Jmo. De Zarate et Jv. Sengers, Fluctuations in fluids in thermal nonequilibrium states below the convective Rayleigh-Benard instability, PHYSICA A, 300(1-2), 2001, pp. 25-52
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 finit
e-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 f
unction 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 interpre
tation of light scattering and shadowgraph experiments is elucidated. The r
elationship with studies on various aspects of the problem by other investi
gators is discussed. The paper thus provides a unified treatment for dealin
g with fluctuations in fluid layers subjected to a stationary temperature g
radient 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 Rayl
eigh-Benard convection. (C) 2001 Elsevier Science B.V. All rights reserved.