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Non-equilibrium Fluctuations in a Ternary Mixture Subjected to a Temperature Gradient

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Abstract

We present the complete theory for the decay rates of non-equilibrium fluctuations in a ternary liquid mixture subjected to a stationary temperature gradient, when the quiescent non-convective state is stable. In the most general case, within Boussinesq approximation, four fluctuating modes exist. Depending on the parameter values, propagative modes may be present, and we discuss numerically some cases where that is so. We complete the work with a discussion of symmetry upon changes in concentration representation, as well as examination of some limiting cases with practical relevance for which analytical progress is possible. We make contact with previous publications, which were based on some kind of approximation.

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Notes

  1. We always assume in this paper that the system is convection-free.

  2. The solutal Rayleigh number is, initially, defined for a binary mixture. Here we extend the concept to a ternary mixture by substituting the single separation ratio of a binary with the net separation ratio.

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Acknowledgements

We acknowledge support from the European Space Agency (ESA) through the MAP-Project TechNEs. Research at Complutense University is further supported by the Research grant ESP2017-83544-C3-2-P of the Spanish Agencia Estatal de Investigación. FC, HB and LGF acknowledge financial support from the Centre National d’Etudes Spatiales (CNES) and from the funding partners of the Industrial Chair CO2ES: E2S-UPPA, TOTAL, CNES and BRGM. We thank Cédric Giraudet for discussions and suggestions. The project leading to this publication has received funding from the Excellence Initiative of Université de Pau et des Pays de l’Adour - I-Site E2S UPPA, a French Investissements d’Avenir program.

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Authors and Affiliations

  1. Facultad de Física, Universidad Complutense, Madrid, Spain

    José M. Ortiz de Zárate

  2. Facultad de Farmacia, Universidad CEU San Pablo, Urbanización Montepríncipe, Boadilla del Monte, Madrid, Spain

    Loreto García-Fernández

  3. Centre National d’Études Spatiales, Paris, France

    Loreto García-Fernández

  4. Universite de Pau et des Pays de l’Adour, E2S UPPA, CNRS, TOTAL, LFCR UMR5150, Anglet, France

    Loreto García-Fernández, Henri Bataller & Fabrizio Croccolo

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  1. José M. Ortiz de Zárate
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  2. Loreto García-Fernández
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  3. Henri Bataller
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  4. Fabrizio Croccolo
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Correspondence to José M. Ortiz de Zárate or Loreto García-Fernández.

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Communicated by Bernard Derrida.

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Ortiz de Zárate, J.M., García-Fernández, L., Bataller, H. et al. Non-equilibrium Fluctuations in a Ternary Mixture Subjected to a Temperature Gradient. J Stat Phys 181, 1–18 (2020). https://doi.org/10.1007/s10955-020-02554-8

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