Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-09-13
Physics
Condensed Matter
Statistical Mechanics
33 pages, 6 figures, accepted for publication: Physica A
Scientific paper
10.1016/S0378-4371(01)00321-1
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 $R_\mathrm{c}$ associated with the appearance of Rayleigh-B\'{e}nard convection.
de Zárate José M. Ortiz
Sengers Jan V.
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