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Travelling waves of density for a fourth-gradient model of fluids

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Abstract

In mean-field theory, the non-local state of fluid molecules can be taken into account using a statistical method. The molecular model combined with a density expansion in Taylor series of the fourth order yields an internal energy value relevant to the fourth-gradient model, and the equation of isothermal motions takes then density’s spatial derivatives into account for waves travelling in both liquid and vapour phases. At equilibrium, the equation of the density profile across interfaces is more precise than the Cahn and Hilliard equation, and near the fluid’s critical point, the density profile verifies an Extended Fisher–Kolmogorov equation, allowing kinks, which converges towards the Cahn–Hillard equation when approaching the critical point. Nonetheless, we also get pulse waves oscillating and generating critical opalescence.

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Authors and Affiliations

  1. CNRS, Centrale Marseille, M2P2 UMR 7340, Aix-Marseille Université, 13451, Marseille, France

    Henri Gouin

  2. Dipartimento di Ingegneria, Università degli Studi di Perugia, 06125, Perugia, Italy

    Giuseppe Saccomandi

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  1. Henri Gouin
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  2. Giuseppe Saccomandi
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Correspondence to Henri Gouin.

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Communicated by Andreas Öchsner.

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Gouin, H., Saccomandi, G. Travelling waves of density for a fourth-gradient model of fluids. Continuum Mech. Thermodyn. 28, 1511–1523 (2016). https://doi.org/10.1007/s00161-016-0492-3

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