Boundary effects in the Rayleigh line for a fluid out of thermal equilibrium

The Journal of Chemical Physics

Bedeaux

et al. 2007

In this paper a simple reaction-diffusion system, namely a binary fluid mixture with an association-dissociation reaction between the two components, is considered. Fluctuations at hydrodynamic spatiotemporal scales when a temperature gradient is present in this chemically reacting system are studied. First, fluctuating hydrodynamics when the system is in global equilibrium ͑isothermal͒ is reviewed. Comparing the two cases, an enhancement of the intensity of concentration fluctuations in the presence of a temperature gradient is predicted. The nonequilibrium concentration fluctuations are spatially long ranged, with an intensity depending on the wave number q. The intensity exhibits a crossover from a ϰq −4 to a ϰq −2 behavior depending on whether the corresponding wavelength is smaller or larger than the penetration depth of the reacting mixture. This opens a possibility to distinguish between diffusion-or activation-controlled regimes of the reaction by measuring these fluctuations. In addition, the possible observation of these fluctuations in nonequilibrium molecular dynamics simulations is considered.

Section: ͑55͒mentioning

confidence: 88%

Concentration fluctuations in nonisothermal reaction-diffusion systems

Zárate

The Journal of Chemical Physics

Bedeaux

et al. 2007

“…Thus, we conclude that the real-space correlation function in the vertical direction is nonlocal, long ranged and does not involve any intrinsic length scale, i.e., the correlation encompasses the entire system only to be cut off by the finite size of the system itself. Hence, the presence of the temperature gradient induces long-range correlations in the direction coincident with the temperature gradient, as has been elucidated by previous investigators, mainly on the basis of the nonequilibrium heat-diffusion equation [14,58,59]. Considering only the heat-diffusion equation means that one neglects any coupling between temperature and velocity fluctuations.…”

Section: Correlations In the Vertical Directionmentioning

confidence: 92%

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

Zárate

Physica A: Statistical Mechanics and its Applications

2001

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 c associated with the appearance of Rayleigh-Bénard convection.

“…The nature of the nonequilibrium fluctuations in the vicinity of a convective instability has also been investigated, 14,16,17 in which case the nonequilibrium modes become propagative. The influence of boundary conditions, which may become important when k is parallel to ٌT, was considered by Pagonabarraga et al 18 Experiments have been performed to study nonequilibrium fluctuations in liquid mixtures. 10,[19][20][21] The three types of nonequilibrium fluctuations have been observed in liquid mixtures of toluene and n-hexane 10,19,20 and the strength of all three types of nonequilibrium fluctuations were indeed proportional to (ٌT) 2 /k 4 , as expected theoretically.…”

Section: 2mentioning

confidence: 99%

“…The nature of the nonequilibrium fluctuations in the vicinity of a convective instability has also been investigated 14,16,17 , in which case the nonequilibrium modes become propagative. The influence of boundary conditions, which may become important when k is parallel to ∇T , was considered by Pagonabarraga et al 18 .…”

Section: Introductionmentioning

confidence: 99%

Light scattering from nonequilibrium concentration fluctuations in a polymer solution

Zhang

The Journal of Chemical Physics

et al. 2000

Effects of viscoelasticity of bulk polymer solution on the surface modes as probed by laser light scattering J. Chem. Phys. 109, 6103 (1998) We have performed light-scattering measurements in dilute and semidilute polymer solutions of polystyrene in toluene when subjected to stationary temperature gradients. Five solutions with concentrations below and one solution with a concentration above the overlap concentration were investigated. The experiments confirm the presence of long-range nonequilibrium concentration fluctuations which are proportional to (ٌT) 2 /k 4 , where ٌT is the applied temperature gradient and k is the wave number of the fluctuations. In addition, we demonstrate that the strength of the nonequilibrium concentration fluctuations, observed in the dilute and semidilute solution regime, agrees with theoretical values calculated from fluctuating hydrodynamics. Further theoretical and experimental work will be needed to understand nonequilibrium fluctuations in polymer solutions at higher concentrations.