FG-02-95ER14509. J.V.S. acknowledges the hospitality of the Departamento deFísica Aplicada I, Universidad Complutense de Madrid, where the manuscript was completed.

Uncontrolled Keywords:Boussinesq equations; light scattering; nonequilibrium fluctuations; Rayleigh-Benard convection; shadowgraph experiments; Swift-Hohenberg equation
Subjects:Sciences > Physics
ID Code:35319
Deposited On:27 Jan 2016 16:59
Last Modified:27 Jan 2016 16:59

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