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

Ortiz de Zárate, Jose’e M. and Jan V. Sengers

Physica A: Statistical Mechanics and its Applications, 2001, vol. 300, issue 1, 25-52

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 q2 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 Rc associated with the appearance of Rayleigh–Bénard convection.

Keywords: Boussinesq equations; Light scattering; Nonequilibrium fluctuations; Rayleigh–Bénard convection; Shadowgraph experiments; Swift–Hohenberg equation (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:300:y:2001:i:1:p:25-52

DOI: 10.1016/S0378-4371(01)00321-1

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