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

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 iso...

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Bibliographic Details
Published in:Continuum mechanics and thermodynamics 2016-09, Vol.28 (5), p.1511-1523
Main Authors: Gouin, Henri, Saccomandi, Giuseppe
Format: Article
Language:English
Subjects:
Classical and Continuum Physics
Computational fluid dynamics
Condensed Matter
Critical point
Density
Engineering Thermodynamics
Fluid dynamics
Fluid mechanics
Fluids
Heat and Mass Transfer
Mathematical analysis
Mathematical models
Mathematical Physics
Mechanics
Original Article
Physics
Physics and Astronomy
Soft Condensed Matter
Statistical methods
Structural Materials
Taylor series
Theoretical and Applied Mechanics
Vibrations
Wave power
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Summary: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.
ISSN:0935-1175
1432-0959
DOI:10.1007/s00161-016-0492-3