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

  • Ortiz De Zárate J
  • Sengers J
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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-4dependence for larger q to a q2dependence 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 Rcassociated with the appearance of Rayleigh-Bénard convection. © 2001 Elsevier Science B.V. All rights reserved.

Author-supplied keywords

  • Boussinesq equations
  • Light scattering
  • Nonequilibrium fluctuations
  • Rayleigh-Bénard convection
  • Shadowgraph experiments
  • Swift-Hohenberg equation

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Authors

  • José M. Ortiz De Zárate

  • Jan V. Sengers

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