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Nonequilibrium fluctuations in the Rayleigh-Benard problem for binary fluid mixtures
J M Ortiz de Zárate1, F Peluso, J V Sengers
1Departamento de Física Aplicada 1, Facultad de Ciencias Físicas, Universidad Complutense, E-28040, Madrid, Spain. jmortizz@fis.ucm.es
The European Physical Journal. E, Soft Matter
|December 14, 2004
Summary
This study explores nonequilibrium temperature and concentration fluctuations in binary fluids. Realistic boundary conditions reveal competition between Rayleigh and Hopf instabilities, affecting fluctuation structure.
Area of Science:
- Thermodynamics
- Fluid Dynamics
- Statistical Mechanics
Background:
- Binary fluid mixtures driven out of thermal equilibrium exhibit complex behaviors.
- Instabilities like Rayleigh (stationary) and Hopf (oscillatory) can arise, leading to long-ranged fluctuations.
- Understanding these fluctuations is crucial for predicting mixture properties under non-equilibrium conditions.
Purpose of the Study:
- To calculate nonequilibrium temperature and concentration fluctuations in a binary fluid.
- To investigate the impact of realistic boundary conditions on these fluctuations.
- To analyze the interplay between different instability mechanisms.
Main Methods:
- Employed a simple Galerkin-approximation scheme.
- Calculated temperature and concentration fluctuations.
- Incorporated realistic boundary conditions, including thermally conducting but impermeable walls.
Main Results:
- The competition between Rayleigh and Hopf instabilities leads to a structure factor with two maxima for temperature fluctuations near convective instability.
- Temperature fluctuation intensity vanishes as wave number q approaches zero with specific boundary conditions.
- Concentration fluctuation intensity remains finite as q approaches zero.
Conclusions:
- A simpler small-Lewis-number approximation scheme is proposed.
- This scheme effectively represents nonequilibrium concentration fluctuations for mixtures with a positive separation ratio, even near convective instability.
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